Triple Trouble!

Calculus Level 4

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

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


\(\implies\) S,G are coprime integers

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

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