September 6th, 2019, 02:13 AM  #1 
Senior Member Joined: Dec 2015 From: somewhere Posts: 642 Thanks: 91  Evaluate integral
$\displaystyle I(n)=\underbrace{\int_{\infty}^{\infty } \int_{\infty }^{\infty} ...\int_{\infty}^{\infty } }_{n}\prod_{j=1}^{n} x_{j}^{j} e^{x_{1}^{2} x_{2}^{2}...x_{n}^{2} } dx_{1} \cdot dx_{2}\cdot ...\cdot dx_n $.

September 6th, 2019, 06:56 PM  #2 
Global Moderator Joined: May 2007 Posts: 6,823 Thanks: 723 
The expression is a product of integrals. The integrals for odd j =0, so the product =0.


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