Integration with fraction in exponential

[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 doesn't work well.i tried substitution too

Thank you.

 

[D H]

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.

 

[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.