Question

How do you find the antiderivative of `int sin(tanx)/cos^2x dx`?

Answer 1

The derivative of `tanx` is `sec^2 x` which is `1/cos^2x`. Use substitution.

Explanation:

`int sin(tanx)/cos^2x dx = int sin(tanx) (sec^2x) dx`

With `u = tanx`, this is `int sinu du = -cosu +C`.

So we get

`int sin(tanx)/cos^2x dx = -cos(tanx) +C`

(Check the answer by differentiation.)