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∫ x ln x dx (integration by parts: u = ln x, dv = x dx):

Ax ln x
B(ln x)²
Cx² ln x - x²/2
D(x²/2) ln x - x²/4 + C
Answer & Solution
Correct answer: D. (x²/2) ln x - x²/4 + C
u = ln x, du = dx/x; dv = x dx, v = x²/2. ∫ x ln x dx = (x²/2) ln x - ∫ (x²/2)(1/x) dx = (x²/2) ln x - x²/4 + C.
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