Formula:65

Digital Library of Mathematical Functions ID 1.4.E17

${\displaystyle{\displaystyle\int x^{n}\mathrm{d}x=\begin{cases}\dfrac{x^{n+1}}{n+1}+C,&\quad n\not=-1,\\ \ln\left|x\right|+C,&\quad n=-1.\end{cases}}}$

Symbols List

• ${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$: differential of x
• ${\displaystyle{\displaystyle\int}}$: integral
• ${\displaystyle{\displaystyle\ln\NVar{z}}}$: principal branch of logarithm function
• ${\displaystyle{\displaystyle n}}$: nonnegative integer
• ${\displaystyle{\displaystyle C}}$: constant
 

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