Let X$_1$ and X$_2$ be identically independent distributions(i.i.d) random variables with
$$\Bbb P(X_i \le x) = 1-x^{-1/2}, \quad x \ge 1 \ \text{and} \ i = 1,2 $$
Find $\Bbb P(X_1 + X_2 \le x)$.
I tried to finding the convolution of $f_{X_1}$ and $f_{X_2}$ (the density functions for $X_1$ and $X_2$) and integrating to get the CDF of $X_1$ + $X_2$ which is what I interpreted the question is asking for. When I integrate it, it got really messy and I could not finish the integration. Am I doing something wrong?