Originally Posted by

**Golodh** I am trying to find a closed-form expression for the following integral:

$\displaystyle \int_{a}^{b}\frac{C}{x}exp^{-\frac{1}{2}(\frac{x-\mu}{\sigma})^2}dx$

with $\displaystyle 0<a<b$

Neither Maple nor Mathematica will give a ready answer.

If I put $\displaystyle \mu$ to 0, Maple gives me:

$\displaystyle \int\frac{C}{x}exp^{-\frac{1}{2}(\frac{x}{\sigma})^2}dx=-\frac{1}{2}*C*Ei(1,\frac{1}{2}\frac{x^2}{\sigma^2} )$

With Ei the exponential integral. This is Ok as far as it goes, but I need the integral for $\displaystyle x-\mu$.

If I add $\displaystyle \mu$ to the function, Maple can no longer find the integral.

I tried taking the derivative of $\displaystyle -\frac{1}{2}*C*Ei(1,\frac{1}{2}\frac{(x-\mu)^2}{\sigma^2})$ for clues, and that gives me $\displaystyle \frac{C}{x-\mu}$ $\displaystyle exp^{-\frac{1}{2}(\frac{x-\mu}{\sigma})^2}$, and the factor $\displaystyle \frac {C}{x-\mu}$ is not what I'm looking for; I need $\displaystyle \frac {C}{x}$.

Any suggestions? Am I overlooking something obvious?