I know: $\sum_{n=1}^\infty \frac{e^{-x^2}}{n^3 + x^2}$ converges uniformly already, by: $\sum_{n=1}^\infty \frac{e^{-x^2}}{n^3 + x^2} \leq \sum_1^\infty \frac{1}{n^3}$ which I know converges by p-test with $p=3\gt1$.
But how do I prove that it has uniform convergence by the Weirstrasse M-Test?