# The longer

Calculus Level 5

$\int_0^1 \int_0^1 \int_0^1\! \dfrac{3}{x+y+z} \: \mathrm{d}x \: \mathrm{d}y \: \mathrm{d}z = \frac{A}{B} \ln \frac{C}{D}$

The above equation holds true for positive integers $$A$$, $$B$$, $$C$$, and $$D$$ such that $$\gcd(A,B) = \gcd(C,D) = 1$$ and that the values of $$C$$ and $$D$$ are minimized.

Determine $$A+B+C+D$$.

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