Post on 19-Apr-2018
INTEGRALSfunction integral
f(x)dg(x)dx
f(x)g(x)−∫df(x)dx
g(x)dx
xn(n 6= −1) xn+1
n+11x `n|x| Note:- `n|x|+K = `n|x/x0|ex ex
sinx − cosx
cosx sinx
tanx `n| secx|cosec x −`n| cosec x+ cotx| or `n
∣∣tan x2
∣∣secx `n| secx+ tanx| = `n
∣∣tan(π4 + x
2
)∣∣cotx `n| sinx|
1a2 + x2
1a
tan−1 x
a
1a2 − x2
12a`na+ x
a− xor
1a
tanh−1 x
a(|x| < a)
1x2 − a2
12a`nx− ax+ a
or − 1a
coth−1 x
a(|x| > a)
1√a2 − x2
sin−1 x
a(a > |x|)
1√a2 + x2
sinh−1 x
aor `n
(x+√x2 + a2
)1√
x2 − a2cosh−1 x
aor `n|x+
√x2 − a2| (|x| > a)
sinhx coshx
coshx sinhx
tanhx `n coshx
cosech x −`n |cosechx+ cothx| or `n∣∣tanh x
2
∣∣sech x 2 tan−1 ex
cothx `n| sinhx|
Double integral ∫ ∫f(x, y)dxdy =
∫ ∫g(r, s)Jdrds
where
J =∂(x, y)∂(r, s)
=
∣∣∣∣∣ ∂x∂r
∂x∂s
∂y∂r
∂y∂s
∣∣∣∣∣