How to use dominated convergence theorem to compute $$lim_{n\rightarrow \infty}\int_0^1\frac{1+nx^2}{(1+x^2)^n}$$
So far I have only done $\frac{1+nx^2}{(1+x^2)^n}\le\frac{1+nx^2}{(1+x^2)}$, I don't know what to do next with $1+nx^2$. Can anyone help me with that? Thanks so much!