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Integration By Parts

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.