Question

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

Answer 1

`((tanx)^2/2)+c`

Explanation:

`int(cosx)^2(tanx)^3(dx)`

=`int(cosx)^2times(sinx)^3/(cosx)^3times(dx)`

=`int(sinx)^3/(cosx)(dx)`

=`int(tanx)(secx)^2(dx)`

Let `tanx = t`
`:.sec^2x dx = dt`

Replacing,
=`inttdt`

=`t^2/2+c`

Replacing back,
=`((tanx)^2/2)+c`