Fun With Integrals 11

The volume of solids bounded by the cylinders $z=\ln(x)$ and $z=\ln(y)$ and planes $z=0$ and $x+y=2 e, \quad (x\geq 1)$ is $a e-be^2-c,$ where $a,b$ and $c$ are positive integers . Find the value of $a+b+c$ .

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