how do I do this? (-) integral of sinx(2x+2), that's a negative sign before the integral...

Question

anonymous · Answer

$$-\int\sin x~(2x+2)~dx~~?$$

kl0723 · Answer

yes... lol forgot to add the dx

anonymous · Answer

Integrate by parts by setting
$$\begin{matrix}
u=2x+2&&&dv=\sin x~dx\
du=2~dx&&&v=-\cos x
\end{matrix}$$
$$\begin{align*}-\int\sin x~(2x+2)~dx&=-\left(-\cos x~(2x+2)-\int(-2\cos x)~dx\right)\
&=(2x+2)\cos x+2\int\cos x~dx\
&=(2x+2)\cos x+2\sin x+C
\end{align*}$$

kl0723 · Answer

Thank you SithsAndGiggles, this is actually a longer problem but for some reason I was getting stuck here because I didn't think I would need to integrate by parts twice in the same problem :)

anonymous · Answer

You're welcome!