Tuesday, 27 August 2019

integration - Looking for closed-form solution of the following integral

I have been trying to calculate the following triple integral:




I(a,b,c)=ax=0by=0cz=0dxdydz(1+x2+y2+z2)3



I can find values numerically for given a,b,c but, since I know that I(a,b,c)π232 as a,b,c, I wondered whether the integral has a closed-form solution for arbitrary a,b,c ? I certainly haven't found one and hoped someone might be able to help.

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