Problem: Find the Fourier Series Representation of -

$\displaystyle f(x)=sin \pi x +3sin2 \pi x - sin 5 \pi x$

$\displaystyle g(x) =0$ $\displaystyle c=1, L=1$

Solution from professor:

$\displaystyle f(x)=sin \pix cos \pi t+3sin2 \pi xcos2 \pi t-sin5 \pi x cos5 \pi t$

Now, I just simply do not understand how it gets here. I use the formula for fourier series, and I got into some very difficult integral that is impossible to solve.

Little help, please?

K