Please solve the following integral:
1) Determine the integral sin^3(3x)cos^6(3x)dx
Make sure to show all of the steps which are required.
When trying to calculate integrals involving the products of sine and cosine, we can often look to make use of the fact that sin is the derivative of cos, and -sin is the derivative of cos. This makes such integrals particularly amenable to the method of substitution. The following solution is comprised of a brief (about 3 line) Word attachment illustrating such a technique in a particular example. It also illustrates the sort of familiarity with basic trigonometric identities which such questions often require before the method of substitution is applied.