Integration by parts

Integration by parts is a special technique to facilitate the integration of the product of two functions that otherwise lack an obvious integral. This technique utilizes the insight of the product rule or chain rule.

The rule for integration by parts is stated as follows:

$\int f(x)g'(x)\,dx=f(x)g(x)-\int f'(x)g(x)\,dx,$

This rule is often useful when one function is a polynomial and the other function is transcendental, such as a trigonometric function or e raised to a power of x.