# Yucky integral oh my!

The following has been extracted from a larger assignment, the details of which I do not believe are necessary. Anywho, here it is:

$$\frac{1}{\pi}\int\frac{1}{x(\lambda-x)} e^{-(\frac{x-\mu_1}{\lambda-x})^2} e^{-(\frac{x-\mu_2}{x})^2} dx$$

things to keep in mind: $$\lambda$$ as well as $$\mu_1$$ and $$\mu_2$$is only a variable, and the integral ranges from -infiniti to +infiniti.

What I've tried: distributing out, trying to combine/reduce exponentials (unsuccessful), tried u/du substitution - this seems like it would work, but i couldn't get it to.

I have completed four semesters of undergraduate calculus, so this isn't new however I'm not quite sure how to go about reducing this. Any tips would be greatly appreciated.

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dextercioby
Homework Helper
The integrand has problems at x=0 and x=\lambda. How would you normally deal with such problems ?

A lazy physicist writes:

Anybody who isn't a mathematician would use Mathematica's the 'Integrator' to solve integrals of this type. (Google 'The Integrator')

It's important to know how to solve a certain number of integrals by rote and experience. However, I don't see the point of torturing yourself over such complicated integrals as the above- unless they represent some physically interesting phenomenon.

HallsofIvy
I assume you mean that $\lambda$ as well as $\mu_1$ and $\mu_2$ are NOT variables but are constants.
christianjb, the integrator doesn't understand the different symbols, like the $\lambda$, it can only integrate things that only have x's in it. No way to tell it that those others are constants.