Integralen av $$$e^{- n^{2}}$$$

Bestäm $$$\int e^{- n^{2}}\, dn$$$.

Denna integral (Felintegral) har ingen sluten form:

$${\color{red}{\int{e^{- n^{2}} d n}}} = {\color{red}{\left(\frac{\sqrt{\pi} \operatorname{erf}{\left(n \right)}}{2}\right)}}$$

Alltså,

$$\int{e^{- n^{2}} d n} = \frac{\sqrt{\pi} \operatorname{erf}{\left(n \right)}}{2}$$

Lägg till integrationskonstanten:

$$\int{e^{- n^{2}} d n} = \frac{\sqrt{\pi} \operatorname{erf}{\left(n \right)}}{2}+C$$

$$$\int e^{- n^{2}}\, dn = \frac{\sqrt{\pi} \operatorname{erf}{\left(n \right)}}{2} + C$$$A