# Fun With Integrals 11

Calculus Level 5

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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