Question

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

Answer 1

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

Answer 2

yes... lol forgot to add the dx

Answer 3

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

Answer 4

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 :)

Answer 5

You're welcome!