AP

MATHEMATICS · Single correct · AP · Calculus BC · Integration and Accumulation of Change · Integration and Accumulation of Change

Problem

Determine

\displaystyle \int x^{3}\cos 2x\,dx

. (a)

\tfrac12 x^{3}\sin 2x - \tfrac34 x^{2}\cos 2x - \tfrac34 x \sin 2x + \tfrac38 \cos 2x + C

(b)

\tfrac12 x^{3}\sin 2x + \tfrac34 x^{2}\cos 2x - \tfrac34 x \sin 2x + C

(c)

\tfrac12 x^{3}\sin 2x + \tfrac34 x^{2}\cos 2x - \tfrac34 x \sin 2x - \tfrac38 \cos 2x + C

(d)

\tfrac14 x^{3}\sin 2x + \tfrac34 x^{2}\cos 2x - \tfrac34 x \sin 2x - \tfrac38 \cos 2x + C