Yucky Integral: Solving w/ Calculus

[NutriGrainKiller]

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

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

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.

 

[dextercioby]

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

 

[christianjb]

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.

 

[Gib Z]

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.

So either fork out some cash and buy mathematica, or start crying.

EDIT: No it seems i was wrong, they obviously changed it >.< Well yea your going to have to change the greek letters into ones on your keyboard and convert back.