How do you know when to integrate by parts?

This is usually a good idea if you have an integral with two functions multiplied together when one of the functions differentiates to a constant (could take more than one differentiation).For example to find integral(xcos(x))we apply the formula: uv' = uv - integral(vu')with u(x) = x and v'(x) = cos(x)This will get: integral(xcos(x)) = xsinx - integral(sin(x)) = xsin(x) + cos(x)
Even if you're not sure it's worth having a go to see if it works and if not try a different method.