I hate using the formula as well. But my way isn't nearly as formal as TPH's. I just always thought of it as: "the integral of one function times the other, minus the of the same function times the derivative of the other" sounds confusing in words, but it helps my weird mind to remember. i just remember to integrate one function, and that appears in both factors. then i put the other function in the first factor, and its derivative in the second factor.