Question

How do you integrate `int sinx/cos^3xdx`?

Answer 1

The derivative of `cosx` is `-sinx`. Use substitution.

Explanation:

`int sinx/cos^3x dx = - int (cosx)^-3 (-sinx) dx`

`= -int u^-3 du`

`= -u^-2/(-2) +C = 1/(2u^2) +C`

`=1/(2cos^2 x) +C`

`=1/2sec^2x + C`

(Check the answer by differentiation.)