Which one of the following gives the correct antiderivative of

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

Problem

e^{ax}\bigl(\sin bx\bigr)

, where

a,\,b\in\mathbb{R}

and

a^{2}+b^{2}\neq0

? (a)

\displaystyle \frac{e^{ax}\bigl(a\cos bx-b\sin bx\bigr)}{a^{2}+b^{2}}+C

(b)

\displaystyle \frac{e^{ax}\bigl(a\sin bx-b\cos bx\bigr)}{a^{2}+b^{2}}+C

(c)

\displaystyle \frac{e^{ax}\bigl(b\sin bx-a\cos bx\bigr)}{a^{2}+b^{2}}+C

(d)

\displaystyle \frac{e^{ax}\bigl(a\sin bx-b\cos bx\bigr)}{a^{2}-b^{2}}+C