Integration By Parts

#Math
Integration technique, undos chain rule

$\displaystyle \int fg' , \mathrm{d}x=fg-\int gf' , \mathrm{d}x$

• $\displaystyle f$ and $\displaystyle g$ are functions of $\displaystyle x$

$\displaystyle \int u , \mathrm{d}v=uv-\int v , \mathrm{d}u$

• Alternative formulation

DI Table Examples

Blackpenredpen Video

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

$\displaystyle \int x^{4}\ln x , \mathrm{d}x$

$\displaystyle \int e^{x}\sin x , \mathrm{d}x$