Free Printable Integration by Parts, Trig, Partial Fractions

Free Printable Worksheets

Worksheets

Integration by Parts, Trig, Partial Fractions

Total questions: 20

Worksheet time: 2hrs 24mins

Name

Class

Date

1.

What would you choose for your u here if you used integration by parts?

a)

t

b)

3t

c)

e^2t

d)

e^t

e)

don't use IBP, let u = 2t

2.

Evaluate the indefinite integral using integration by parts.
$\int3x\ e^{2x}\ dx\$

a)

$-\frac{xe^{2x}}{2}+\frac{e^{2x}}{4}+C$

b)

$\frac{3xe^{2x}}{2}-\frac{3e^{2x}}{4}+C$

c)

$xe^{-2x}+\frac{\left(1-x^2\right)^{ }}{2}+C$

d)

$-\frac{xe^{2x}}{2}+\frac{\ln e^{2x}}{4}+C$

3.

Evaluate the indefinite integral using integration by parts. $\int t^2\ln t\ dt\$

a)

$\frac{2t^2\ln2t-t^2}{4}+C$

b)

$\frac{t^3\ \ln t}{3}-\frac{t^3}{9}+C$

c)

$\frac{e^t}{2t+2}+C$

d)

$\frac{-2t-1}{4e^{2t}}+C$

4.

$\int_{ }xe^x\ dx$ by using integration by parts.

a)

$xe^x-\ e^x+c$

b)

$xe^x+e^x+c$

c)

$xe^x+c$

d)

$xe^x-e^x$

5.

What would you choose for your u here if you used integration by parts?

a)

x

b)

sin(x)

c)

cos(x)

d)

e^x

6.

What method would you use here?

a)

antiderivative rules.

b)

u-substitution

c)

integration by parts

d)

Stare at the question... forever.

7.

What trig substitution should be made?

a)

b)

c)

d)

8.

Base on the trig substitution for this integral, choose the correct triangle format

a)

b)

c)

d)

9.

Evaluate the integral without simplifying

a)

b)

c)

d)

10.

What trig substitution should be used?

a)

b)

c)

d)

11.

Based on the trig substitution made for this integral, choose the correct triangle format

a)

b)

c)

d)

12.

Solve the integral without simplifying

a)

b)

c)

d)

13.

What trig substitution should be made?

a)

b)

c)

d)

14.

Based on the trig substitution for this integral, choose the correct triangle

a)

b)

c)

d)

15.

Solve the integral without simplifying

a)

b)

c)

d)

16.

Which technique should be used to integrate this:

a)

natural log pattern

b)

u-substitution

c)

integration by parts

d)

partial fractions

17.

Find the partial fraction decomposition...

a)

b)

c)

d)

18.

$\int\frac{dx}{x^2+2x-15}$

a)

$\frac{1}{8}\ln\left|x-3\right|-\frac{1}{8}\ln\left|x+5\right|+c$

b)

$\frac{1}{4}\ln\left|x-3\right|-\frac{1}{8}\ln\left|x+5\right|+c$

c)

$\frac{1}{8}\ln\left|x+5\right|-\frac{1}{8}\ln\left|x-3\right|+c$

d)

$\frac{1}{4}\ln\left|x+5\right|-\frac{1}{4}\ln\left|x-3\right|+c$

19.

a)

A

b)

B

c)

C

d)

D

e)

E

20.

a)

A

b)

B

c)

C

d)

D

e)

E

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