Integration Techniques
Integration Techniques

Integration Techniques

Lead Author(s): Kelly Cline

Student Price: FREE

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

[Integration by parts] 1

What is the derivative of f(x)=13xe3x19e3x+25 f(x) = \frac{1}{3}xe^{3x} – \frac{1}{9}e^{3x} + 25 ?

A

f(x)=xe3xf ‘(x) = xe^{3x}

B

f(x)=23e3xf ‘(x) = \frac{2}{3}e^{3x}

C

f(x)=13e3x+xe3xf ‘(x) = \frac{1}{3}e^{3x} + xe^{3x}

D

f(x)=e3xf ‘(x) = e^{3x}

[Integration by parts] 2

What is xe4xdx\int xe^{4x} dx ?

A

18x2e4x+C\frac{1}{8}x^2e^{4x} + C

B

14xe4x116e4x+C\frac{1}{4}xe^{4x} – \frac{1}{16}e^{4x} + C

C

14xe4x14e4x+C\frac{1}{4}xe^{4x} – \frac{1}{4}e^{4x} + C

D

116e4x14xe4x+C\frac{1}{16}e^{4x} – \frac{1}{4}xe^{4x} + C

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