(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

[tex]\int e^{-\frac{1}{2}(ax^{2}+\frac{b}{x^{2}})} dx[/tex]

from [tex]-\infty[/tex] to [tex]\infty[/tex]

2. Relevant equations

it says to solve this, given that, again from [tex]-\infty[/tex]to [tex]\infty[/tex]:

[tex]\int e^{-\frac{1}{2}x^{2}}}dx[/tex]

= [tex]\sqrt{}2\pi[/tex]

and suggests that the substitution

[tex]u = x\sqrt{a}- \frac{\sqrt{b}}{x}[/tex]

may be helpful taking into account the limits carefully

3. The attempt at a solution

i did all this and all i ended up with was another integral which was no more helpful than the one i had in the beginning, and didnt resemble the stated gaussian integral. i am also unsure as to what to make of the "taking into account the limits carefully" im not sure if there is something that im missing out which is blindingly obvious, but any help would be greatly appreciated!

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# Homework Help: Problem involving Gaussian Integrals

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