A calculus problem by Rahil Sehgal

Calculus Level 4

000dx  dy  dz(1+x+y+z)7/2\displaystyle\int_{0}^{\infty} \displaystyle\int_{0}^{\infty} \displaystyle\int_{0}^{\infty} \dfrac{dx \; dy \; dz}{( 1+x+y+z)^{{7/2}}}

If the multiple integral above can be expressed as ab \dfrac ab, where aa and bb are coprime positive integers, find a+ba+b.

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