Math& 152Chapter 7 Review (Exam 3) Worksheet Select Solutions

*Use at your own discretion*

1. (a) 13arctan(x/3) + C

(b) 12ln(x2 + 9) + C

(c) 12(x2 − 9 ln(x2 + 9)) + C

(d) 3x2

2− 4x+ 18 ln(x+ 4)− 40 + C

(e) ex2

2+ C

(f) ex(x2 − 2x+ 2) + C

(g) 272

(h) 643

(i) 64 + 20π

(j) − 14(x2+4x+9)2

+ C

(k) 38(x4 + 6)4/3 + C

(l) 13arcsin(3x/2) + C

(m) 12ln(x2 + 12x+ 40)− arctan

(x+6

2

)+ C

(n) −18cos4(2x) + C

(o) −2 cos√x+ C

(p) 1

(q) 25

(r) divergent

(s) ln(ex + 1) + C

(t) arctan(ex) + C

(u) ex − ln(ex + 1) + C

(v) 2 ln(x2 + 1)− 2x

+ lnx− arctanx+ C

(w) 15(lnx− ln(x+ 5)) + C

(x) −2 ln(x2 + 1) + 4 lnx+ arctanx+ C

(y) −12ln(x2 + 2x+ 4) + ln |2− x| −

√3 arctan

(x+1√

3

)+ C

(z)√u2 − a2 + a arctan

(a√

u2−a2

)+ C

2. (a) Divergent.

(b) Convergent.

1