This Demonstration shows the first two steps in how to put an odd power of a sine into a form suitable for integration. Suppose the expression is

.
(1) split off one sine to get

(2) use

to express

in terms of
(3) substitute

, because

, which absorbs the split-off sine
(4) expand the polynomial in

(unless

)
(5) integrate the resulting polynomial in terms of

(6) substitute back