When do you know to use integration by parts?

You use integration by parts if there's more than one function of x. For example; to integrate xsin(x) you'd use integration by parts as this is two functions of x. The formula to remember is I(udv) = uv - I(vdu) For xsin(x) you would set u = x, and dv = sin(x). So du = 1, and v = -cos(x). Putting theses values into the formula gives you; I(xsin(x))= -xcos(x) - I(-cos(x)) = -xcos(x) + sin(x) However, for x(x + 2) you wouldn't use integration by parts as this is equal to x² + 2x which is one function of x.