# Integration Techniques

Lead Author(s): **Kelly Cline**

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These questions make use of substitution and integration by parts techniques.

Content Index

[Integration by parts] 1

What is the derivative of $f(x) = \frac{1}{3}xe^{3x} – \frac{1}{9}e^{3x} + 25$ ?

A

$f ‘(x) = xe^{3x}$

B

$f ‘(x) = \frac{2}{3}e^{3x}$

C

$f ‘(x) = \frac{1}{3}e^{3x} + xe^{3x}$

D

$f ‘(x) = e^{3x}$

[Integration by parts] 2

What is $\int xe^{4x} dx$ ?

A

$\frac{1}{8}x^2e^{4x} + C$

B

$\frac{1}{4}xe^{4x} – \frac{1}{16}e^{4x} + C$

C

$\frac{1}{4}xe^{4x} – \frac{1}{4}e^{4x} + C$

D

$\frac{1}{16}e^{4x} – \frac{1}{4}xe^{4x} + C$

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