第1992题：the second kind of integrals

Evalute $\int \mathrm{e}^x \sin(2x) dx$ .

A. $\dfrac{\mathrm{e}^x \sin(2x)+2\mathrm{e}^x \cos(2x)}{5}$ $+C$

B. $\dfrac{\mathrm{e}^x \sin(2x)-2\mathrm{e}^x \cos(2x)}{5}$ $+C$

C. $-\dfrac{\mathrm{e}^x \sin(2x)+2\mathrm{e}^x \cos(2x)}{3}$ $+C$

D. $-\dfrac{\mathrm{e}^x \cos(2x)}{2}$ $+C$

Neither $\mathrm{e}^x$ nor $\sin(2x)$ will reduce to zero no matter how many times we differentiate them. So we must use Integration by Parts twice and solve for the integral algebraicly to find the answer.