first when u use substitution let's say "u" in your case, where is your "du" ?
there is no sin 2x.
Jones: from here:
multiply out (1-cos2x)^3 to get
Separate into four integrals. The first two are straight forward. For the third, re-apply the power-reduction identity
For the fourth, note that
Use this to evaluate the 4th integral.