Math 9B Worksheet 8 Spring 2023
1. (Hyperbolic Functions) Solve the integrals
(a) (U- Sub)
∫
sinh(x)
3 + 2 cosh(x)
dx
(b) (IBP)
∫
x coshx dx
2. (a) For what values of p > 0 does the integral
∫ 1
0
1
xp
dx converge? When the integral
does converge, what is its value?
(b) Use part (b) and determine if the integral converges or diverges. Do not solve∫ 3
0
1
( 5
√
x)2
dx
3. Do the following integrals converge or diverge?
(a) (Unbounded interval+sub)
∫ ∞
−∞
x2e−x
3
dx
(b) (Unbounded integrand+sub)
∫ 2
0
x2
(x3 − 1)4 dx
4. (optional extra practice) You don’t need to turn these in.
ˆ
∫ 0
−2
e1/x
x2
dx
ˆ
∫ ∞
0
(2x+ 3) lnx dx
ˆ
∫ −1
−∞
e−2t dt
ˆ
∫
tanh(4x) dx

∫ ∞
2
2 coshx
4 + sinh2 x
dx
ˆ
∫ ∞
1
sech2 x dx.
ˆ
∫ ∞
0
x
(x2 + 1)(x+ 1)
.
ˆ
∫ √
x2 + 2x dx
ˆ
∫ ∞
1
ln(x)
x4
dx