Any solution to quasi-gaussian integral ?

[nlama]

Hello everybody,

Do you know if the following integral has an analytical solution ?

\int^{}_{} \exp{(x-\frac{(x-\mu)^2}{\sigma})} dx

Thanks in advance for your help.

Nicola

 

[dextercioby]

$$\int^{}_{} \exp{\left[x-\frac{(x-\mu)^2}{\sigma}\right]} \ dx$$

This you mean?Try the Mathematica integrator from the wolfram site.

Daniel.

 

[dextercioby]

There it is

$$\int \exp\left[x-\frac{(x-a)^{2}}{b}}\right] \ dx =-\frac{\sqrt{b}}{2}e^{a+\frac{b}{4}} \sqrt{\pi} \ \mbox{erf}\left[\frac{b+2(a-x)}{2\sqrt{b}}\right] +C$$

Daniel.