# Integration with fraction in exponential

1. Dec 21, 2011

### Elsasw

Hi all, am stuck with the integral with fraction in exponential

The equation

I=∫exp(bz)/(a+iz)*exp[(6*a^2-ik*w^2*z)/(z^2+a^2)]*dz

I already tried to partial fraction the 2nd exponential term, then i tried to perform integration by parts but it doesnt work well.i tried substitution too

Thank you.

2. Dec 21, 2011

### D H

Staff Emeritus
The function $f(z) = \exp\left(bz +\frac{6a^2-ik\omega^2z}{z^2+a^2} \right)/(a+iz)$ is not integrable in the elementary functions. In other words, you can try every standard integration trick in the books and you will not come up with a closed form solution for this integral.

About the best you can do is to expand this function as a power series and integrate term by term.

Where did you come up with this problem? If this is homework you may have made a mistake somewhere along the way. Math homework problems typically don't involve functions that aren't integrable in the elementary functions, at least not until you start working with special functions.

3. Dec 21, 2011

### Elsasw

Thanks DH..Nop..it is not homework...its a part of my work...but thanks to you or i will be still trying to integrate it in terms of elementary function.