13: This is a trig integral. Although there is an extra sine there, substitution would not help as the cosine has a different multiple in the argument. It is possible to transform this expression into a function featuring powers of sines and cosines without their arguments multiplied by anything; then one would use the standard substitution and it would get really ugly. So the recommendation is to reduce the powers (in exchange for more multiples of arguments) using trig formulas.