The longer

Calculus Level 5

010101 ⁣3x+y+zdxdydz=ABlnCD \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 AA, BB, CC, and DD such that gcd(A,B)=gcd(C,D)=1 \gcd(A,B) = \gcd(C,D) = 1 and that the values of CC and DD are minimized.

Determine A+B+C+DA+B+C+D.


Here is a generalized version.

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