Triple Trouble!

Calculus Level 4

000 dx dy dz(1+x+y+z)7\displaystyle\int_0^{\infty}\displaystyle\int_0^{\infty}\displaystyle\int_0^{\infty} \dfrac{\ dx \ dy \ dz}{\sqrt{(1+x+y+z)^7}}

If the above integral can be expressed as SG\dfrac{S}{G}. Find SG\overline{SG}


    \implies S,G are coprime integers

    \implies If the answer is 17/15 the you should input 1715.

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