Integration by parts deliberately creates a harder-looking integral than the one you started with — but if you choose correctly, the second integral actually solves itself. Drag the slider to see different choices of u and watch how complexity flows from one side to the other.
The key insight: choose u to be the part that becomes simpler when you differentiate it. Logarithms and inverse trig functions are almost always the right choice for u because they vanish or reduce when differentiated, while exponentials and powers stay manageable when integrated. If you choose u to be e^x or sin x, you just move complexity around without reducing it.