Potential functions

Exponential functions

${\displaystyle \int x^n\text{d}x}=\frac{x^{n+1}}{n+1}\left(n\ne 1\right)$

${\displaystyle \int \frac{\text{d}x}{x}}=\ln \left|x\right|$

${\displaystyle \int {\text{e}}^x\text{d}x}={\text{e}}^x$

${\displaystyle \int a^x\text{d}x}=\frac{a^x}{\ln a}$

Trigonometric functions

Hyperbolic functions

${\displaystyle \int \sin x\text{d}x}=-\cos x$

${\displaystyle \int \cos x\text{d}x}=\sin x$

${\displaystyle \int \tan x\text{d}x}=-\ln \cos x^{*}$

${\displaystyle \int \cot x\text{d}x}=\ln \sin x^{*}$

${\displaystyle \int \frac{\text{d}x}{{\cos }^{2}x}}=\tan x$

${\displaystyle \int \frac{\text{d}x}{{\sin }^{2}x}}=-\cot x$

${\displaystyle \int \text{sh}x\text{d}x}=\text{ch}x$

${\displaystyle \int \text{ch}x\text{d}x}=\text{sh}x$

${\displaystyle \int \text{th}x\text{d}x}=\ln \text{ch}{x}^{*}$

${\displaystyle \int \text{cth}x\text{d}x}=\ln \text{sh}{x}^{*}$

${\displaystyle \int \frac{\text{d}x}{{\text{ch}}^{2}x}}=\text{th}x$

${\displaystyle \int \frac{\text{d}x}{{\text{sh}}^{2}x}}=-\text{ch}x$