AP® Calculus AB-BC

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Integration By Parts

APCALC-LDYLS4

Evaluate the following integral:

$$\int { x\ln { xdx } } $$

A

$\cfrac{1}{2}x+C$

B

$\cfrac{1}{2}{ ( \ln { x } ) }^{ 2 }+C$

C

$\cfrac{1}{2}{ { x }^{ 2 } }\ln { x } -\cfrac{1}{4}{ x }^{ 2 }+C$

D

$\cfrac{1}{2}{ { x }^{ 2 } }\ln { x } +\cfrac{1}{4}{ x }^{ 2 }+C$