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

[tex]\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

[/tex]

things to keep in mind: [tex]\lambda[/tex] as well as [tex]\mu_1[/tex] and [tex]\mu_2[/tex]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.

[tex]\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

[/tex]

things to keep in mind: [tex]\lambda[/tex] as well as [tex]\mu_1[/tex] and [tex]\mu_2[/tex]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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