Improper integral of a function

Question

I want to study the nature of an improper integral. I separate the integral from $0$ to $1$ and from $1$ to $\infty$. The first integral is divergent (I proved that it is equivalent to Riemann integral, which is divergent in the neighborhood of $0$). But I didn't find how I can prove the convergence or divergence of the second one. The integral can be found below: $$\int_0^{\infty}\frac{\ln(1+x)^2}{\sin^2x}e^{-x}\ \text d x$$

Answer 1

The integrand has a singularity at every value $x=k\pi.$ And it will diverge at each of those values.