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Integration by Parts

Oct 06, 20231 min read

Math

Integration technique, undos chain rule

$\int f g^{'} d x = f g - \int g f^{'} d x$

$f$ and $g$ are functions of $x$

$\int u d v = uv - \int v d u$

Alternative formulation

DI Table Examples

Blackpenredpen Video

$\int x^{2} sin (3 x) d x$

$\int x^{4} ln x d x$

$\int e^{x} sin x d x$

Graph View

$\displaystyle \int fg' \, \mathrm{d}x=fg-\int gf' \, \mathrm{d}x$
$\displaystyle \int u \, \mathrm{d}v=uv-\int v \, \mathrm{d}u$
DI Table Examples
$\displaystyle \int x^{2}\sin(3x) \, \mathrm{d}x$
$\displaystyle \int x^{4}\ln x \, \mathrm{d}x$
$\displaystyle \int e^{x}\sin x \, \mathrm{d}x$

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Gamma Function
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Integration by Parts

$\int f g^{'} d x = f g - \int g f^{'} d x$

$\int u d v = uv - \int v d u$

DI Table Examples

$\int x^{2} sin (3 x) d x$

$\int x^{4} ln x d x$

$\int e^{x} sin x d x$

Graph View

Table of Contents

Backlinks

Knowledge

Explorer

Integration by Parts

∫fg′dx=fg−∫gf′dx

∫udv=uv−∫vdu

DI Table Examples

∫x2sin(3x)dx

∫x4lnxdx

∫exsinxdx

Graph View

Table of Contents

Backlinks

$\int f g^{'} d x = f g - \int g f^{'} d x$

$\int u d v = uv - \int v d u$

$\int x^{2} sin (3 x) d x$

$\int x^{4} ln x d x$

$\int e^{x} sin x d x$