1. ## Integration by parts

Sorry to be back so soon, I am once again having problems with integration. The integration problem is x*cos^2[x], I am not sure whether to start with integration by parts first, or if there is a trigonometric integral that specifically relates to problems like this. Any help would be appreciated, thanks!

2. Originally Posted by MikeDube
Sorry to be back so soon, I am once again having problems with integration. The integration problem is x*cos^2[x], I am not sure whether to start with integration by parts first, or if there is a trigonometric integral that specifically relates to problems like this. Any help would be appreciated, thanks!
power reduction identity ...

$x\cos^2{x} = x\left(\frac{1 + \cos(2x)}{2}\right)$

$\frac{1}{2}\int x \, dx + \frac{1}{2}\int x\cos(2x) \, dx$

parts for the second integral

3. ## Thanks

Thanks a ton, it seems these integrals are much easier than I am making them out to be as long as you know the identities