Question

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

Answer 1

You can't evaluate this integral by parts.

Explanation:

If you try `u = e^x`, then you'll need to integrate `cos^2(x^2) dx` which just uses a Frensel integral.

If you try `u = cos^2x^2`, then

`uv-int vdu = e^xcos^2x^2 + 4int x e^x sin(x^2) cos(x^2) dx`