The answer
Integration by parts is a technique to integrate products of two functions. The formula is ∫u dv = uv - ∫v du. Choose 'u' as the function that simplifies when differentiated, and 'dv' as the rest. Use the ILATE rule: Inverse, Logarithmic, Algebraic, Trigonometric, Exponential — pick 'u' in that order. Then differentiate 'u' to get du and integrate 'dv' to get v. Plug into the formula. It's basically the product rule in reverse. Practice with ∫x e^x dx: let u=x, dv=e^x dx, so du=dx, v=e^x, giving x e^x - ∫e^x dx = x e^x - e^x + C.
