June 21st, 2019, 08:15 AM  #1 
Senior Member Joined: Dec 2015 From: somewhere Posts: 546 Thanks: 83  Evaluate integral
$\displaystyle I(x,y,z)=\int_{\infty}^{\infty} \int_{\infty}^{\infty} \int_{\infty}^{\infty} e^{x^{2} y^{2} z^{2} }dz\; dy \; dx .$

June 21st, 2019, 10:39 AM  #2 
Senior Member Joined: Dec 2015 From: somewhere Posts: 546 Thanks: 83 
$\displaystyle I(x,y,z)=I(x)\cdot I(y) \cdot I(z)=I^{3}(t)$. $\displaystyle I(x,y,z) =(\int_{\infty }^{\infty} e^{t^{2}})^{3}=\pi^{3/2}$. 

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