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Question Number 206773 by MaruMaru last updated on 24/Apr/24

\int_{0}^{\infty} \frac{e^{- x^{2}}}{{(x^{2} + \frac{1}{2})}^{2}} d x =

I^{2} = \int \int_{D} \frac{e^{- x^{2} - y^{2}}}{{(x^{2} + \frac{1}{2})}^{2} {(y^{2} + \frac{1}{2})}^{2}} d A

x = r \cos (θ) y = r \sin (θ)

J =∣ \frac{\partial (x, y)}{\partial (r, θ)} ∣ d r d θ = r d r d θ

\int \int_{D} \frac{{r e}^{- r^{2}}}{{(r^{2} \cos^{2} (θ) + \frac{1}{2})}^{2} {(r^{2} \sin^{2} (θ) + \frac{1}{2})}^{2}} d r d θ

Commented by MaruMaru last updated on 24/Apr/24

n e x t \dots ? ? ?

Commented by Frix last updated on 24/Apr/24

Differnt paths see question 206549

Commented by MaruMaru last updated on 25/Apr/24

w o w t h x