Formula:667

Digital Library of Mathematical Functions ID 2.1.E12

${\displaystyle{\displaystyle\int f(x)\mathrm{d}x\sim\begin{cases}\text{a constant,}&\Re\nu<-1,\\ \ln x,&\phantom{\Re missing}\nu=-1,\\ x^{\nu+1}/(\nu+1),&\Re\nu>-1.\end{cases}}}$

Symbols List

• ${\displaystyle{\displaystyle\sim}}$: asymptotic equality
• ${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$: differential of x
• ${\displaystyle{\displaystyle\int}}$: integral
• ${\displaystyle{\displaystyle\ln\NVar{z}}}$: principal branch of logarithm function
• ${\displaystyle{\displaystyle\Re}}$: real part
• ${\displaystyle{\displaystyle f(x)}}$: continuous function
• ${\displaystyle{\displaystyle\nu}}$: complex constant
 

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