I have been trying to calculate the following triple integral:
I(a,b,c)=∫ax=0∫by=0∫cz=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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