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September 6th, 2019, 02:13 AM   #1
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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 $.
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September 6th, 2019, 06:56 PM   #2
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The expression is a product of integrals. The integrals for odd j =0, so the product =0.
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