Computing the limit of an integral of a function series I am trying to figure out how to compute the limit
$$\lim_{t \rightarrow \infty} \int_{-1}^1 \frac{\cos^2(t^3x^{10})}{tx^2 + 1} \, dx.$$
If I exchange the limit and integral (when is this allowed?) then I get the integral of 0.  This seems too easy.  What should I be looking for?

Exchanging integral and limit is allowed here:
Your integrand is bounded by 1 so you can use dominated convergence theorem.
