# How do you integrate int e^x cos ^2 x^2 dx  using integration by parts?

If you try $u = {e}^{x}$, then you'll need to integrate ${\cos}^{2} \left({x}^{2}\right) \mathrm{dx}$ which just uses a Frensel integral.
If you try $u = {\cos}^{2} {x}^{2}$, then
$u v - \int v \mathrm{du} = {e}^{x} {\cos}^{2} {x}^{2} + 4 \int x {e}^{x} \sin \left({x}^{2}\right) \cos \left({x}^{2}\right) \mathrm{dx}$