Question

Find `int sin^5 (x/2).cos (x/2) dx`

Answer 1

`int sin^5 (x/2) cos (x/2) dx`

Let `sin  x/2 = t`

`cos  x/2 xx 1/2 dx = dt`

`cos (x/2) dx = 2dt`

I = `2 int t^5 dt`

I = `(2t^6)/6 + "C"`

I = `(sin^6  x/2)/3 + "C"`