`int sin^2(x) cos^3(x) dx` Evaluate the integral

`intsin^2x cos^3x dx=intsin^2x cos^2x cos xdx`

Use Pythagorean trigonometric identity: `sin^2x+cos^2x=1=>cos^2x=1-sin^2x`

`int sin^2x(1-sin^2x)cos xdx=`

`intsin^2x cos xdx-intsin^4x cosxdx`

``Make substitution: `t=sin x=>` `dt=cos x dx`

`int t^2dt-intt^4 dt=t^3/3-t^5/5+C=`

Return substitution to get the solution.

`(sin^3x)/3-(sin^5x)/5+C`