# Hot Integral-3

Calculus Level 5

$\large \int_0^\infty \frac{t^2 e^{-3t} }{2-e^{-t}} \, dt$

The above integral can be expressed as

$\displaystyle A\zeta(B) - \frac{C}{D} + \frac{E}{F}\log^G(H) - \frac{J}{K}\pi^L\log(M)$

for positive integers $$A,B,C,D,E,F,G,H,J,K,L$$ and $$M$$. And $$\gcd(C,D)=\gcd(E,F)=\gcd(J,K)=1$$ with $$H$$ and $$M$$ are square free.

Evaluate $$A+B+C+D+E+F+G+H+J+K+L+M$$.

$$\blacksquare$$ This is a part of Hot Integrals

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