How to do Integration by Parts?

If we are given an integral where the integrand (stuff in between the integral symbol and dx) is a product of two separate functions. we then allow whichever of the functions that will be easier to differentiate to be say u, and we call the other function dv. we then differentiate u to get du/dx and we integrate what we have called dv to get v. we then use the expressions that we have obtained and plug them into the formula integral(udv)dx = uv - integral(v)du and now evaluate.