The problem is asking to check the convergence of the improper integral $$\int_{0}^{\pi}{\frac{x}{\sin{x}}}\,dx.$$
Besides some substitution and partial integration I've tried browsing through stackexchange and haven't found any useful tips really. The only test we've seen at uni is the comparison test or just doing it like any other integral except for watching that it's not a definite integral, but it's getting closer to $0$ and $\pi$. I'm really not sure what I'm supposed to do here, any tips would help!
Hint. As $x\to \pi^-$, we have that $$0<\frac{x}{\sin(x)}\sim\frac{\pi}{\pi-x}$$ (recall that $f\sim g$ as $x\to x_0$ iff $\lim_{x\to x_0}\frac{f(x)}{g(x)}=1$.)
Can you take it from here?