The integration by parts method comes from the product rule for derivatives. Given two functions f , g , the product rule states that
|[f (x)g(x)] = f'(x)g(x) + f (x)g'(x)|
As usual, equating antiderivatives of these two expressions that agree at one point, we obtain a formula for definite integrals:
|f (x)g'(x)dx = f (x)g(x)|a b - f'(x)g(x)dx|
This final formula is integration by parts. It is useful when the function we want to integrate is the product of one function ( f ) for which we know the derivative and another function ( g' ) for which we know the antiderivative.