- #1
iggyonphysics
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I(α) = 0∞∫e-(x2+α/x2) dx
Differentiating under the integral sign leads to:
I(α) = 0∞∫-e-(x2+α/x2)/x2 dx
Here I am supposed to let u = sqrt(a)/x, but the -x2 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!
Differentiating under the integral sign leads to:
I(α) = 0∞∫-e-(x2+α/x2)/x2 dx
Here I am supposed to let u = sqrt(a)/x, but the -x2 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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