Question

How do you find the integral of `(sin^3(x/2))(cos(x/2))`?

Answer 1

`intsin^3(x/2)cos(x/2)dx=sin^4(x/2)/2`

Explanation:

Let `sin(x/2)=t`

Then `1/2cos(x/2)dx=dt`

And `2*int t^3 dt=t^ 4 * 2/4=sin^4( x/2)/2`