$\displaystyle \int udv$ $\,=\,$ $uv$ $-$ $\displaystyle \int vdu$

A mathematical approach of finding the integral of a product of functions from the integral of their derivative and antiderivative, is called the integration by parts.

$f{(x)}$ and $g{(x)}$ are two functions. Take $u = f{(x)}$ and $v = g{(x)}$

The derivatives of both functions in differential form are written in the following mathematical form.

$(1) \,\,\,$ $du = f'{(x)}dx$

$(2) \,\,\,$ $dv = g'{(x)}dx$

Let’s study each part of this integral property.

$\displaystyle \int udv \,=\, \int f{(x)}.g'{(x)} dx$ and $\displaystyle \int vdu \,=\, \int g{(x)}.f'{(x)} dx$

Each equation represents the integration of a product of a function and derivative of another function, and $uv$ is a product of a function and an antiderivative of another function.

Learn how to derive the integration by parts formula in mathematical form.

Latest Math Topics

Latest Math Problems

Email subscription

Math Doubts is a best place to learn mathematics and from basics to advanced scientific level for students, teachers and researchers.
Know more

Learn how to solve easy to difficult mathematics problems of all topics in various methods with step by step process and also maths questions for practising.