I(α) =(adsbygoogle = window.adsbygoogle || []).push({}); _{0}^{∞}∫e^{-(x2+α/x2)}dx

Differentiating under the integral sign leads to:

I(α) =_{0}^{∞}∫-e^{-(x2+α/x2)}/x^{2}dx

Here I am supposed to let u = sqrt(a)/x, but the -x^{2}doesn't cancel out,

Wolfram-Alpha tells me the answer is: e^{(-2 sqrt(α) sqrt(π))/(2 sqrt(α))}. I understand where the sqrt(π))/(2)sqrt(α) comes from, but not the 2 sqrt(α)) in the numerator.

Thanks!

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# Differentiating Under Integral Sign

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