Guys my head is gonna explode with this problem... i have been trying to solve it for the past 2 weeks non-stop... basically it's a problem involving integration and periodic functions. the problem states the following:
If f is a periodic function with its period a, prove that: $$ \int _0^{+\infty}\:\frac{f\left(x\right)}{x}dx=\frac{\pi }{a}\int _0^{\frac{a}{2}}\:\frac{f\left(x\right)}{tan\left(\frac{\pi x}{a}\right)}dx $$
I've been given this problem from a friend(he doesn't know how to solve it either..) and, I hope that you guys help me with this it because i do not even know how to begin...