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.

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