Evaluate the integral (in book, this is the "Integration by parts" section):

$\displaystyle \int x\cos(5x)dx$

Something like...

$\displaystyle x(\frac{1}{5})\sin5x - \int\frac{1}{5}\sin(5x)dx$

and then...? Or am I way off?

Wait, I think I got it. Is the answer:

$\displaystyle \frac{1}{5}x\sin5x + \frac{1}{25}\cos5x + C$

?