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Single Variable Calculus

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Integration by Parts: $x$ Times a Sine Function

SVCALC-H1GEJ5

Find the integral

$$\int x \sin(3x)dx$$

A

$x^2\sin(3x)+C$

B

$-\cfrac{1}{3}x\cos(3x) + \cfrac{1}{9} \sin(3x)+C$

C

$-\cfrac{1}{3}x\cos(3x) - \cfrac{1}{9} \sin(3x)+C$

D

$-\cfrac{1}{3}x\cos(3x) - \cfrac{1}{3} \sin(3x)+C$