# 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 \(a+b+c\).