Integral of a power of a cosine:

If the correct factors are present, this can be handled by the Power rule for integrals:

, where and using the derivative of the cosine,

Hence a combination of factors in the original problem can be replaced:

With this substitution, we get

Finally, we substitute for u to get the result in terms of x:

Notice that the argument of the resulting trig function is the same as that in the original problem.