Question

How do you evaluate the integral `int sec^2x/(1+tanx)dx`?

Answer 1

`intsec^2x/(1 + tanx)dx = ln|1 + tanx| + C`

Explanation:

This is a u-subsitution problem. Our goal is to cancel out the numerator. Let `u = 1 + tanx`. Then `du = sec^2xdx` and `dx= (du)/sec^2x`

`=intsec^2x/u * (du)/sec^2x`

`= int(1/u) du`

This can be integrated as `int(1/x)dx = ln|x| + C`.

`= ln|u| + C`

`= ln|1 + tanx| + C`, where `C` is a constant

Hopefully this helps!