Question

What's the integral of `int cos^2(x) tan^3(x) dx`?

Answer 1

`-lnabs(cosx)+1/2cos^2x+C`

Explanation:

`cos^2(x) tan^3(x) = cos^2xsin^3x/cos^3x`

`= sin^2x/cosx sinx`

`= (1-cos^2x)/cosx sinx`

`int cos^2(x) tan^3(x) dx = int (1/cosx + cosx) sinx dx`

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