Home Test 3

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  • MA , 3, 001

    1. c x dx6x

    2 567

    2. c 13(x2 + 6x 1)

    (x + 7)(x2 + 8x + 20)dx .

    3. c 2 + 3xx 2 + 1 dx .

    4. c 0

    12

    sin6x

    cos26x 36dx

    5. c 0

    14

    (x2 5x 1) sin7x dx .

    6. c 0

    12

    sin24x dx .

    7. c cc 215

    5dx

    (x 4) ln5(x 4)

    .

    8. c , y = 4x2 + 9x 12,

    y = 5x2 . .

    9. c , c Ox ,

    y = x2 + 7x y = 0 x [ 8, 7] .10. R(x), x

    MR = x8 360 .

    . 1 300 2012/2013 .

  • MA , 3, 002

    1. c dx(3 + 4x)95 .

    2. c 18(x2 + x 9)

    x3 + 3x2 18xdx .

    3. c x + 9 2

    x + 18dx .

    4. c e78

    e2

    8dx

    x ln28x.

    5. c 13

    13 3

    arctg3x dx .

    6. c 0

    15

    sin25x dx .

    7. c cc 7

    1dx

    (x + 8) ln(x + 8)

    .

    8. c , yx = 63, x + y = 16 .

    .

    9. c , c Ox ,

    y =9

    x 6, x = 2 x = 3 .

    10. e

    z(t) = 36t 5 . 06t2 , t ( ), .

    C 7 . 57

    , 70 .

    . 2 300 2012/2013 .

  • MA , 3, 003

    1. c x dx5x

    2 635

    2. c 3x2 3x 12

    3x2 x3dx .

    3. c x 8x + 7 1 dx .

    4. c 18

    116

    4 ctg24x + 2 ctg4x 1

    sin24xdx .

    5. c 13

    13 3

    arctg3x dx .

    6. c 0

    2

    cos6x sin7x dx .

    7. c cc 1

    +

    23x1 dx

    .

    8. c , yx = 7, x + y = 8 .

    .

    9. c , c Ox ,

    y =6

    x + 4, x = 8 x = 6 .

    10. ()

    8 20

    f (t) = 3000 + 77t 3t2, t , 8 t 20.

    , 13 15 ,

    1 5 . .

    . 3 300 2012/2013 .

  • MA , 3, 004

    1. c dx(1 2x)45 .

    2. c 53(x2 5x + 7)

    (x + 5)(x2 4x + 8)dx .

    3. c x 7x 2 3 dx .

    4. c e5

    9

    e1

    9dx

    x ln49x.

    5. c 0

    12

    arctg2x dx .

    6. c 0

    2

    cos2x sin7x dx .

    7. c cc

    4

    sin2x dx

    .

    8. c , x + y = 5, yx = 6 .

    .

    9. c , c Ox ,

    y = x2 x y = 0 x [ 4, 3] .

    10. ,

    : z(t) = 0 . 376t2 + 3 . 1t + 8 . 3 t

    ( ), .

    . 4 300 2012/2013 .

  • MA , 3, 005

    1. c 14x + 37x

    2 + 3x + 63dx .

    2. c 15(x2 6x 3)

    (x 6)(x 7)(x 1)dx .

    3. c x 4x + 1 2 dx .

    4. c ln3

    ln2e2x

    49 81e4xdx .

    5. c 0

    10

    (x2 x 4) cos5x dx .

    6. c 0

    2

    cos3x sin7x dx .

    7. c cc 2

    3x 8 7 3 x

    3 xdx

    .

    8. c , yx = 5, x + y = 6 .

    .

    9. c , c Ox ,

    y =8

    x + 9, x = 0 x = 9 .

    10. K(t),

    ( , )

    I(t) = 390 t58 , ( t = 0) 170 .

    . 5 300 2012/2013 .

  • MA , 3, 006

    1. c dx(1 + x2) arctg5x9

    .

    2. c 20(x2 + 3x 5)

    (x 4)(x2 + 4)dx .

    3. c x + 2 + 1

    x 7dx .

    4. c 0

    14

    cos7x

    sin27x + 4dx

    5. c 0

    12

    3

    arctg2x dx .

    6. c 0

    18

    cos26x dx .

    7. c cc 1

    36 + 7 3 x

    3 xdx

    .

    8. c , y = 3x2,

    y = 2x2 3x 2 . .

    9. c , c Ox ,

    y =1

    x + 5, x = 1 x = 2 .

    10. q TC(q),

    q

    MC = e3.2q, 58 .

    . 6 300 2012/2013 .

  • MA , 3, 007

    1. c dx2x 6 .

    2. c 2x2 + 12x + 14

    (x + 4)2(x + 2)dx .

    3. c x 2x + 5 + 1 dx .

    4. c ln2

    ln3e2x

    e4x 7dx .

    5. c 0

    12

    (x2 5x + 2) sin6x dx .

    6. c 0

    2

    sin4x sin3x dx .

    7. c cc

    1

    85x2 dx

    .

    8. c , y = x2 + 2x + 4,

    y = 2x2 + 4x + 12 . .

    9. c , c Ox ,

    y = x2 4 y = 0 x [2, 3] .

    10.

    e t (t )

    V(t) = 77 + 7 cos

    6(t + 7)

    . .

    . 7 300 2012/2013 .

  • MA , 3, 008

    1. c x 3x2 578 dx .

    2. c 17(x2 + 3x + 4)

    (x + 3)(x2 + 4x + 20)dx .

    3. c x 8 + 1

    x + 17dx .

    4. c 118

    124

    ctg6x dx .

    5. c 0

    14

    (x2 + 4x + 5) sin7x dx .

    6. c 0

    18

    cos26x dx .

    7. c cc 0

    e2xdx

    .

    8. c , yx = 3, x + y = 4 .

    .

    9. c , c Ox ,

    y = x2 + 3x y = 0 x [0, 3] .

    10. V(t) ,

    , 23% , . .

    t V

    V= 0 . 23t .

    12 , , V(0) = 52 .

    . 8 300 2012/2013 .

  • MA , 3, 009

    1. c 4x + 52x

    2 + 5x 313

    dx .

    2. c 29(x2 3x + 7)

    (x 5)(x2 + 4)dx .

    3. c 1 + xx 4 2 dx .

    4. c 34

    78

    3 ctg32x + ctg2x + 1

    sin22xdx .

    5. c 0

    4

    (x2 + 3x 3) cos2x dx .

    6. c 0

    28

    sin27x dx .

    7. c cc e79

    e9

    9dx

    x 7 + ln9x

    .

    8. c , x + y = 9, yx = 14 .

    .

    9. c , c Ox ,

    y =1

    x 2, x = 8 x = 0 .

    10. ,

    : z(t) = 1 . 095t2 + 9 . 7t + 6 . 9 t

    ( ), .

    . 9 300 2012/2013 .

  • MA , 3, 010

    1. c 4x 32x

    2 3x + 278

    dx .

    2. c 2x2 + 4x 16

    (x 1)(x2 6x + 9)dx .

    3. c 9 + x 6

    x 2dx .

    4. c e78

    e4

    8dx

    x ln28x.

    5. c 0

    13 3

    arctg3x dx .

    6. c 0

    2

    cos6x sin3x dx .

    7. c cc 5

    9x + 4 x 5

    x 5dx

    .

    8. c , y =4

    x2 + 8, y =

    1

    12x2 .

    .

    9. c , c Ox ,

    y =9

    x + 8, x = 3 x = 7 .

    10. q TC(q),

    q

    MC = e1.4q, 45 .

    . 10 300 2012/2013 .

  • MA , 3, 011

    1. c dx(3x + 5)106 .

    2. c x2 + 4x 6

    x3 2x2 + xdx .

    3. c x + 3 4

    x + 12dx .

    4. c ln5

    ln6e2x

    e4x + 25dx .

    5. c 13

    13 3

    arctg3x dx .

    6. c 0

    2

    cos5x sin4x dx .

    7. c cc 1

    5x + 2 4 5 x

    5 xdx

    .

    8. c , y =36

    x2 + 216,

    y =1

    252x2 . .

    9. c , c Ox ,

    y = x2 + 6x y = 0 x [0, 1] .

    10.

    MC(x) = 92 4x 5x2, 82 .

    .

    . 11 300 2012/2013 .

  • MA , 3, 012

    1. c dx4x + 5 .

    2. c 2x2 14x + 16

    (x 2)(x2 6x + 8)dx .

    3. c x 4 + 8

    x 20dx .

    4. c ln3

    ln4e2x

    e4x 9dx .

    5. c 0

    12

    (x2 + x 5) cos6x dx .

    6. c 0

    6

    sin23x dx .

    7. c cc 3

    7dx

    (x + 4) ln4(x + 4)

    .

    8. c , y = x2 + 7x + 3,

    y = x 5 . .

    9. c , c Ox ,

    y =7

    x + 3, x = 2 x = 0 .

    10. ,

    CM = 12q5 + 15q4 + 6q , 460 .

    . 12 300 2012/2013 .

  • MA , 3, 013

    1. c (10x + 4) 5x2 + 4x 7 dx .

    2. c 10(x2 + x + 4)

    x3 2x2 + 10xdx .

    3. c x

    9 7 x34dx .

    4. c 0

    6

    sin3x

    cos23x 36dx

    5. c 0

    3

    arctg x dx .

    6. c 0

    2

    cos6x sin2x dx .

    7. c cc

    1dx

    1 + x2

    .

    8. c , y = 4x2 + 4x + 7,

    y = 5x2 + 6x + 10 . .

    9. c , c Ox ,

    y =2

    x 6, x = 0 x = 5 .

    10. ,

    : z(t) = 1 . 264t2 + 8 . 7t + 6 . 2 t

    ( ), .

    . 13 300 2012/2013 .

  • MA , 3, 014

    1. c (14x + 5) 7x2 + 5x + 217 dx .

    2. c 20(x2 2x + 3)

    (x + 1)(x2 6x + 13)dx .

    3. c 2 x

    5 + 9 x34dx .

    4. c 12

    716

    2 tg34x + tg4x + 1

    cos24xdx .

    5. c 0

    6

    (x2 + 5x + 1) cos3x dx .

    6. c 0

    18

    sin26x dx .

    7. c cc 1

    +

    75x+4 dx

    .

    8. c , x + y = 6, yx = 5 .

    .

    9. c , c Ox ,

    y =1

    x + 3, x = 2 x = 2 .

    10. ()

    8 20

    f (t) = 70000 + 75t 3t2, t , 8 t 20.

    , 11 16 ,

    1 4 . .

    . 14 300 2012/2013 .

  • MA , 3, 015

    1. c dx(4 + x)102 .

    2. c 10(x2 2x 9)

    (x + 7)(x + 3)(x 2)dx .

    3. c dxx2

    3 + 3 x.

    4. c 0

    10

    sin5x

    cos25x 36dx

    5. c 1

    3

    1

    arctg x dx .

    6. c 0

    18

    sin26x dx .

    7. c cc 1

    265 + 2 x 1

    x 1dx

    .

    8. c , y = 2x2 x 5,

    y = 4x2 9x 5 . .

    9. c , c Ox ,

    y = x2 4x y = 0 x [6, 7] .

    10.

    e t (t )

    V(t) = 78 + 8 cos

    4(t + 6)

    . .

    . 15 300 2012/2013 .

  • MA , 3, 016

    1. c dx6 2x .

    2. c x2 5x 2

    (x 7)(x2 12x + 36)dx .

    3. c x + 9 7

    x + 13dx .

    4. c e3

    6

    e11

    6dx

    x ln6x.

    5. c 12

    12 3

    arctg2x dx .

    6. c 0

    24

    sin26x dx .

    7. c cc 52

    +

    62x1 dx

    .

    8. c , y = 5x2 + 4x + 5,

    y = 2x2 3x + 5 . .

    9. c , c Ox ,

    y =5

    x 6, x = 3 x = 0 .

    10.

    MC(x) = 6 2x 4x2, 67 .

    .

    . 16 300 2012/2013 .

  • MA , 3, 017

    1. c dx2x + 7 .

    2. c 4(x2 5x 8)

    x3 12x2 + 32xdx .

    3. c 5 xx + 4 + 2 dx .

    4. c 12

    14

    5 ctg3x + 2 ctg2x 3

    sin2xdx .

    5. c 0

    8

    (x2 x 2) cos4x dx .

    6. c 0

    24

    cos26x dx .

    7. c cc 2

    dx

    4 + x2

    .

    8. c , yx = 42, x + y = 13 .

    .

    9. c , c Ox ,

    y =4

    x + 2, x = 3 x = 6 .

    10. K(t),

    ( , )

    I(t) = 220 t74 , K(0) = 470 .

    . 17 300 2012/2013 .

  • MA , 3, 018

    1. c dx(1 + x2) arctg8x .

    2. c 2x2 + 8x + 14

    2x2 x3dx .

    3. c 4 x3

    8 x23

    dx .

    4. c 13

    38

    3 tg36x + 2 tg6x 3

    cos26xdx .

    5. c 0

    6

    (x2 2x 4) cos3x dx .

    6. c 0

    10

    sin25x dx .

    7. c cc

    10

    sin5x dx

    .

    8. c , y = x2 6x 7,

    y = 4x + 1 . .

    9. c , c Ox ,

    y =8

    x 6, x = 6 x = 1 .

    10. R(x), x

    MR = 7x2 320 .

    . 18 300 2012/2013 .

  • MA , 3, 019

    1. c dx(4 + 5x)30 .

    2. c 8(x2 + 6x + 6)

    (x + 2)(x2 + 4)dx .

    3. c 1 xx 5 + 2 dx .

    4. c ln2

    ln4e3x

    e6x + 4dx .

    5. c 0

    8

    (x2 x + 2) cos4x dx .

    6. c 0

    2

    sin5x sin3x dx .

    7. c cc 12

    45 4 4 x

    4 xdx

    .

    8. c , y = 7x2 + 5x + 4,

    y = 8x2 + x + 4 . .

    9. c , c Ox ,

    y = x2 3x y = 0 x [5, 6] .10. e

    z(t) = 90t 8 . 94t2 , t ( ), .

    C 8 . 64

    , 29 .

    . 19 300 2012/2013 .

  • MA , 3, 020

    1. c arcsin x

    1 x2dx .

    2. c 2x2 + 8x 14

    (x 1)(x2 + 2x + 1)dx .

    3. c x + 4 6

    x + 13dx .

    4. c e44

    e3

    4dx

    x ln34x.

    5. c 14

    3

    14

    arctg4x dx .

    6. c 0

    2

    cos4x cos3x dx .

    7. c cc 3

    cos3x dx

    .

    8. c , y =1

    x2 + 6, y =

    1

    7x2 .

    .

    9. c , c Ox ,

    y =7

    x + 1, x = 3 x = 9 .

    10. R(x), x

    MR = 9x5 230 .

    . 20 300 2012/2013 .

  • MA , 3, 021

    1. c dx5 6x .

    2. c 5(x2 + 5x + 5)

    (x + 2)(x2 + 2x + 5)dx .

    3. c dxx2

    3 + x.

    4. c ln6

    ln5e2x

    4 9e4xdx .

    5. c 0

    12

    (x2 + 3x 2) cos6x dx .

    6. c 0

    18

    cos23x dx .

    7. c cc

    36

    sin6x dx

    .

    8. c , yx = 42, x + y = 13 .

    .

    9. c , c Ox ,

    y =1

    x + 3, x = 0 x = 8 .

    10. e

    z(t) = 68t 7 . 46t2 , t ( ), .

    C 8 . 11

    , 55 .

    . 21 300 2012/2013 .

  • MA , 3, 022

    1. c dx4x 3 .

    2. c 12(x2 7x + 2)

    x3 4x2 12xdx .

    3. c 5 4xx 1 + 1 dx .

    4. c 54

    12 tg3x + 2 tg2x + 1

    cos2xdx .

    5. c 1

    2 3

    12

    arctg2x dx .

    6. c 0

    9

    sin23x dx .

    7. c cc 15e2

    15

    dx

    x ln5x

    .

    8. c , x + y = 11, yx = 28 .

    .

    9. c , c Ox ,

    y =4

    x 4, x = 7 x = 3 .

    10. q TC(q),

    q

    MC = e0.5q, 25 .

    . 22 300 2012/2013 .

  • MA , 3, 023

    1. c dx1 4x .

    2. c 5(x2 3x 2)

    (x + 1)(x2 + 4x + 8)dx .

    3. c 3 xx 2 2 dx .

    4. c 0

    10

    sin5x

    cos25x 25dx

    5. c 13

    0

    arctg3x dx .

    6. c 0

    15

    sin25x dx .

    7. c cc

    0

    e8xdx

    .

    8. c , y =36

    x2 + 72,

    y =1

    108x2 . .

    9. c , c Ox ,

    y =6

    x 4, x = 8 x = 1 .

    10. R(x), x

    MR = 5x9 380 .

    . 23 300 2012/2013 .

  • MA , 3, 024

    1. c dx2 6x .

    2. c 2x2 + 14x 2

    x3 + 4x2 + 4xdx .

    3. c 7x + 2x 1 + 1 dx .

    4. c e34

    e5

    4dx

    x ln4x.

    5. c 0

    14

    (x2 2x 3) cos7x dx .

    6. c 0

    2

    cos3x sin4x dx .

    7. c cc 12

    1dx

    1 x2

    .

    8. c , yx = 7, x + y = 8 .

    .

    9. c , c Ox ,

    y =2

    x 1, x = 6 x = 1 .

    10. R(x), x

    MR = 7x3 940 .

    . 24 300 2012/2013 .

  • MA , 3, 025

    1. c x 5x2 + 7 dx .

    2. c 29(x2 3x + 5)

    (x 7)(x2 4x + 8)dx .

    3. c dxx2

    3 2 x.

    4. c ln3

    ln4e2x

    e4x 17dx .

    5. c 13

    13 3

    arctg3x dx .

    6. c 0

    2

    sin3x sin6x dx .

    7. c cc 5

    6x + 5

    6 xdx

    .

    8. c , y = x2 + 4x, y = x2 .

    .

    9. c , c Ox ,

    y = x2 + 6x y = 0 x [0, 2] .

    10. ()

    8 20

    f (t) = 30000 + 63t 3t2, t , 8 t 20.

    , 11 12 ,

    1 2 . .

    . 25 300 2012/2013 .

  • MA , 3, 026

    1. c dx2 7x .

    2. c 6(x2 6x + 3)

    (x 2)(x 5)(x 4)dx .

    3. c x

    1 + x34

    dx .

    4. c 98

    13 tg32x 5 tg2x 2

    cos22xdx .

    5. c 0

    12

    (x2 + 5x 5) sin6x dx .

    6. c 0

    2

    cos6x sin2x dx .

    7. c cc 34

    +

    84x+1 dx

    .

    8. c , y = 8x2 7x + 4,

    y = 4x2 3x + 4 . .

    9. c , c Ox ,

    y = x2 + 3x y = 0 x [0, 1] .

    10. K(t),

    ( , )

    I(t) = 80(t 1)57 , ( t = 1)

    310 .

    . 26 300 2012/2013 .

  • MA , 3, 027

    1. c dx(1 + 2x)83 .

    2. c x2 7x 2

    (x 2)(x2 11x + 30)dx .

    3. c x 7 + 1

    x 43dx .

    4. c 128

    128

    2 tg37x 3 tg27x 1

    cos27xdx .

    5. c 0

    13

    3

    arctg3x dx .

    6. c 0

    21

    cos27x dx .

    7. c cc 0

    e8xdx

    .

    8. c , x + y = 8, yx = 7 .

    .

    9. c , c Ox ,

    y = x2 + 4x y = 0 x [ 7, 6] .

    10. K(t),

    ( , )

    I(t) = 560(t 1)43 , K(1) = 890 .

    . 27 300 2012/2013 .

  • MA , 3, 028

    1. c dx(2x + 3)39 .

    2. c 5(x2 3x + 7)

    (x + 1)(x2 + 4)dx .

    3. c 1 x 3

    x 3 1dx .

    4. c ln2

    ln3e2x

    e4x + 33dx .

    5. c 12

    12

    3

    arctg2x dx .

    6. c 0

    2

    sin5x sin6x dx .

    7. c cc

    10

    sin5x dx

    .

    8. c , y =4

    x2 + 12, y =

    1

    16x2 .

    .

    9. c , c Ox ,

    y =5

    x 2, x = 5 x = 2 .

    10. ()

    8 20

    f (t) = 4000 + 88t 3t2, t , 8 t 20.

    , 14 19 ,

    1 4 . .

    . 28 300 2012/2013 .

  • MA , 3, 029

    1. c dx(4 + 5x)82 .

    2. c 4(x2 + 5x 6)

    (x + 1)(x2 + 2x + 5)dx .

    3. c x + 2x 2 + 1 dx .

    4. c 14

    38

    3 ctg22x + 5 ctg2x + 2

    sin22xdx .

    5. c 13

    3

    13

    arctg3x dx .

    6. c 0

    9

    cos23x dx .

    7. c cc

    13

    dx

    1 + x2

    .

    8. c , x + y = 13, yx = 42 .

    .

    9. c , c Ox ,

    y = x2 + 16 y = 0 x [0, 1] .

    10. ,

    : z(t) = 1 . 175t2 + 9 . 8t + 3 . 6 t

    ( ), .

    . 29 300 2012/2013 .

  • MA , 3, 030

    1. c x dx5x

    2 325

    2. c x2 + 6x + 6

    (x + 1)(x2 + 3x + 2)dx .

    3. c 7 + x 3

    x 39dx .

    4. c 512

    13

    2 tg23x + tg3x + 3

    cos23xdx .

    5. c 1

    13

    arctg x dx .

    6. c 0

    15

    cos25x dx .

    7. c cc 0

    e5xdx

    .

    8. c , yx = 40, x + y = 13 .

    .

    9. c , c Ox ,

    y =5

    x + 4, x = 2 x = 8 .

    10. ,

    : z(t) = 1 . 271t2 + 8 . 5t + 0 . 1 t

    ( ), .

    . 30 300 2012/2013 .

  • MA , 3, 031

    1. c dx(4 + 3x)58 .

    2. c 3x2 6x + 24

    x3 3x2dx .

    3. c 3 + x 2

    x 18dx .

    4. c 14

    310

    ctg35x + 3 ctg5x + 5

    sin25xdx .

    5. c 0

    12

    (x2 6x 6) cos6x dx .

    6. c 0

    42

    sin27x dx .

    7. c cc 3

    7x + 2

    x 3dx

    .

    8. c , y = x2 + 7x + 6,

    y = 4x + 2 . .

    9. c , c Ox ,

    y =9

    x + 9, x = 7 x = 1 .

    10. e

    z(t) = 68t 8 . 17t2 , t ( ), .

    C 7 . 83

    , 12 .

    . 31 300 2012/2013 .

  • MA , 3, 032

    1. c dx(1 + 4x)93 .

    2. c 8(x2 3x 4)

    x3 + 4x2 + 8xdx .

    3. c 8 + xx 9 1 dx .

    4. c 0

    6

    cos3x

    sin23x 25dx

    5. c 0

    6

    (x2 + x + 2) cos3x dx .

    6. c 0

    2

    cos4x sin6x dx .

    7. c cc

    0

    sin5x dx

    .

    8. c , x + y = 13, yx = 40 .

    .

    9. c , c Ox ,

    y = x2 8x y = 0 x [ 1, 0] .

    10.

    MC(x) = 64 2x 8x2, 23 .

    .

    . 32 300 2012/2013 .

  • MA , 3, 033

    1. c dx(2x 5)34 .

    2. c 13(x2 3x + 5)

    (x + 1)(x2 4x + 8)dx .

    3. c 9 x + 2

    x + 2 + 2dx .

    4. c 136

    112

    ctg6x dx .

    5. c 0

    10

    (x2 + 2x + 6) cos5x dx .

    6. c 0

    24

    sin26x dx .

    7. c cc 16

    e7

    6dx

    x ln6x

    .

    8. c , y =25

    x2 + 75,

    y =1

    100x2 . .

    9. c , c Ox ,

    y =7

    x + 9, x = 8 x = 5 .

    10. ,

    : z(t) = 0 . 411t2 + 2 . 4t + 9 . 1 t

    ( ), .

    . 33 300 2012/2013 .

  • MA , 3, 034

    1. c (12x + 5) 6x2 + 5x 665 dx .

    2. c x2 6x + 8

    (x + 4)(x + 8)(x + 3)dx .

    3. c 4 + xx 5 + 1 dx .

    4. c ln3

    ln4e2x

    e4x 45dx .

    5. c 0

    6

    (x2 x 6) sin3x dx .

    6. c 0

    30

    cos25x dx .

    7. c cc 1

    12

    dx

    1 x2

    .

    8. c , y = x2 + 7x + 9,

    y = 2x + 3 . .

    9. c , c Ox ,

    y = x2 1 y = 0 x [1, 3] .

    10. ,

    : z(t) = 0 . 625t2 + 6 . 6t + 1 . 2 t

    ( ), .

    . 34 300 2012/2013 .

  • MA , 3, 035

    1. c x dx 5x

    2 + 695

    2. c x2 + x 8

    (x + 3)(x2 + 6x + 8)dx .

    3. c dxx2

    3 3 x.

    4. c 542

    17

    tg7x dx .

    5. c 0

    12 3

    arctg2x dx .

    6. c 0

    20

    sin25x dx .

    7. c cc 1

    +

    e3x1 dx

    .

    8. c , y = 3x2 8x + 2,

    y = 5x2 6x + 6 . .

    9. c , c Ox ,

    y = x2 1 y = 0 x [ 4, 3] .

    10.

    e t (t )

    V(t) = 67 + 2 sin

    12(t + 9)

    . .

    . 35 300 2012/2013 .

  • MA , 3, 036

    1. c 2x 2x2 2x 5

    6dx .

    2. c 2x2 14x + 4

    (x 8)(x2 14x + 48)dx .

    3. c dxx2

    3 3 x.

    4. c 524

    724

    3 ctg36x 4 ctg26x + 2

    sin26xdx .

    5. c 12 3

    12

    arctg2x dx .

    6. c 0

    28

    sin27x dx .

    7. c cc 1

    dx

    1 + x2

    .

    8. c , y = x2 + 2x + 3,

    y = x 1 . .

    9. c , c Ox ,

    y = x2 6x y = 0 x [ 2, 1] .10. e

    z(t) = 68t 8 . 41t2 , t ( ), .

    C 8 . 15

    , 70 .

    . 36 300 2012/2013 .

  • MA , 3, 037

    1. c (14x 3) 7x2 3x + 7 dx .

    2. c 14(x2 2x 9)

    (x + 5)(x 8)(x 2)dx .

    3. c 8 + xx 8 1 dx .

    4. c 0

    12

    cos6x

    sin26x + 9dx

    5. c 0

    10

    (x2 4x 6) sin5x dx .

    6. c 0

    2

    cos6x cos3x dx .

    7. c cc e24

    e9

    4dx

    x2 + ln4x

    .

    8. c , y = 2x2 + 9x 1,

    y = 5x2 + 6x 7 . .

    9. c , c Ox ,

    y = x2 5x y = 0 x [ 2, 0] .

    10. R(x), x

    MR = x2 620 .

    . 37 300 2012/2013 .

  • MA , 3, 038

    1. c dx2x + 6 .

    2. c 18(x2 x + 8)

    (x 2)(x2 4x 32)dx .

    3. c 5x 1x 1 1 dx .

    4. c 120

    115

    ctg5x dx .

    5. c 0

    4

    (x2 7x 2) sin2x dx .

    6. c 0

    2

    cos3x cos6x dx .

    7. c cc e43

    e5

    3dx

    x 5 + ln3x5

    .

    8. c , yx = 21, x + y = 10 .

    .

    9. c , c Ox ,

    y =2

    x + 1, x = 0 x = 3 .

    10.

    e t (t )

    V(t) = 50 + 6 cos

    2(t + 6)

    . .

    . 38 300 2012/2013 .

  • MA , 3, 039

    1. c dx1 x2 arcsin6x

    .

    2. c 85(x2 + 4x + 7)

    (x 7)(x2 + 4x + 8)dx .

    3. c 2 xx + 3 + 1 dx .

    4. c ln2

    ln3e2x

    e4x 7dx .

    5. c 13

    13 3

    arctg3x dx .

    6. c 0

    2

    sin7x sin4x dx .

    7. c cc

    72

    e2x4 dx

    .

    8. c , y =16

    x2 + 80, y =

    1

    96x2 .

    .

    9. c , c Ox ,

    y = x2 2x y = 0 x [2, 5] .

    10. ,

    CM = 20q4 + 9q2 + 6q , 180 .

    . 39 300 2012/2013 .

  • MA , 3, 040

    1. c dx1 x2 arcsin x4

    .

    2. c 3x2 + 3x 21

    x3 + 3x2dx .

    3. c 7 x3

    3 + 8 x23dx .

    4. c ln2

    ln3e2x

    e4x 7dx .

    5. c 12 3

    12

    arctg2x dx .

    6. c 0

    6

    cos23x dx .

    7. c cc 19

    e5

    9dx

    x ln59x4

    .

    8. c , yx = 10, x + y = 7 .

    .

    9. c , c Ox ,

    y = x2 2x y = 0 x [2, 3] .

    10. ,

    CM = 18q5 + 10q4 + 6q2, 400 .

    . 40 300 2012/2013 .

  • MA , 3, 041

    1. c dx(3 5x)93 .

    2. c 10(x2 3x 2)

    (x 3)(x2 8x + 25)dx .

    3. c x + 4 4

    x + 0dx .

    4. c 0

    6

    cos3x

    sin23x + 25dx

    5. c 0

    8

    (x2 + 6x 3) sin4x dx .

    6. c 0

    10

    sin25x dx .

    7. c cc 52

    +

    72x2 dx

    .

    8. c , yx = 6, x + y = 5 .

    .

    9. c , c Ox ,

    y =7

    x + 8, x = 0 x = 4 .

    10. e

    z(t) = 83t 7 . 12t2 , t ( ), .

    C 7 . 15

    , 88 .

    . 41 300 2012/2013 .

  • MA , 3, 042

    1. c x dx4x

    2 375

    2. c 3x2 + 6x 15

    x3 6x2 + 9xdx .

    3. c 3x + 2x 3 + 1 dx .

    4. c 0

    6

    sin3x

    cos23x 36dx

    5. c 1

    13

    arctg x dx .

    6. c 0

    2

    cos5x sin3x dx .

    7. c cc 1

    dx

    1 + x2

    .

    8. c , y =25

    x2 + 100,

    y =1

    125x2 . .

    9. c , c Ox ,

    y =5

    x 4, x = 5 x = 1 .

    10. V(t) ,

    , 0 . 38, . .

    t V

    V= 0 . 38t .

    , 13 ,

    , ,

    V(0) = 25 .

    . 42 300 2012/2013 .

  • MA , 3, 043

    1. c 4x 32x2 3x + 6 dx .

    2. c 18(x2 + 2x + 8)

    (x + 3)(x2 + 9)dx .

    3. c x + 5 + 2

    5 + x + 5dx .

    4. c e9

    e4

    9dx

    x ln9x.

    5. c 0

    8

    (x2 4x + 4) sin4x dx .

    6. c 0

    2

    cos6x sin4x dx .

    7. c cc 5

    67 2 x 5

    x 5dx

    .

    8. c , y = x2 + 4x + 15,

    y = 3x + 3 . .

    9. c , c Ox ,

    y = x2 + 7x y = 0 x [0, 2] .

    10. V(t) ,

    , 0 . 19, . .

    t V

    V= 0 . 19t .

    , 31 ,

    , ,

    V(0) = 11 .

    . 43 300 2012/2013 .

  • MA , 3, 044

    1. c (10x 3) 5x2 3x + 54 dx .

    2. c 4(x2 + 2x 8)

    (x + 3)(x2 + 6x + 13)dx .

    3. c 3 x3

    9 + 7 x23

    dx .

    4. c 0

    142

    tg7x dx .

    5. c 0

    14

    (x2 + 6x + 3) cos7x dx .

    6. c 0

    2

    cos5x cos3x dx .

    7. c cc 61

    32 3 x 1

    3 xdx

    .

    8. c , y = 7x2,

    y = 5x2 10x 6 . .

    9. c , c Ox ,

    y =1

    x 2, x = 3 x = 5 .

    10. V(t) ,

    , 0 . 18, . .

    t V

    V= 0 . 18t .

    31 , , V(0) = 28 .

    . 44 300 2012/2013 .

  • MA , 3, 045

    1. c dx(3x 2)41 .

    2. c 5(x2 3x + 4)

    x3 + 2x2 + 5xdx .

    3. c 7 x + 6

    x + 6 + 1dx .

    4. c ln6

    ln7e2x

    e4x + 36dx .

    5. c 0

    6

    (x2 + 7x + 3) sin3x dx .

    6. c 0

    12

    sin24x dx .

    7. c cc

    1

    e5x+4 dx

    .

    8. c , y =16

    x2 + 112,

    y =1

    128x2 . .

    9. c , c Ox ,

    y = x2 + 3x y = 0 x [0, 3] .

    10. ,

    CM = 20q4 + 8q3 + 12q2, 380 .

    . 45 300 2012/2013 .

  • MA , 3, 046

    1. c x 4x2 77 dx .

    2. c x2 6x + 8

    x3 + x2 2xdx .

    3. c 4 x + 4

    x + 4 3dx .

    4. c 16

    14

    tg4x dx .

    5. c 0

    4

    (x2 + 3x 2) cos2x dx .

    6. c 0

    12

    sin23x dx .

    7. c cc 18

    sin3x dx

    .

    8. c , y = 7x2,

    y = 5x2 4x + 11 . .

    9. c , c Ox ,

    y = x2 + 6x y = 0 x [ 8, 6] .

    10. e

    z(t) = 64t 5 . 78t2 , t ( ), .

    C 7 . 71

    , 64 .

    . 46 300 2012/2013 .

  • MA , 3, 047

    1. c 10x + 45x2 + 4x 5

    dx .

    2. c 5(x2 8x + 4)

    (x + 1)(x2 + 4)dx .

    3. c 8 x

    1 + 5 x34

    dx .

    4. c 16

    14

    tg4x dx .

    5. c 0

    10

    (x2 + 5x + 4) cos5x dx .

    6. c 0

    9

    sin23x dx .

    7. c cc 5

    545 x 5 6

    x 5dx

    .

    8. c , y =1

    x2 + 5, y =

    1

    6x2 .

    .

    9. c , c Ox ,

    y =7

    x 9, x = 8 x = 1 .

    10. ()

    8 20

    f (t) = 8000 + 96t 3t2, t , 8 t 20.

    , 15 17 ,

    1 8 . .

    . 47 300 2012/2013 .

  • MA , 3, 048

    1. c dx(1 + x2) arctg6x7

    .

    2. c x2 8x + 6

    x3 3x2 + 2xdx .

    3. c 2 xx + 3 + 1 dx .

    4. c ln3

    ln4e2x

    e4x 25dx .

    5. c 13

    13 3

    arctg3x dx .

    6. c 0

    2

    cos4x sin3x dx .

    7. c cc 7

    8x + 5

    8 xdx

    .

    8. c , x + y = 12, yx = 35 .

    .

    9. c , c Ox ,

    y = x2 4x y = 0 x [ 1, 0] .

    10.

    e t (t )

    V(t) = 61 + 2 cos

    12(t + 6)

    . .

    . 48 300 2012/2013 .

  • MA , 3, 049

    1. c dx(5x 4)104 .

    2. c 2x2 18x + 16

    2x2 x3dx .

    3. c 3 + x 2

    x 18dx .

    4. c 29

    13

    tg3x dx .

    5. c 13

    13 3

    arctg3x dx .

    6. c 0

    2

    cos3x sin4x dx .

    7. c cc 1

    dx

    1 + x2

    .

    8. c , y =36

    x2 + 180,

    y =1

    216x2 . .

    9. c , c Ox ,

    y = x2 9x y = 0 x [ 1, 0] .

    10. V(t) ,

    , 42% , . .

    t V

    V= 0 . 42t .

    14 , , V(0) = 94 .

    . 49 300 2012/2013 .

  • MA , 3, 050

    1. c x 2x2 543 dx .

    2. c x2 8x + 8

    (x 5)(x2 12x + 36)dx .

    3. c 5x 6x 1 + 1 dx .

    4. c e72

    e11

    2dx

    x ln2x.

    5. c 12 3

    12

    arctg2x dx .

    6. c 0

    8

    sin24x dx .

    7. c cc

    14

    74x+3 dx

    .

    8. c , y = 9x2 + 5x 7,

    y = 5x2 7x + 1 . .

    9. c , c Ox ,

    y =1

    x + 7, x = 0 x = 3 .

    10. R(x), x

    MR = 3x4 670 .

    . 50 300 2012/2013 .

  • MA , 3, 051

    1. c dx2 6x .

    2. c 25(x2 + 3x + 8)

    (x 3)(x2 + 2x + 10)dx .

    3. c 3x + 4x 3 1 dx .

    4. c 0

    12

    sin6x

    cos26x + 36dx

    5. c 0

    12 3

    arctg2x dx .

    6. c 0

    21

    cos27x dx .

    7. c cc 0

    e8xdx

    .

    8. c , y = x2 + 11x + 7,

    y = 4x 3 . .

    9. c , c Ox ,

    y =3

    x + 2, x = 6 x = 4 .

    10. ,

    CM = 8q3 + 12q2 + 8q , 570 .

    . 51 300 2012/2013 .

  • MA , 3, 052

    1. c dx8x + 3 .

    2. c 13(x2 + 4x 3)

    (x 2)(x2 + 2x + 5)dx .

    3. c 2 + x 3

    x 28dx .

    4. c 916

    12

    3 tg34x 4 tg24x + 3

    cos24xdx .

    5. c 12

    12

    3

    arctg2x dx .

    6. c 0

    15

    cos25x dx .

    7. c cc e64

    e4

    4dx

    x6 + ln4x

    .

    8. c , y =4

    x2 + 20, y =

    1

    24x2 .

    .

    9. c , c Ox ,

    y =6

    x 2, x = 6 x = 1 .

    10. ,

    : z(t) = 0 . 932t2 + 9 . 3t + 1 . 1 t

    ( ), .

    . 52 300 2012/2013 .

  • MA , 3, 053

    1. c 4x + 72x2 + 7x + 2

    dx .

    2. c 8(x2 + 2x + 3)

    x3 + 4x2 + 8xdx .

    3. c x + 3 + 3

    x + 39dx .

    4. c ln3

    ln4e2x

    e4x 65dx .

    5. c 0

    6

    (x2 5x + 1) sin3x dx .

    6. c 0

    2

    cos6x sin3x dx .

    7. c cc

    23

    e3x3 dx

    .

    8. c , x + y = 8, yx = 15 .

    .

    9. c , c Ox ,

    y =3

    x 3, x = 8 x = 2 .

    10.

    e t (t )

    V(t) = 87 + 2 cos

    4(t + 6)

    . .

    . 53 300 2012/2013 .

  • MA , 3, 054

    1. c dx(3 + x)98 .

    2. c 85(x2 2x + 1)

    (x + 8)(x2 2x + 5)dx .

    3. c x 1 8

    1 + x 1dx .

    4. c ln6

    ln5e2x

    4 81e4xdx .

    5. c 12 3

    12

    arctg2x dx .

    6. c 0

    4

    cos22x dx .

    7. c cc 4

    5x + 4

    5 xdx

    .

    8. c , yx = 15, x + y = 8 .

    .

    9. c , c Ox ,

    y = x2 + 2x y = 0 x [0, 3] .10.

    e t (t )

    V(t) = 12 + 6 sin

    12(t + 2)

    . .

    . 54 300 2012/2013 .

  • MA , 3, 055

    1. c x dx4x

    2 387

    2. c 3x2 3x + 12

    x3 3x2dx .

    3. c 8x 5x 1 + 1 dx .

    4. c 58

    12

    5 tg32x + 5 tg22x + 2

    cos22xdx .

    5. c 3

    0

    arctg x dx .

    6. c 0

    4

    cos22x dx .

    7. c cc 15e7

    15

    dx

    x ln5x

    .

    8. c , y =9

    x2 + 36, y =

    1

    45x2 .

    .

    9. c , c Ox ,

    y = x2 3x y = 0 x [5, 6] .10.

    MC(x) = 74 4x 3x2, 38 .

    .

    . 55 300 2012/2013 .

  • MA , 3, 056

    1. c dx4 8x .

    2. c 13(x2 + 4x 5)

    (x + 6)(x2 + 6x + 13)dx .

    3. c x 1 + 4

    x + 15dx .

    4. c ln3

    ln6e2x

    e4x 16dx .

    5. c 13

    13 3

    arctg3x dx .

    6. c 0

    18

    cos26x dx .

    7. c cc

    e2xdx

    .

    8. c , x + y = 13, yx = 36 .

    .

    9. c , c Ox ,

    y = x2 + 6x y = 0 x [1, 2] .

    10. e

    z(t) = 58t 7 . 61t2 , t ( ), .

    C 7 . 69

    , 49 .

    . 56 300 2012/2013 .

  • MA , 3, 057

    1. c 14x 57x

    2 5x + 217

    dx .

    2. c 3(x2 + 3x 4)

    x3 + 4x2 + 3xdx .

    3. c 1 + xx 1 1 dx .

    4. c 0

    12

    sin6x

    cos26x 9dx

    5. c 0

    13

    3

    arctg3x dx .

    6. c 0

    30

    cos25x dx .

    7. c cc

    0

    e7xdx

    .

    8. c , yx = 21, x + y = 10 .

    .

    9. c , c Ox ,

    y = x2 8x y = 0 x [ 2, 0] .

    10. V(t) ,

    , 0 . 34, . .

    t V

    V= 0 . 34t .

    , 13 ,

    , ,

    V(0) = 81 .

    . 57 300 2012/2013 .

  • MA , 3, 058

    1. c (2x + 1)51dx .

    2. c 13(x2 + 5x + 7)

    x3 + 6x2 + 13xdx .

    3. c 3 + 4xx 2 + 1 dx .

    4. c 0

    6

    cos3x

    sin23x + 25dx

    5. c 0

    12

    (x2 + 3x 3) cos6x dx .

    6. c 0

    20

    sin25x dx .

    7. c cc 53

    6

    8dx

    (x + 9) ln9(x + 9)

    .

    8. c , y = x2 + 1,

    y = 4x + 4 . .

    9. c , c Ox ,

    y = x2 4 y = 0 x [ 4, 2] .10. V(t) ,

    , 35% , . .

    t V

    V= 0 . 35t .

    , 13 ,

    , ,

    V(0) = 56 .

    . 58 300 2012/2013 .

  • MA , 3, 059

    1. c x dx 5x

    2 + 645

    2. c 18(x2 6x 4)

    x3 36xdx .

    3. c x 2x 3 1 dx .

    4. c 19

    118

    ctg3x dx .

    5. c 0

    14

    (x2 + 6x + 4) cos7x dx .

    6. c 0

    8

    sin22x dx .

    7. c cc 8

    176 5 x 8

    x 8dx

    .

    8. c , y = 4x2 x,

    y = 7x2 + 5x + 9 . .

    9. c , c Ox ,

    y = x2 9 y = 0 x [3, 4] .

    10. e

    z(t) = 56t 6 . 07t2 , t ( ), .

    C 7 . 77

    , 89 .

    . 59 300 2012/2013 .

  • MA , 3, 060

    1. c (1 3x)93dx .

    2. c 8(x2 8x 3)

    (x + 2)(x2 + 4)dx .

    3. c 8 + x + 7

    x + 7 + 1dx .

    4. c ln2

    ln4e3x

    e6x + 4dx .

    5. c 12 3

    12

    arctg2x dx .

    6. c 0

    2

    cos3x sin6x dx .

    7. c cc e74

    e2

    4dx

    x (7 + ln4x)94

    .

    8. c , x + y = 8, yx = 7 .

    .

    9. c , c Ox ,

    y = x2 + x y = 0 x [ 4, 1] .10.

    e t (t )

    V(t) = 97 + 8 cos

    3(t + 5)

    . .

    . 60 300 2012/2013 .

  • MA , 3, 061

    1. c x dx5x2 3

    .

    2. c 8(x2 + 2x + 4)

    x3 4x2 + 8xdx .

    3. c dxx2

    3 + 5 x.

    4. c ln4

    ln7e2x

    e4x + 16dx .

    5. c 0

    6

    (x2 x 7) cos3x dx .

    6. c 0

    2

    cos5x cos4x dx .

    7. c cc 4

    534 x 4 + 5

    x 4dx

    .

    8. c , y = 7x2 + 3x + 3,

    y = 5x2 11x + 3 . .

    9. c , c Ox ,

    y = x2 + 8x y = 0 x [1, 2] .

    10. e

    z(t) = 84t 8 . 56t2 , t ( ), .

    C 8 . 26

    , 87 .

    . 61 300 2012/2013 .

  • MA , 3, 062

    1. c dx(4 5x)84 .

    2. c x2 4x 5

    x3 2x2 + xdx .

    3. c x 4x 5 2 dx .

    4. c 0

    14

    cos7x

    sin27x + 9dx

    5. c 0

    8

    (x2 5x 2) sin4x dx .

    6. c 0

    2

    cos4x sin6x dx .

    7. c cc 4

    5x 7

    x + 4dx

    .

    8. c , y =4

    x2 + 24, y =

    1

    28x2 .

    .

    9. c , c Ox ,

    y =8

    x 1, x = 6 x = 0 .

    10. e

    z(t) = 55t 6 . 15t2 , t ( ), .

    C 8 . 47

    , 51 .

    . 62 300 2012/2013 .

  • MA , 3, 063

    1. c (14x + 6) 7x2 + 6x + 58 dx .

    2. c 73(x2 x + 4)

    (x + 8)(x2 + 9)dx .

    3. c dxx2

    3 3 x.

    4. c 0

    12

    cos6x

    sin26x 25dx

    5. c 0

    12

    (x2 6x + 6) sin6x dx .

    6. c 0

    2

    cos6x sin3x dx .

    7. c cc 1

    +

    ex5 dx

    .

    8. c , y = 7x2 5x 6,

    y = 10x2 14x + 6 . .

    9. c , c Ox ,

    y = x2 5x y = 0 x [5, 6] .

    10. V(t) ,

    , 39% , . .

    t V

    V= 0 . 39t .

    , 13 ,

    , ,

    V(0) = 24 .

    . 63 300 2012/2013 .

  • MA , 3, 064

    1. c x 2x2 3 dx .

    2. c x2 + 7x + 6

    (x 2)(x2 9x + 18)dx .

    3. c 5x + 2x 1 + 1 dx .

    4. c 0

    8

    cos4x

    sin24x + 36dx

    5. c 14

    14 3

    arctg4x dx .

    6. c 0

    30

    cos25x dx .

    7. c cc

    4

    sin4x dx

    .

    8. c , x + y = 11, yx = 28 .

    .

    9. c , c Ox ,

    y = x2 + 4x y = 0 x [0, 2] .

    10. R(x), x

    MR = 3x4 660 .

    . 64 300 2012/2013 .

  • MA , 3, 065

    1. c arctg6x7

    1 + x2dx .

    2. c 5(x2 + 2x 9)

    x3 8x2 + 15xdx .

    3. c 8 + x 4

    x + 32dx .

    4. c ln2

    ln7e2x

    e4x + 4dx .

    5. c 12

    12 3

    arctg2x dx .

    6. c 0

    2

    cos5x sin3x dx .

    7. c cc 5

    3

    dx

    25 + x2

    .

    8. c , y =16

    x2 + 64, y =

    1

    80x2 .

    .

    9. c , c Ox ,

    y = x2 8x y = 0 x [ 3, 0] .10. e

    z(t) = 59t 7 . 14t2 , t ( ), .

    C 8 . 48

    , 71 .

    . 65 300 2012/2013 .

  • MA , 3, 066

    1. c arctg4x3

    1 + x2dx .

    2. c 85(x2 + x + 5)

    (x + 9)(x2 + 4)dx .

    3. c x 7 9

    x + 2dx .

    4. c 58

    34

    4 ctg22x ctg2x + 4

    sin22xdx .

    5. c 0

    4

    (x2 2x + 5) cos2x dx .

    6. c 0

    2

    cos3x sin2x dx .

    7. c cc 1

    0dx

    1 x2

    .

    8. c , y =36

    x2 + 216,

    y =1

    252x2 . .

    9. c , c Ox ,

    y = x2 6x y = 0 x [ 2, 1] .10.

    e t (t )

    V(t) = 83 + 4 cos

    3(t + 4)

    . .

    . 66 300 2012/2013 .

  • MA , 3, 067

    1. c dx8 5x .

    2. c x2 + 7x + 4

    (x + 4)(x + 5)(x + 3)dx .

    3. c 3 + x 3

    x 28dx .

    4. c e5

    e6

    5dx

    x ln25x.

    5. c 0

    8

    (x2 4x + 4) sin4x dx .

    6. c 0

    2

    cos3x cos5x dx .

    7. c cc 2

    5dx

    (x 1) ln(x 1)

    .

    8. c , y = 4x2 + x + 1,

    y = 6x2 11x 9 . .

    9. c , c Ox ,

    y = x2 1 y = 0 x [ 4, 2] .

    10. q TC(q),

    q

    MC = e5.9q, 26 .

    . 67 300 2012/2013 .

  • MA , 3, 068

    1. c x 7x2 56 dx .

    2. c 2x2 6x + 16

    2x2 x3dx .

    3. c dxx x3

    .

    4. c ln6

    ln7e2x

    e4x 49dx .

    5. c 14

    14 3

    arctg4x dx .

    6. c 0

    2

    cos6x sin4x dx .

    7. c cc

    1dx

    1 + x2

    .

    8. c , y = 8x2 5x 7,

    y = 2x2 + 7x 7 . .

    9. c , c Ox ,

    y = x2 7x y = 0 x [8, 9] .

    10. ,

    CM = 16q3 + 6q2 + 6q , 740 .

    . 68 300 2012/2013 .

  • MA , 3, 069

    1. c dx(5x + 3)39 .

    2. c 5(x2 3x + 6)

    x3 2x2 + 5xdx .

    3. c x 2 7

    x 27dx .

    4. c 0

    6

    cos3x

    sin23x + 36dx

    5. c 0

    14 3

    arctg4x dx .

    6. c 0

    24

    sin24x dx .

    7. c cc 0

    1dx

    1 x2

    .

    8. c , y = 7x2 3x 8,

    y = 6x2 + 3x 1 . .

    9. c , c Ox ,

    y = x2 6x y = 0 x [ 6, 0] .

    10. e

    z(t) = 78t 7 . 22t2 , t ( ), .

    C 8 . 20

    , 63 .

    . 69 300 2012/2013 .

  • MA , 3, 070

    1. c (4x + 3)57dx .

    2. c 5(x2 7x + 1)

    (x 1)(x2 4x + 8)dx .

    3. c x + 6 7

    x 3dx .

    4. c ln5

    ln4e2x

    4 25e4xdx .

    5. c 0

    6

    (x2 + 6x 2) cos3x dx .

    6. c 0

    2

    sin3x sin5x dx .

    7. c cc

    2

    cos x dx

    .

    8. c , y =49

    x2 + 294,

    y =1

    343x2 . .

    9. c , c Ox ,

    y = x2 + 7x y = 0 x [0, 2] .

    10. e

    z(t) = 59t 5 . 47t2 , t ( ), .

    C 8 . 18

    , 31 .

    . 70 300 2012/2013 .

  • MA , 3, 071

    1. c dx1 x2 arcsin4x

    3.

    2. c 5(x2 + 6x 4)

    x3 2x2 + 5xdx .

    3. c x 4 + 6

    x + 12dx .

    4. c e6

    e5

    6dx

    x ln6x.

    5. c 13

    3

    0

    arctg3x dx .

    6. c 0

    2

    cos5x sin6x dx .

    7. c cc

    48

    cos8x dx

    .

    8. c , y = x2 + 2x + 7,

    y = 4x 1 . .

    9. c , c Ox ,

    y = x2 1 y = 0 x [ 3, 1] .10. V(t) ,

    , 16% , . .

    t V

    V= 0 . 16t .

    , 31 ,

    , ,

    V(0) = 47 .

    . 71 300 2012/2013 .

  • MA , 3, 072

    1. c (12x + 7) 6x2 + 7x + 56 dx .

    2. c 4(x2 x + 7)

    (x 2)(x2 4x + 8)dx .

    3. c 2 x

    1 9 x34dx .

    4. c ln5

    ln6e2x

    e4x 16dx .

    5. c 0

    4

    (x2 4x + 6) sin2x dx .

    6. c 0

    36

    cos26x dx .

    7. c cc

    43

    dx

    16 + x2

    .

    8. c , y = x2 2x 3,

    y = 4x + 5 . .

    9. c , c Ox ,

    y = x2 + 7x y = 0 x [1, 2] .10.

    MC(x) = 26 4x 2x2, 76 .

    .

    . 72 300 2012/2013 .

  • MA , 3, 073

    1. c (10x 1) 5x2 x 6 dx .

    2. c 10(x2 + 3x + 7)

    x3 + 2x2 + 10xdx .

    3. c x + 7x 7 + 1 dx .

    4. c e28

    e1

    8dx

    x ln38x.

    5. c 0

    8

    (x2 + 7x 4) cos4x dx .

    6. c 0

    12

    cos24x dx .

    7. c cc

    30

    sin5x dx

    .

    8. c , y = 7x2 + 8x 6,

    y = 6x2 + 6x 6 . .

    9. c , c Ox ,

    y = x2 + 8x y = 0 x [0, 1] .

    10. ,

    : z(t) = 1 . 123t2 + 6 . 1t + 5 . 6 t

    ( ), .

    . 73 300 2012/2013 .

  • MA , 3, 074

    1. c (6x 2) 3x2 2x + 5 dx .

    2. c x2 5x 7

    (x 3)(x2 8x + 16)dx .

    3. c 8 x3

    3 x23

    dx .

    4. c 320

    15

    tg5x dx .

    5. c 0

    10

    (x2 + x 6) sin5x dx .

    6. c 0

    2

    cos5x sin3x dx .

    7. c cc

    4

    sin4x dx

    .

    8. c , yx = 21, x + y = 10 .

    .

    9. c , c Ox ,

    y =5

    x 9, x = 1 x = 7 .

    10. ()

    8 20

    f (t) = 5000 + 86t 3t2, t , 8 t 20.

    , 15 19 ,

    1 9 . .

    . 74 300 2012/2013 .

  • MA , 3, 075

    1. c dx5x 4 .

    2. c 13(x2 2x 7)

    (x + 3)(x2 + 4)dx .

    3. c 8 + x 1

    x + 3dx .

    4. c 0

    10

    sin5x

    cos25x 16dx

    5. c 0

    14

    (x2 2x + 4) cos7x dx .

    6. c 0

    15

    sin25x dx .

    7. c cc 14

    e6

    4dx

    x ln84x

    .

    8. c , y =36

    x2 + 144,

    y =1

    180x2 . .

    9. c , c Ox ,

    y = x2 3x y = 0 x [ 3, 0] .

    10. R(x), x

    MR = 4x5 630 .

    . 75 300 2012/2013 .

  • MA , 3, 076

    1. c (12x + 7) 6x2 + 7x 4 dx .

    2. c 9(x2 3x + 3)

    (x 2)(x2 4x + 13)dx .

    3. c 3x + 1x 3 + 1 dx .

    4. c 54

    32

    4 ctg3x + ctg x + 3

    sin2xdx .

    5. c 0

    12

    (x2 + 5x + 1) cos6x dx .

    6. c 0

    2

    sin5x sin4x dx .

    7. c cc 6

    15x 6 + 5

    x 6dx

    .

    8. c , y = 4x2 7x + 2,

    y = 3x2 2x 4 . .

    9. c , c Ox ,

    y =2

    x + 8, x = 6 x = 4 .

    10. ()

    8 20

    f (t) = 3000 + 96t 3t2, t , 8 t 20.

    , 11 14 ,

    1 6 . .

    . 76 300 2012/2013 .

  • MA , 3, 077

    1. c dx(5 + 4x)88 .

    2. c x2 + 7x 1

    (x + 5)(x2 + 11x + 30)dx .

    3. c x 1x 3 + 2 dx .

    4. c 14

    13

    2 tg23x + 5 tg3x + 3

    cos23xdx .

    5. c 12 3

    12

    arctg2x dx .

    6. c 0

    10

    sin25x dx .

    7. c cc e53

    e2

    3dx

    x5 + ln3x8

    .

    8. c , y = 6x2 + 2x + 1,

    y = 7x2 3x 5 . .

    9. c , c Ox ,

    y =4

    x + 7, x = 2 x = 4 .

    10. ,

    CM = 24q5 + 15q4 + 8q , 410 .

    . 77 300 2012/2013 .

  • MA , 3, 078

    1. c arcsin x1 x2

    dx .

    2. c 5(x2 + 4x 8)

    (x + 5)(x2 + 12x + 40)dx .

    3. c 1 6xx 2 + 1 dx .

    4. c 0

    12

    cos6x

    sin26x 4dx

    5. c 1

    0

    arctg x dx .

    6. c 0

    2

    cos6x cos2x dx .

    7. c cc 6

    3dx

    (x + 7) ln(x + 7)

    .

    8. c , x + y = 16, yx = 63 .

    .

    9. c , c Ox ,

    y = x2 + 6x y = 0 x [0, 1] .

    10. q TC(q),

    q

    MC = e4.7q, 95 .

    . 78 300 2012/2013 .

  • MA , 3, 079

    1. c dx(3x 1)97 .

    2. c 13(x2 3x 2)

    (x 5)(x2 4x + 8)dx .

    3. c x + 3 + 1

    3 x + 3dx .

    4. c 17

    328

    4 tg37x + 4 tg27x 1

    cos27xdx .

    5. c 0

    13

    3

    arctg3x dx .

    6. c 0

    2

    cos3x sin4x dx .

    7. c cc

    e8xdx

    .

    8. c , x + y = 7, yx = 10 .

    .

    9. c , c Ox ,

    y =1

    x + 8, x = 2 x = 9 .

    10. R(x), x

    MR = 7x6 750 .

    . 79 300 2012/2013 .

  • MA , 3, 080

    1. c dx5 2x .

    2. c 3x2 9x 15

    (x 1)(x2 5x + 4)dx .

    3. c x3

    7 x23

    dx .

    4. c e2

    e2

    2dx

    x ln72x.

    5. c 0

    8

    (x2 + 3x 4) sin4x dx .

    6. c 0

    36

    cos26x dx .

    7. c cc 1

    3x + 1

    3 xdx

    .

    8. c , y = x2 6x 6,

    y = x2 + 2x + 4 . .

    9. c , c Ox ,

    y = x2 + 4x y = 0 x [0, 1] .10. q TC(q),

    q

    MC = e1.2q, 48 .

    . 80 300 2012/2013 .

  • MA , 3, 081

    1. c (8x 1) 4x2 x + 47 dx .

    2. c 17(x2 x + 3)

    x3 + 2x2 + 17xdx .

    3. c x + 7 7

    x + 32dx .

    4. c ln4

    ln7e2x

    e4x 25dx .

    5. c 12

    0

    arctg2x dx .

    6. c 0

    2

    cos4x sin3x dx .

    7. c cc 12

    sin2x dx

    .

    8. c , y = x2 + 5x 23,

    y = 4x 3 . .

    9. c , c Ox ,

    y =5

    x 5, x = 8 x = 0 .

    10. V(t) ,

    , 34% , . .

    t V

    V= 0 . 34t .

    , 13 ,

    , ,

    V(0) = 25 .

    . 81 300 2012/2013 .

  • MA , 3, 082

    1. c dx3x 5 .

    2. c 9(x2 + 4x + 6)

    (x + 1)(x2 + 2x + 10)dx .

    3. c 6 + x 1

    x 1 + 1dx .

    4. c ln5

    ln4e2x

    9 16e4xdx .

    5. c 12

    0

    arctg2x dx .

    6. c 0

    24

    sin26x dx .

    7. c cc 7

    2x 5 + 6 2 x

    2 xdx

    .

    8. c , y = x2 + 3x + 8,

    y = 2x2 + 5x + 8 . .

    9. c , c Ox ,

    y = x2 36 y = 0 x [6, 7] .10.

    MC(x) = 82 x x2, 13 .

    .

    . 82 300 2012/2013 .

  • MA , 3, 083

    1. c (3 + 4x)84dx .

    2. c 10(x2 + 3x + 6)

    (x + 3)(x2 + 4x + 13)dx .

    3. c x 4x + 2 1 dx .

    4. c ln2

    ln3e2x

    e4x + 20dx .

    5. c 0

    8

    (x2 5x 4) sin4x dx .

    6. c 0

    2

    cos6x sin7x dx .

    7. c cc

    25

    85x+1 dx

    .

    8. c , yx = 63, x + y = 16 .

    .

    9. c , c Ox ,

    y = x2 + 4x y = 0 x [0, 2] .

    10. ,

    CM = 10q4 + 12q3 + 9q2, 970 .

    . 83 300 2012/2013 .

  • MA , 3, 084

    1. c dx6 7x .

    2. c 20(x2 3x + 6)

    (x 4)(x2 4x + 20)dx .

    3. c x 1x + 2 + 2 dx .

    4. c 0

    6

    cos3x

    sin23x + 16dx

    5. c 13 3

    13

    arctg3x dx .

    6. c 0

    2

    cos3x sin5x dx .

    7. c cc

    6

    ex dx

    .

    8. c , yx = 14, x + y = 9 .

    .

    9. c , c Ox ,

    y = x2 9 y = 0 x [ 5, 4] .

    10. R(x), x

    MR = 5x 700 .

    . 84 300 2012/2013 .

  • MA , 3, 085

    1. c arctg x3

    1 + x2dx .

    2. c 8(x2 5x 5)

    (x 5)(x2 14x + 53)dx .

    3. c 7 + 2xx 4 + 1 dx .

    4. c ln4

    ln7e2x

    e4x 36dx .

    5. c 12

    12 3

    arctg2x dx .

    6. c 0

    15

    sin25x dx .

    7. c cc 0

    dx

    81 + x2

    .

    8. c , yx = 12, x + y = 7 .

    .

    9. c , c Ox ,

    y = x2 1 y = 0 x [ 3, 2] .

    10. q TC(q),

    q

    MC = e8.4q, 47 .

    . 85 300 2012/2013 .

  • MA , 3, 086

    1. c dx4 7x .

    2. c 5(x2 + 4x 4)

    (x + 4)(x2 + 10x + 29)dx .

    3. c x + 8 8

    x + 33dx .

    4. c 128

    121

    tg7x dx .

    5. c 1

    2 3

    12

    arctg2x dx .

    6. c 0

    2

    cos7x sin4x dx .

    7. c cc 12

    1dx

    1 x2

    .

    8. c , y = 5x2 + 2x + 6,

    y = 3x2 6x 4 . .

    9. c , c Ox ,

    y = x2 + 4x y = 0 x [0, 1] .10. e

    z(t) = 84t 7 . 67t2 , t ( ), .

    C 7 . 86

    , 38 .

    . 86 300 2012/2013 .

  • MA , 3, 087

    1. c dx(2x 3)78 .

    2. c 10(x2 5x + 1)

    x3 2x2 + 10xdx .

    3. c 6 + x 6

    x + 30dx .

    4. c e38

    e2

    8dx

    x ln28x.

    5. c 13

    13 3

    arctg3x dx .

    6. c 0

    2

    cos6x sin5x dx .

    7. c cc 2

    3dx

    (x 1) ln(x 1)

    .

    8. c , y =4

    x2 + 8, y =

    1

    12x2 .

    .

    9. c , c Ox ,

    y =1

    x + 7, x = 0 x = 1 .

    10. e

    z(t) = 55t 7 . 55t2 , t ( ), .

    C 7 . 76

    , 61 .

    . 87 300 2012/2013 .

  • MA , 3, 088

    1. c dx4 2x .

    2. c 2x2 6x + 4

    2x2 x3dx .

    3. c dxx 3 x3

    .

    4. c ln5

    ln6e2x

    e4x 36dx .

    5. c 0

    8

    (x2 + x 1) cos4x dx .

    6. c 0

    15

    cos25x dx .

    7. c cc

    0

    cos5x dx

    .

    8. c , y = x2 x + 15,

    y = 2x + 5 . .

    9. c , c Ox ,

    y =5

    x 5, x = 6 x = 1 .

    10. ,

    : z(t) = 1 . 067t2 + 5 . 5t + 6 . 3 t

    ( ), .

    . 88 300 2012/2013 .

  • MA , 3, 089

    1. c (8x 7) 4x2 7x + 578 dx .

    2. c x2 + 7x + 5

    (x + 5)(x2 + 8x + 16)dx .

    3. c 8 3xx + 3 + 1 dx .

    4. c 0

    8

    cos4x

    sin24x + 9dx

    5. c 12

    12 3

    arctg2x dx .

    6. c 0

    2

    cos5x cos6x dx .

    7. c cc

    43

    e3x+3 dx

    .

    8. c , y = 2x2 6x + 1,

    y = x2 3x + 1 . .

    9. c , c Ox ,

    y = x2 16 y = 0 x [ 6, 5] .

    10. V(t) ,

    , 0 . 26, . .

    t V

    V= 0 . 26t .

    12 , , V(0) = 41 .

    . 89 300 2012/2013 .

  • MA , 3, 090

    1. c (14x + 6) 7x2 + 6x 718 dx .

    2. c x2 x + 6

    x2 x3dx .

    3. c 7 x + 8

    x + 8 + 2dx .

    4. c 0

    6

    cos3x

    sin23x 25dx

    5. c 0

    12

    (x2 4x 5) cos6x dx .

    6. c 0

    18

    sin23x dx .

    7. c cc 2

    6x 5

    6 xdx

    .

    8. c , y = x2 + 3x 3,

    y = 2x + 3 . .

    9. c , c Ox ,

    y = x2 4 y = 0 x [ 4, 3] .

    10. R(x), x

    MR = x6 770 .

    . 90 300 2012/2013 .

  • MA , 3, 091

    1. c dx3x 2 .

    2. c 3x2 + 9x + 24

    (x + 4)(x2 + 5x + 4)dx .

    3. c 5 xx + 2 2 dx .

    4. c ln3

    ln6e2x

    e4x 36dx .

    5. c 0

    14

    (x2 3x + 2) cos7x dx .

    6. c 0

    4

    cos22x dx .

    7. c cc e76

    e6

    6dx

    x (7 + ln6x)5

    .

    8. c , y = 8x2 + 4x,

    y = 7x2 + 5x . .

    9. c , c Ox ,

    y =9

    x + 8, x = 6 x = 9 .

    10. V(t) ,

    , 27% , . .

    t V

    V= 0 . 27t .

    , 22 a,

    , ,

    V(0) = 18 .

    . 91 300 2012/2013 .

  • MA , 3, 092

    1. c dx1 6x .

    2. c x2 + 5x 5

    (x + 3)(x2 + 4x + 4)dx .

    3. c 3x 7x + 4 + 1 dx .

    4. c 0

    6

    sin3x

    cos23x 9dx

    5. c 13

    13 3

    arctg3x dx .

    6. c 0

    6

    sin22x dx .

    7. c cc

    sin7x dx

    .

    8. c , y =49

    x2 + 196,

    y =1

    245x2 . .

    9. c , c Ox ,

    y = x2 + 5x y = 0 x [0, 4] .10. R(x), x

    MR = 7x4 410 .

    . 92 300 2012/2013 .

  • MA , 3, 093

    1. c dx1 x2 arcsin x6

    .

    2. c 20(x2 + 3x + 1)

    (x 4)(x2 + 4)dx .

    3. c x + 7 + 2

    x + 16dx .

    4. c 0

    6

    sin3x

    cos23x 16dx

    5. c 1

    13

    arctg x dx .

    6. c 0

    9

    sin23x dx .

    7. c cc 15

    +

    35x3 dx

    .

    8. c , yx = 20, x + y = 9 .

    .

    9. c , c Ox ,

    y = x2 3x y = 0 x [4, 5] .

    10. K(t),

    ( , )

    I(t) = 880 t74 , K(0) = 650 .

    . 93 300 2012/2013 .

  • MA , 3, 094

    1. c (5 2x)33dx .

    2. c 2x2 + 14x + 10

    2x2 x3dx .

    3. c 2 + x + 6

    x + 31dx .

    4. c 0

    6

    sin3x

    cos23x + 16dx

    5. c 0

    1

    arctg x dx .

    6. c 0

    24

    cos24x dx .

    7. c cc 13

    +

    33x+2 dx

    .

    8. c , y =16

    x2 + 80, y =

    1

    96x2 .

    .

    9. c , c Ox ,

    y =5

    x 6, x = 7 x = 5 .

    10. ,

    CM = 24q5 + 8q3 + 9q2, 430 .

    . 94 300 2012/2013 .

  • MA , 3, 095

    1. c (5x + 2)92dx .

    2. c 4(x2 3x + 8)

    x3 12x2 + 32xdx .

    3. c 2 + xx 1 + 1 dx .

    4. c 0

    14

    cos7x

    sin27x + 25dx

    5. c 0

    10

    (x2 4x 6) cos5x dx .

    6. c 0

    21

    cos27x dx .

    7. c cc 12

    cos2x dx

    .

    8. c , x + y = 3, yx = 2 .

    .

    9. c , c Ox ,

    y = x2 4x y = 0 x [ 1, 0] .10. V(t) ,

    , 0 . 24, . .

    t V

    V= 0 . 24t .

    12 , , V(0) = 26 .

    . 95 300 2012/2013 .

  • MA , 3, 096

    1. c (4x 5) 2x2 5x 487 dx .

    2. c x2 x + 6

    (x 3)(x 6)(x 5)dx .

    3. c x + 8 4

    x + 17dx .

    4. c 116

    03 tg24x + 4 tg4x 1

    cos24xdx .

    5. c 0

    6

    (x2 + 7x + 1) cos3x dx .

    6. c 0

    18

    sin26x dx .

    7. c cc 0

    3dx

    (x + 1) ln(x + 1)

    .

    8. c , y = x2 + x 8,

    y = 5x 3 . .

    9. c , c Ox ,

    y = x2 5x y = 0 x [ 2, 1] .10.

    MC(x) = 21 8x 3x2, 64 .

    .

    . 96 300 2012/2013 .

  • MA , 3, 097

    1. c dx(3 + 5x)70 .

    2. c x2 + 5x + 8

    (x + 6)(x2 + 10x + 25)dx .

    3. c 8 xx + 9 + 1 dx .

    4. c 18

    0tg32x 2 tg22x + 4

    cos22xdx .

    5. c 0

    8

    (x2 + 6x 4) sin4x dx .

    6. c 0

    2

    cos2x sin5x dx .

    7. c cc 1

    12

    dx

    1 x2

    .

    8. c , y = x2 10x,

    y = x2 + 4x . .

    9. c , c Ox ,

    y =3

    x + 5, x = 4 x = 7 .

    10. q TC(q),

    q

    MC = e2.9q, 92 .

    . 97 300 2012/2013 .

  • MA , 3, 098

    1. c dx7 6x .

    2. c 3x2 + 6x 12

    (x + 1)(x2 4x + 4)dx .

    3. c 6 + x 9

    x 9 + 4dx .

    4. c 0

    4

    cos2x

    sin22x + 9dx

    5. c 12

    12 3

    arctg2x dx .

    6. c 0

    12

    cos23x dx .

    7. c cc 1

    12

    dx

    1 x2

    .

    8. c , yx = 30, x + y = 11 .

    .

    9. c , c Ox ,

    y = x2 + x y = 0 x [ 5, 4] .

    10.

    e t (t )

    V(t) = 92 + 5 sin

    4(t + 7)

    . .

    . 98 300 2012/2013 .

  • MA , 3, 099

    1. c (8x 7) 4x2 7x 3 dx .

    2. c 45(x2 + 2x + 8)

    (x 6)(x2 + 9)dx .

    3. c dxx 3 x3

    .

    4. c 0

    12

    cos6x

    sin26x 9dx

    5. c 0

    4

    (x2 + 7x + 7) sin2x dx .

    6. c 0

    18

    sin26x dx .

    7. c cc 1

    12

    dx

    1 x2

    .

    8. c , y =36

    x2 + 180,

    y =1

    216x2 . .

    9. c , c Ox ,

    y =7

    x + 8, x = 8 x = 9 .

    10. q TC(q),

    q

    MC = e1.4q, 65 .

    . 99 300 2012/2013 .

  • MA , 3, 100

    1. c dx1 7x .

    2. c 15(x2 + 4x 1)

    (x 2)(x + 1)(x + 3)dx .

    3. c 4 + 3xx 2 + 1 dx .

    4. c 16

    112

    ctg33x + 4 ctg3x + 3

    sin23xdx .

    5. c 12 3

    0

    arctg2x dx .

    6. c 0

    20

    sin25x dx .

    7. c cc 4

    683 7 x 4

    x 4dx

    .

    8. c , y = x2 8x 14,

    y = x 4 . .

    9. c , c Ox ,

    y =9

    x 3, x = 5 x = 2 .

    10. q TC(q),

    q

    MC = e0.4q, 81 .

    . 100 300 2012/2013 .

  • MA , 3, 101

    1. c x dx6x

    2 + 535

    2. c 5(x2 8x + 3)

    (x 2)(x2 2x + 5)dx .

    3. c 7x 3x 1 1 dx .

    4. c 18

    112

    ctg36x + 4 ctg26x 2

    sin26xdx .

    5. c 0

    6

    (x2 + x 4) sin3x dx .

    6. c 0

    16

    sin24x dx .

    7. c cc e73

    e7

    3dx

    x7 + ln3x

    .

    8. c , yx = 3, x + y = 4 .

    .

    9. c , c Ox ,

    y =6

    x + 1, x = 6 x = 5 .

    10. R(x), x

    MR = 2x 210 .

    . 101 300 2012/2013 .

  • MA , 3, 102

    1. c (5 + x)43dx .

    2. c 4(x2 + 6x 5)

    (x + 6)(x2 + 12x + 40)dx .

    3. c 4 + x 7

    x + 18dx .

    4. c ln2

    ln6e2x

    e4x + 4dx .

    5. c 1

    0

    arctg x dx .

    6. c 0

    2

    sin3x sin7x dx .

    7. c cc 0

    e2xdx

    .

    8. c , x + y = 7, yx = 10 .

    .

    9. c , c Ox ,

    y =4

    x + 5, x = 3 x = 4 .

    10. V(t) ,

    , 13% , . .

    t V

    V= 0 . 13t .

    11 , , V(0) = 44 .

    . 102 300 2012/2013 .

  • MA , 3, 103

    1. c 14x + 47x2 + 4x + 7

    dx .

    2. c x2 + 6x + 8

    (x 2)(x 1)(x 4)dx .

    3. c x 1x + 1 1 dx .

    4. c 0

    8

    cos4x

    sin24x + 9dx

    5. c 0

    12

    (x2 5x 5) sin6x dx .

    6. c 0

    2

    cos3x sin6x dx .

    7. c cc 7

    8x 5 + 4 8 x

    8 xdx

    .

    8. c , y =16

    x2 + 96,

    y =1

    112x2 . .

    9. c , c Ox ,

    y = x2 4x y = 0 x [5, 6] .10. q TC(q),

    q

    MC = e0.8q, 37 .

    . 103 300 2012/2013 .

  • MA , 3, 104

    1. c (x + 4)36dx .

    2. c x2 + 7x 4

    x3 + x2dx .

    3. c 8 xx + 6 + 1 dx .

    4. c 38

    14

    3 ctg22x + ctg2x + 2

    sin22xdx .

    5. c 0

    4

    (x2 2x 6) cos2x dx .

    6. c 0

    24

    cos26x dx .

    7. c cc

    sin7x dx

    .

    8. c , y = x2 + 4x 5,

    y = 3x + 1 . .

    9. c , c Ox ,

    y = x2 + 7x y = 0 x [0, 3] .10.

    MC(x) = 54 5x 4x2, 68 .

    .

    . 104 300 2012/2013 .

  • MA , 3, 105

    1. c dx1 x2 arcsin x4

    .

    2. c 13(x2 + 4x + 5)

    (x + 3)(x2 + 4)dx .

    3. c x 2 + 1

    x 18dx .

    4. c 15

    14

    tg35x tg25x 2

    cos25xdx .

    5. c 0

    6

    (x2 + x + 4) cos3x dx .

    6. c 0

    12

    sin26x dx .

    7. c cc 12

    cos2x dx

    .

    8. c , y =25

    x2 + 125,

    y =1

    150x2 . .

    9. c , c Ox ,

    y =1

    x + 8, x = 2 x = 3 .

    10.

    MC(x) = 73 8x 2x2, 77 .

    .

    . 105 300 2012/2013 .

  • MA , 3, 106

    1. c dx1 5x .

    2. c 5(x2 3x 6)

    (x 2)(x2 6x + 13)dx .

    3. c 6 x + 3

    x + 3 + 4dx .

    4. c ln3

    ln4e3x

    e6x 4dx .

    5. c 0

    6

    (x2 5x 2) sin3x dx .

    6. c 0

    2

    cos5x sin6x dx .

    7. c cc 17

    e8

    7dx

    x ln97x

    .

    8. c , y = 2x2 9x + 14,

    y = 3x2 2x + 6 . .

    9. c , c Ox ,

    y = x2 9 y = 0 x [ 5, 4] .

    10. ,

    CM = 20q4 + 8q3 + 9q2, 160 .

    . 106 300 2012/2013 .

  • MA , 3, 107

    1. c 6x + 43x

    2 + 4x 66dx .

    2. c 5(x2 + x 5)

    (x 2)(x2 6x + 13)dx .

    3. c 7 + x + 8

    x 1dx .

    4. c 0

    12

    cos6x

    sin26x + 9dx

    5. c 1

    4 3

    14

    arctg4x dx .

    6. c 0

    2

    sin3x sin4x dx .

    7. c cc 5

    sin5x dx

    .

    8. c , yx = 72, x + y = 17 .

    .

    9. c , c Ox ,

    y = x2 + 3x y = 0 x [0, 1] .10. V(t) ,

    , 19% , . .

    t V

    V= 0 . 19t .

    , 31 ,

    , ,

    V(0) = 68 .

    . 107 300 2012/2013 .

  • MA , 3, 108

    1. c 14x + 67x2 + 6x + 1

    dx .

    2. c 6(x2 7x 5)

    x3 + 4x2 5xdx .

    3. c x + 2 + 4

    x + 6dx .

    4. c 0

    8

    cos4x

    sin24x + 4dx

    5. c 0

    4

    (x2 4x + 7) sin2x dx .

    6. c 0

    2

    sin4x sin7x dx .

    7. c cc 8

    dx

    64 + x2

    .

    8. c , yx = 9, x + y = 10 .

    .

    9. c , c Ox ,

    y =9

    x + 2, x = 1 x = 3 .

    10. R(x), x

    MR = 7x3 170 .

    . 108 300 2012/2013 .

  • MA , 3, 109

    1. c x dx7x2 + 4

    .

    2. c 6(x2 2x + 6)

    x3 9xdx .

    3. c dxx2

    3 + 5 x.

    4. c 221

    542

    tg7x dx .

    5. c 0

    3

    arctg x dx .

    6. c 0

    18

    cos26x dx .

    7. c cc 9

    73 7 x 2

    7 xdx

    .

    8. c , yx = 12, x + y = 7 .

    .

    9. c , c Ox ,

    y = x2 1 y = 0 x [2, 3] .10. ,

    CM = 18q5 + 6q2 + 6q , 460 .

    . 109 300 2012/2013 .

  • MA , 3, 110

    1. c dx7x 6 .

    2. c 2(x2 8x + 5)

    x3 3x2 + 2xdx .

    3. c 7 x + 9

    x + 9 + 9dx .

    4. c 19

    118

    ctg3x dx .

    5. c 0

    4

    (x2 7x 7) cos2x dx .

    6. c 0

    12

    cos22x dx .

    7. c cc

    48

    cos8x dx

    .

    8. c , y = x2 3x, y = 2x 4 .

    .

    9. c , c Ox ,

    y =3

    x 6, x = 7 x = 1 .

    10. q TC(q),

    q

    MC = e0.8q, 51 .

    . 110 300 2012/2013 .

  • MA , 3, 111

    1. c dx1 4x .

    2. c 15(x2 + 5x + 2)

    (x + 7)(x + 2)(x 1)dx .

    3. c x + 4x 6 + 1 dx .

    4. c ln3

    ln4e2x

    e4x 77dx .

    5. c 13

    13 3

    arctg3x dx .

    6. c 0

    2

    sin4x sin6x dx .

    7. c cc 8

    7x 5

    x + 8dx

    .

    8. c , x + y = 4, yx = 3 .

    .

    9. c , c Ox ,

    y = x2 + x y = 0 x [ 3, 2] .

    10.

    MC(x) = 28 4x 6x2, 38 .

    .

    . 111 300 2012/2013 .

  • MA , 3, 112

    1. c dx(x + 4)41 .

    2. c 13(x2 5x + 9)

    (x 3)(x2 + 4)dx .

    3. c x 2 + 9

    x + 14dx .

    4. c 0

    12

    sin6x

    cos26x 25dx

    5. c 0

    12

    (x2 x 3) cos6x dx .

    6. c 0

    12

    cos26x dx .

    7. c cc 9 3

    dx

    81 + x2

    .

    8. c , yx = 10, x + y = 7 .

    .

    9. c , c Ox ,

    y =5

    x + 1, x = 6 x = 8 .

    10. R(x), x

    MR = 5x6 780 .

    . 112 300 2012/2013 .

  • MA , 3, 113

    1. c dx(3x + 1)77 .

    2. c 5(x2 7x + 6)

    (x 2)(x2 6x + 13)dx .

    3. c 7 + x + 8

    x 8dx .

    4. c ln3

    ln5e2x

    e4x 16dx .

    5. c 14

    14

    3

    arctg4x dx .

    6. c 0

    42

    sin27x dx .

    7. c cc

    4

    sin2x dx

    .

    8. c , x + y = 7, yx = 10 .

    .

    9. c , c Ox ,

    y = x2 + 3x y = 0 x [0, 3] .

    10. ,

    CM = 24q5 + 10q4 + 9q2, 840 .

    . 113 300 2012/2013 .

  • MA , 3, 114

    1. c dx(4 + x)22 .

    2. c 13(x2 5x 4)

    (x + 3)(x2 + 4)dx .

    3. c 2x 7x + 7 + 1 dx .

    4. c 0

    6

    sin3x

    cos23x 25dx

    5. c 13

    0

    arctg3x dx .

    6. c 0

    42

    sin27x dx .

    7. c cc

    10

    sin5x dx

    .

    8. c , y = x2 + 2x + 7,

    y = 2x + 4 . .

    9. c , c Ox ,

    y =2

    x 1, x = 5 x = 0 .

    10. q TC(q),

    q

    MC = e5.2q, 74 .

    . 114 300 2012/2013 .

  • MA , 3, 115

    1. c x 5x2 + 7 dx .

    2. c 15(x2 + 4x 9)

    (x + 5)(x2 x 6)dx .

    3. c x + 5 3

    x 20dx .

    4. c 514

    1128

    2 ctg37x ctg27x 5

    sin27xdx .

    5. c 0

    10

    (x2 + 2x + 1) sin5x dx .

    6. c 0

    12

    cos24x dx .

    7. c cc 1

    0dx

    1 x2

    .

    8. c , y = 10x2 12x 3,

    y = 7x2 3x + 3 . .

    9. c , c Ox ,

    y =9

    x 9, x = 3 x = 1 .

    10. K(t),

    ( , )

    I(t) = 300 t78 , K(0) = 380 .

    . 115 300 2012/2013 .

  • MA , 3, 116

    1. c (8x + 5) 4x2 + 5x + 46 dx .

    2. c x2 + 4x 2

    (x + 8)(x2 + 13x + 42)dx .

    3. c x 3 + 2

    x 19dx .

    4. c 720

    310

    ctg35x + ctg25x 1

    sin25xdx .

    5. c 0

    6

    (x2 + 6x 7) cos3x dx .

    6. c 0

    12

    sin24x dx .

    7. c cc 0

    dx

    1 + x2

    .

    8. c , y = 4x2 + 4x + 3,

    y = 2x2 + 12x + 13 . .

    9. c , c Ox ,

    y = x2 + 7x y = 0 x [0, 2] .

    10.

    e t (t )

    V(t) = 23 + 8 cos

    3(t + 4)

    . .

    . 116 300 2012/2013 .

  • MA , 3, 117

    1. c 6x 53x

    2 5x + 47dx .

    2. c 12(x2 6x + 5)

    x3 + x2 20xdx .

    3. c x + 1 3

    2 x + 1dx .

    4. c 320

    120

    5 ctg25x 4 ctg5x + 4

    sin25xdx .

    5. c 0

    12 3

    arctg2x dx .

    6. c 0

    8

    sin22x dx .

    7. c cc 0

    4x 3

    4 xdx

    .

    8. c , y = 5x2 + 7x + 12,

    y = 2x2 + 7x + 5 . .

    9. c , c Ox ,

    y = x2 + 5x y = 0 x [ 6, 5] .10. V(t) ,

    , 28% , . .

    t V

    V= 0 . 28t .

    , 22 a,

    , ,

    V(0) = 30 .

    . 117 300 2012/2013 .

  • MA , 3, 118

    1. c (12x + 5) 6x2 + 5x + 58 dx .

    2. c x2 9x + 4

    x3 + 3x2 + 2xdx .

    3. c 1 + x 3

    x 3 + 5dx .

    4. c e2

    e2

    2dx

    x ln82x.

    5. c 0

    12

    (x2 x + 6) sin6x dx .

    6. c 0

    2

    cos2x cos3x dx .

    7. c cc e32

    e5

    2dx

    x 3 + ln2x

    .

    8. c , y = 6x2,

    y = 7x2 + 8x + 6 . .

    9. c , c Ox ,

    y = x2 36 y = 0 x [6, 7] .10. q TC(q),

    q

    MC = e9.8q, 12 .

    . 118 300 2012/2013 .

  • MA , 3, 119

    1. c 6x + 43x

    2 + 4x 494

    dx .

    2. c x2 + 8x + 4

    x3 x2dx .

    3. c x 5x + 1 + 3 dx .

    4. c e37

    e5

    7dx

    x ln7x.

    5. c 0

    13

    arctg3x dx .

    6. c 0

    6

    sin22x dx .

    7. c cc 1

    0dx

    1 x2

    .

    8. c , y = 5x2 + 4x + 6,

    y = 4x2 + 3x + 4 . .

    9. c , c Ox ,

    y =6

    x + 7, x = 2 x = 4 .

    10. K(t),

    ( , )

    I(t) = 550 t38 , K(0) = 860 .

    . 119 300 2012/2013 .

  • MA , 3, 120

    1. c x 6x2 + 723 dx .

    2. c 85(x2 + x + 2)

    (x + 9)(x2 + 4)dx .

    3. c 4 xx + 5 2 dx .

    4. c 0

    8

    cos4x

    sin24x + 36dx

    5. c 12 3

    0

    arctg2x dx .

    6. c 0

    12

    cos23x dx .

    7. c cc 3

    676 7 x 3

    x 3dx

    .

    8. c , y = x2 + 2x 5,

    y = x 1 . .

    9. c , c Ox ,

    y = x2 x y = 0 x [4, 5] .

    10.

    e t (t )

    V(t) = 38 + 4 sin

    3(t + 4)

    . .

    . 120 300 2012/2013 .

  • MA , 3, 121

    1. c arcsin9x

    1 x2dx .

    2. c 10(x2 + 2x + 4)

    (x 1)(x2 + 9)dx .

    3. c x + 2 + 8

    x 23dx .

    4. c ln2

    ln5e2x

    e4x 9dx .

    5. c 0

    13

    arctg x dx .

    6. c 0

    2

    cos7x cos6x dx .

    7. c cc 0

    dx

    1 + x2

    .

    8. c , y = 8x2 + 3x 3,

    y = 10x2 + 7x + 3 . .

    9. c , c Ox ,

    y = x2 4 y = 0 x [ 3, 2] .

    10.

    e t (t )

    V(t) = 74 + 5 sin

    6(t + 9)

    . .

    . 121 300 2012/2013 .

  • MA , 3, 122

    1. c 6x 23x2 2x 5

    dx .

    2. c 5(x2 6x 6)

    (x + 1)(x2 + 4)dx .

    3. c x + 6 + 9

    x + 2dx .

    4. c 0

    12

    sin6x

    cos26x + 49dx

    5. c 0

    4

    (x2 6x 6) sin2x dx .

    6. c 0

    2

    cos4x sin3x dx .

    7. c cc

    48

    sin8x dx

    .

    8. c , y = x2 7,

    y = 5x 1 . .

    9. c , c Ox ,

    y =4

    x 3, x = 6 x = 9 .

    10. V(t) ,

    , 06% , . .

    t V

    V= 0 . 06t .

    , 20 ,

    , ,

    V(0) = 45 .

    . 122 300 2012/2013 .

  • MA , 3, 123

    1. c dx6x 2 .

    2. c 4(x2 + 3x + 4)

    (x 2)(x2 4x + 8)dx .

    3. c x + 8 2

    x + 24dx .

    4. c 34

    78

    5 ctg32x + 2 ctg2x + 3

    sin22xdx .

    5. c 13 3

    0

    arctg3x dx .

    6. c 0

    15

    cos25x dx .

    7. c cc 8

    sin4x dx

    .

    8. c , x + y = 11, yx = 30 .

    .

    9. c , c Ox ,

    y =4

    x + 8, x = 4 x = 6 .

    10. q TC(q),

    q

    MC = e0.2q, 52 .

    . 123 300 2012/2013 .

  • MA , 3, 124

    1. c 10x 45x

    2 4x 516

    dx .

    2. c x2 5x 2

    x3 xdx .

    3. c 9 x3

    5 8 x23

    dx .

    4. c ln4

    ln3e2x

    9 25e4xdx .

    5. c 0

    14

    3

    arctg4x dx .

    6. c 0

    2

    cos3x sin6x dx .

    7. c cc 0

    1x 6

    1 xdx

    .

    8. c , y =4

    x2 + 4, y =

    1

    8x2 .

    .

    9. c , c Ox ,

    y = x2 1 y = 0 x [ 3, 1] .10. ,

    CM = 20q4 + 9q2 + 8q , 670 .

    . 124 300 2012/2013 .

  • MA , 3, 125

    1. c (6x 4) 3x2 4x 56 dx .

    2. c 6(x2 + 5x 2)

    (x + 7)(x2 4x 5)dx .

    3. c 5 + x 3

    x 28dx .

    4. c 0

    8

    sin4x

    cos24x 4dx

    5. c 13

    3

    13

    arctg3x dx .

    6. c 0

    4

    sin22x dx .

    7. c cc

    24

    sin4x dx

    .

    8. c , y = 4x2 + 10x 1,

    y = 3x2 + 3x 1 . .

    9. c , c Ox ,

    y = x2 x y = 0 x [ 3, 2] .

    10.

    MC(x) = 13 4x 3x2, 96 .

    .

    . 125 300 2012/2013 .

  • MA , 3, 126

    1. c dx(3x + 2)89 .

    2. c 2x2 + 12x + 2

    (x + 1)(x2 + 6x + 9)dx .

    3. c 9 x

    7 2 x34

    dx .

    4. c 58

    1116

    ctg34x + 3 ctg4x + 2

    sin24xdx .

    5. c 0

    8

    (x2 + 4x 1) sin4x dx .

    6. c 0

    2

    sin3x sin6x dx .

    7. c cc 0

    cos2x dx

    .

    8. c , yx = 8, x + y = 9 .

    .

    9. c , c Ox ,

    y = x2 8x y = 0 x [ 2, 1] .

    10. V(t) ,

    , 44% , . .

    t V

    V= 0 . 44t .

    , 14 ,

    , ,

    V(0) = 88 .

    . 126 300 2012/2013 .

  • MA , 3, 127

    1. c dx(3x 5)32 .

    2. c 13(x2 + x + 5)

    x3 4x2 + 13xdx .

    3. c 1 x + 1

    x + 1 + 4dx .

    4. c 58

    34

    ctg32x 3 ctg22x 3

    sin22xdx .

    5. c 0

    8

    (x2 + 2x 1) sin4x dx .

    6. c 0

    2

    cos3x cos4x dx .

    7. c cc 3

    4dx

    (x 2) ln(x 2)

    .

    8. c , y = x2 + 6x + 8,

    y = x 4 . .

    9. c , c Ox ,

    y =9

    x + 3, x = 0 x = 4 .

    10. e

    z(t) = 65t 7 . 74t2 , t ( ), .

    C 7 . 13

    , 92 .

    . 127 300 2012/2013 .

  • MA , 3, 128

    1. c dx4 8x .

    2. c 45(x2 + x + 5)

    (x + 6)(x2 + 9)dx .

    3. c dxx2

    3 + x.

    4. c 516

    38

    3 ctg34x 3 ctg4x + 4

    sin24xdx .

    5. c 13

    3

    0

    arctg3x dx .

    6. c 0

    15

    cos25x dx .

    7. c cc 1

    dx

    1 + x2

    .

    8. c , x + y = 7, yx = 10 .

    .

    9. c , c Ox ,

    y = x2 + 5x y = 0 x [0, 1] .

    10. K(t),

    ( , )

    I(t) = 80(t 1)78 , ( t = 1)

    560 .

    . 128 300 2012/2013 .

  • MA , 3, 129

    1. c (x + 4)55dx .

    2. c 2(x2 + 6x + 4)

    x3 xdx .

    3. c x 7 + 2

    6 + x 7dx .

    4. c ln2

    ln3e3x

    e6x 36dx .

    5. c 1

    3

    arctg x dx .

    6. c 0

    2

    sin7x sin5x dx .

    7. c cc 1

    1dx

    1 x2

    .

    8. c , yx = 15, x + y = 8 .

    .

    9. c , c Ox ,

    y =6

    x + 8, x = 6 x = 5 .

    10. ,

    : z(t) = 0 . 736t2 + 5 . 8t + 7 . 4 t

    ( ), .

    . 129 300 2012/2013 .

  • MA , 3, 130

    1. c arctg x1 + x2 dx .

    2. c 5(x2 + 2x + 1)

    (x + 4)(x2 + 6x + 13)dx .

    3. c 2x 7x + 1 1 dx .

    4. c ln2

    ln6e2x

    e4x + 4dx .

    5. c 0

    6

    (x2 + 5x 5) cos3x dx .

    6. c 0

    2

    sin4x sin6x dx .

    7. c cc 36

    cos6x dx

    .

    8. c , y = 8x2 8x + 1,

    y = 7x2 3x + 7 . .

    9. c , c Ox ,

    y =9

    x + 2, x = 3 x = 6 .

    10. ,

    CM = 12q3 + 6q2 + 6q , 540 .

    . 130 300 2012/2013 .

  • MA , 3, 131

    1. c dx7 5x .

    2. c 5(x2 + x + 2)

    (x + 3)(x2 + 4x + 8)dx .

    3. c 8 + x 4

    x + 5dx .

    4. c 34

    12

    5 ctg3x + 3 ctg2x 4

    sin2xdx .

    5. c 0

    6

    (x2 + 5x 1) sin3x dx .

    6. c 0

    2

    cos2x sin3x dx .

    7. c cc e34

    e3

    4dx

    x3 + ln4x

    85

    .

    8. c , y = x2 + 5x + 11,

    y = 3x + 3 . .

    9. c , c Ox ,

    y = x2 1 y = 0 x [ 4, 1] .

    10.

    MC(x) = 16 5x 4x2, 62 .

    .

    . 131 300 2012/2013 .

  • MA , 3, 132

    1. c dx7 2x .

    2. c 29(x2 x + 3)

    (x + 3)(x2 4x + 8)dx .

    3. c dxx + x3

    .

    4. c 38

    14

    4 ctg22x 4 ctg2x 1

    sin22xdx .

    5. c 0

    6

    (x2 x + 6) sin3x dx .

    6. c 0

    2

    cos5x sin6x dx .

    7. c cc 4

    cos2x dx

    .

    8. c , y =49

    x2 + 343,

    y =1

    392x2 . .

    9. c , c Ox ,

    y = x2 + x y = 0 x [ 4, 3] .

    10. R(x), x

    MR = x8 820 .

    . 132 300 2012/2013 .

  • MA , 3, 133

    1. c dx4x + 1 .

    2. c 10(x2 x + 7)

    x3 + 2x2 + 10xdx .

    3. c 2x 1x 3 1 dx .

    4. c ln3

    ln4e3x

    e6x 25dx .

    5. c 0

    12

    3

    arctg2x dx .

    6. c 0

    2

    cos6x sin7x dx .

    7. c cc 6

    sin3x dx

    .

    8. c , x + y = 11, yx = 24 .

    .

    9. c , c Ox ,

    y = x2 + 5x y = 0 x [ 7, 6] .10. R(x), x

    MR = 8x3 950 .

    . 133 300 2012/2013 .

  • MA , 3, 134

    1. c dx2x + 4 .

    2. c x2 + x + 4

    (x + 8)(x2 + 9x + 20)dx .

    3. c 4x 5x + 1 1 dx .

    4. c ln3

    ln4e3x

    e6x + 9dx .

    5. c 0

    12

    (x2 5x 2) cos6x dx .

    6. c 0

    6

    sin23x dx .

    7. c cc 5

    413 + 5 x 5

    x 5dx

    .

    8. c , yx = 21, x + y = 10 .

    .

    9. c , c Ox ,

    y =3

    x + 3, x = 2 x = 6 .

    10.

    MC(x) = 40 8x x2, 56 .

    .

    . 134 300 2012/2013 .

  • MA , 3, 135

    1. c dx5x + 4 .

    2. c x2 + 5x 8

    (x 2)(x2 8x + 15)dx .

    3. c x + 2 + 6

    1 + x + 2dx .

    4. c 14

    18

    2 ctg32x 4 ctg22x 1

    sin22xdx .

    5. c 12

    3

    0

    arctg2x dx .

    6. c 0

    6

    cos22x dx .

    7. c cc 12

    1dx

    1 x2

    .

    8. c , y = x2 + 11,

    y = x 1 . .

    9. c , c Ox ,

    y = x2 16 y = 0 x [ 5, 4] .

    10. ()

    8 20

    f (t) = 5000 + 68t 3t2, t , 8 t 20.

    , 16 17 ,

    1 6 . .

    . 135 300 2012/2013 .

  • MA , 3, 136

    1. c x dx7x2 4 .

    2. c 8(x2 + x 6)

    x3 4x2 + 8xdx .

    3. c 9 + x + 1

    x + 10dx .

    4. c ln3

    ln2e2x

    36 25e4xdx .

    5. c 0

    10

    (x2 5x 3) cos5x dx .

    6. c 0

    18

    sin26x dx .

    7. c cc 4

    dx

    16 + x2

    .

    8. c , y = 5x2 + 3x,

    y = 3x2 + 3x + 8 . .

    9. c , c Ox ,

    y =3

    x 6, x = 9 x = 1 .

    10. ,

    CM = 12q5 + 15q4 + 9q2, 950 .

    . 136 300 2012/2013 .

  • MA , 3, 137

    1. c (12x 5) 6x2 5x 595 dx .

    2. c 9(x2 + 3x 8)

    (x 2)(x2 + 4x 21)dx .

    3. c dxx 3 x3

    .

    4. c 14

    518

    tg3x dx .

    5. c 13

    3

    0

    arctg3x dx .

    6. c 0

    14

    cos27x dx .

    7. c cc 4

    sin2x dx

    .

    8. c , y =16

    x2 + 112,

    y =1

    128x2 . .

    9. c , c Ox ,

    y = x2 + 2x y = 0 x [ 5, 3] .10. V(t) ,

    , 0 . 16, . .

    t V

    V= 0 . 16t .

    11 , , V(0) = 67 .

    . 137 300 2012/2013 .

  • MA , 3, 138

    1. c 6x 53x

    2 5x 412

    dx .

    2. c x2 + 8x + 2

    x3 + x2dx .

    3. c x 8x + 2 3 dx .

    4. c ln2

    ln4e2x

    e4x + 65dx .

    5. c 0

    6

    (x2 2x + 4) sin3x dx .

    6. c 0

    2

    cos3x sin2x dx .

    7. c cc 1

    1dx

    1 x2

    .

    8. c , y = x2 + 3x + 5,

    y = 2x + 1 . .

    9. c , c Ox ,

    y =7

    x 6, x = 2 x = 1 .

    10. V(t) ,

    , 0 . 03, . .

    t V

    V= 0 . 03t .

    20 , , V(0) = 71 .

    . 138 300 2012/2013 .

  • MA , 3, 139

    1. c dx8x + 3 .

    2. c 5(x2 + x 8)

    (x 2)(x2 6x + 13)dx .

    3. c 9 + x 1

    x 37dx .

    4. c ln5

    ln6e2x

    e4x + 25dx .

    5. c 1

    3 3

    13

    arctg3x dx .

    6. c 0

    2

    cos4x sin5x dx .

    7. c cc 18

    e3

    8dx

    x ln4(8x)

    .

    8. c , yx = 56, x + y = 15 .

    .

    9. c , c Ox ,

    y =4

    x 3, x = 4 x = 2 .

    10. R(x), x

    MR = 5x2 710 .

    . 139 300 2012/2013 .

  • MA , 3, 140

    1. c dx1 5x .

    2. c 6(x2 2x + 7)

    x3 5x2 14xdx .

    3. c x 3 + 7

    x + 6dx .

    4. c ln3

    ln4e3x

    e6x 25dx .

    5. c 1

    13

    arctg x dx .

    6. c 0

    18

    cos26x dx .

    7. c cc

    12

    cos2x dx

    .

    8. c , yx = 24, x + y = 11 .

    .

    9. c , c Ox ,

    y = x2 5x y = 0 x [ 3, 0] .10. K(t),

    ( , )

    I(t) = 600 t75 , K(0) = 740 .

    . 140 300 2012/2013 .

  • MA , 3, 141

    1. c (6x + 5) 3x2 + 5x + 69 dx .

    2. c 10(x2 4x + 7)

    x3 2x2 + 10xdx .

    3. c dxx2

    3 + x.

    4. c 32

    74

    5 ctg3x 2 ctg2x + 3

    sin2xdx .

    5. c 0

    13

    arctg3x dx .

    6. c 0

    24

    cos26x dx .

    7. c cc 0

    e2xdx

    .

    8. c , yx = 56, x + y = 15 .

    .

    9. c , c Ox ,

    y = x2 x y = 0 x [1, 3] .10. R(x), x

    MR = 9x 160 .

    . 141 300 2012/2013 .

  • MA , 3, 142

    1. c dx(5x 3)26 .

    2. c x2 3x + 2

    (x 3)(x2 8x + 16)dx .

    3. c dxx2

    3 + 5 x.

    4. c 38

    14

    3 ctg32x + 5 ctg22x 3

    sin22xdx .

    5. c 0

    12

    (x2 2x 1) cos6x dx .

    6. c 0

    2

    sin5x sin6x dx .

    7. c cc 3

    1x + 3

    1 xdx

    .

    8. c , y = 5x2 + 7x 3,

    y = 3x2 5x + 11 . .

    9. c , c Ox ,

    y = x2 5x y = 0 x [ 3, 0] .

    10. V(t) ,

    , 0 . 03, . .

    t V

    V= 0 . 03t .

    , 20 ,

    , ,

    V(0) = 49 .

    . 142 300 2012/2013 .

  • MA , 3, 143

    1. c x 2x2 + 756 dx .

    2. c 9(x2 + 2x + 5)

    (x + 3)(x2 + 6x + 18)dx .

    3. c x 5x + 4 1 dx .

    4. c 0

    112

    tg33x 4 tg23x + 4

    cos23xdx .

    5. c 0

    12

    (x2 3x + 6) cos6x dx .

    6. c 0

    2

    cos3x sin5x dx .

    7. c cc

    5

    cos5x dx

    .

    8. c , y =49

    x2 + 245,

    y =1

    294x2 . .

    9. c , c Ox ,

    y =2

    x + 5, x = 3 x = 2 .

    10. K(t),

    ( , )

    I(t) = 260(t 1)58 , K(1) = 250 .

    . 143 300 2012/2013 .

  • MA , 3, 144

    1. c (2x 3) x2 3x 4 dx .

    2. c x2 5x + 3

    (x 5)(x2 12x + 36)dx .

    3. c 6 xx 1 3 dx .

    4. c ln2

    ln3e2x

    e4x + 20dx .

    5. c 0

    12

    (x2 + x + 1) sin6x dx .

    6. c 0

    2

    cos5x sin3x dx .

    7. c cc 1

    12

    dx

    1 x2

    .

    8. c , y = 6x2 7x 6,

    y = 7x2 + x 6 . .

    9. c , c Ox ,

    y = x2 + 3x y = 0 x [ 6, 5] .

    10. e

    z(t) = 35t 3 . 39t2 , t ( ), .

    C 8 . 22

    , 90 .

    . 144 300 2012/2013 .

  • MA , 3, 145

    1. c 8x 54x2 5x + 56

    dx .

    2. c x2 + x + 4

    x2 x3dx .

    3. c dxx x3

    .

    4. c ln4

    ln2e2x

    25 81e4xdx .

    5. c 0

    4

    (x2 4x + 1) cos2x dx .

    6. c 0

    12

    cos23x dx .

    7. c cc

    24

    sin4x dx

    .

    8. c , yx = 6, x + y = 5 .

    .

    9. c , c Ox ,

    y =3

    x 9, x = 6 x = 8 .

    10. ,

    : z(t) = 0 . 954t2 + 8 . 1t + 8 . 1 t

    ( ), .

    . 145 300 2012/2013 .

  • MA , 3, 146

    1. c dx3x + 2 .

    2. c 8(x2 x 5)

    (x + 1)(x2 2x + 5)dx .

    3. c x + 6 9

    x 10dx .

    4. c 0

    6

    cos3x

    sin23x + 36dx

    5. c 1

    13

    arctg x dx .

    6. c 0

    2

    cos3x sin6x dx .

    7. c cc

    cos8x dx

    .

    8. c , yx = 18, x + y = 11 .

    .

    9. c , c Ox ,

    y =1

    x 2, x = 5 x = 8 .

    10.

    e t (t )

    V(t) = 26 + cos

    6(t + 1)

    . .

    . 146 300 2012/2013 .

  • MA , 3, 147

    1. c arcsin2x

    1 x2dx .

    2. c 8(x2 + 2x + 3)

    x3 + 4x2 + 8xdx .

    3. c 2x 7x + 3 + 1 dx .

    4. c 0

    10

    sin5x

    cos25x 25dx

    5. c 0

    12

    (x2 + 6x + 5) sin6x dx .

    6. c 0

    21

    sin27x dx .

    7. c cc 0

    e4xdx

    .

    8. c , y = x2 + 2x, y = 4x + 3 .

    .

    9. c , c Ox ,

    y =7

    x 8, x = 4 x = 1 .

    10. R(x), x

    MR = 3x8 340 .

    . 147 300 2012/2013 .

  • MA , 3, 148

    1. c dx(4x 5)105 .

    2. c x2 7x 5

    (x 7)(x2 12x + 36)dx .

    3. c x 9 + 6

    x 45dx .

    4. c 14

    512

    3 tg33x tg23x + 4

    cos23xdx .

    5. c 12

    3

    0

    arctg2x dx .

    6. c 0

    16

    cos24x dx .

    7. c cc

    35

    55x+2 dx

    .

    8. c , y = 4x2 5x + 7,

    y = 6x2 x + 7 . .

    9. c , c Ox ,

    y =2

    x + 8, x = 1 x = 5 .

    10. V(t) ,

    , 22% , . .

    t V

    V= 0 . 22t .

    , 12 ,

    , ,

    V(0) = 88 .

    . 148 300 2012/2013 .

  • MA , 3, 149

    1. c arcsin x1 x2

    dx .

    2. c 3(x2 + 2x + 7)

    (x + 9)(x 6)(x 5)dx .

    3. c x 6 + 4

    1 x 6dx .

    4. c 0

    6

    cos3x

    sin23x + 36dx

    5. c 0

    6

    (x2 + 7x 4) cos3x dx .

    6. c 0

    8

    sin24x dx .

    7. c cc 14

    +

    54x1 dx

    .

    8. c , y = 2x2 2x 5,

    y = 9x2 2x + 2 . .

    9. c , c Ox ,

    y = x2 3x y = 0 x [ 2, 0] .

    10. ,

    : z(t) = 0 . 811t2 + 5 . 7t + 4 . 8 t

    ( ), .

    . 149 300 2012/2013 .

  • MA , 3, 150

    1. c x dx3x2 + 5

    .

    2. c 8(x2 + 8x 3)

    (x 2)(x2 + 4)dx .

    3. c x + 4 3

    1 + x + 4dx .

    4. c 16

    15

    tg5x dx .

    5. c 0

    8

    (x2 7x 1) sin4x dx .

    6. c 0

    6

    sin22x dx .

    7. c cc 12

    cos6x dx

    .

    8. c , yx = 28, x + y = 11 .

    .

    9. c , c Ox ,

    y = x2 8x y = 0 x [ 4, 3] .

    10.

    MC(x) = 48 7x 4x2, 59 .

    .

    . 150 300 2012/2013 .

  • MA , 3, 151

    1. c 90x dx( 4x2 + 7)91

    .

    2. c 4(x2 + 4x + 1)

    (x + 3)(x2 + 6x + 13)dx .

    3. c 1 + x + 2

    x 7dx .

    4. c 0

    14

    cos7x

    sin27x + 16dx

    5. c 1

    3

    1

    arctg x dx .

    6. c 0

    12

    sin24x dx .

    7. c cc 6 3

    dx

    36 + x2

    .

    8. c , y = x2 + x,

    y = 2x 2 . .

    9. c , c Ox ,

    y =5

    x + 5, x = 3 x = 0 .

    10. ()

    8 20

    f (t) = 6000 + 85t 3t2, t , 8 t 20.

    , 10 14 ,

    1 4 . .

    . 151 300 2012/2013 .

  • MA , 3, 152

    1. c x dx7x2 4 .

    2. c 13(x2 2x 1)

    (x + 4)(x2 + 2x + 5)dx .

    3. c 2x 7x