`int (tan^2x)/sec^5x dx` Find the indefinite integral

Given to solve,

`int (tan^2 x )/(sec^5 x) dx`

=`int (sin^2 x )(cos^3 x )dx`

= `int sin^2 x * cos^2 x * cosx dx`

= `int sin^2 x * (1-sin^2(x) )*cosx dx`

let `u=sinx => du =cosx dx`

so ,

 `int sin^2 x * (1-sin^2(x) )*cosx dx`

=`int u^2 * (1-u^2) du`

= `int u^2 -u^4 du`

= `(u^3)/3 - (u^5)/5 +c`

= `(sin^3 (x))/3 -(sin^5 (x))/5 +c`