5.17 Remarks on integration by parts

When applying this, we hope that $f^{\prime}(x)g(x)$ is easier to integrate than $f(x)g^{\prime}(x)$. The integration-by-parts formula corresponds to the product rule 3.6(iii) for differentiation: beware the minus sign. When writing an integration by parts calculation, it helps to warn the reader. It is important not to confuse the integration–by–parts formulæ for definite and indefinite integrals; an indefinite integral is a function, whereas a definite integral is a number.