allery∫ x sin x dx (by parts):
A-x cos x - sin x + C
Bx cos x + sin x + C
C-x cos x + sin x + C
Dx cos x - sin x + C
Answer & Solution
Correct answer: C. -x cos x + sin x + C
u = x, dv = sin x dx; du = dx, v = -cos x.
We have ∫ u dv = uv - ∫ v.
Then du = -x cos x + ∫ cos x.
So dx = -x cos x + sin x + C.
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