Find the integral of (cosx)*(sinx)^2 with respect to x

This is a common example of an integral that is a product of two functions whose derivatives are related. As we know the derivative of sinx is cosx, we can use substitution to easily solve this - let our U= sinx, and dU/dx = cosx so dU = cosxdx. Input the substitution to give the integral of U²dU, which by the power rule is simply solved as U³/3, without forgetting the constant C. Substituting U we find that the final answer is (sin³x)/3 + C