What is the integral of Sin^2 x Cos^3 x dx?

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

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

put 

`therefore
int sin^2 x (1- sin^2 x) cos x dx = int [t^2 (1-t^2)] dt
`

`= int (t^2 - t^4 ) dt
`

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

now plug in `t` value as `sin
x`

required integral =`1/3 sin^3 x - 1/5 sin^5 x+
c`