The integral is .

(a)

 is positive and odd.

Save one sine factor and convert the remaining factors to cosines.Then expand and integrate.

(b)

 is positive and odd.

Save one cosine factor and convert the remaining factors to sines.Then expand and integrate.

(c)

 and  are both positive and even.

Make repeated use of power reducing formulas to convert the integrand to odd powers of the cosine.Then proceed as in part .

(a) Save one sine factor and convert the remaining factors to cosines.Then expand and integrate.

(b) Save one cosine factor and convert the remaining factors to sines.Then expand and integrate.

(c) Make repeated use of power reducing formulas to convert the integrand to odd powers of the cosine.

Then proceed as in part .