Question

How do you find `int x*sec^2x`?

Answer 1

Integrate by parts (then by subsitution).

Explanation:

`int x*sec^2x`

Let `u = x` and `dv = sec^2x dx`.

This makes `du=dx` and `v=tanx`

`uv-intvdu = xtanx-int tanx dx`

`= xtanx-int sinx/cosx dx`

`= xtanx + ln abs cosx +C`