# Hot Integral - 4

Calculus Level 5

$\large\displaystyle \int\limits_0^{\infty} \frac{\log^2(1 - e^{-x})x^5}{e^x - 1} \, dx$

Let $$I$$ denotes the above integral which can be expressed the form of

$$\displaystyle I = A\pi^B\zeta^C(D) - E\zeta(F)\zeta(G) + H\pi^J\zeta(K)$$

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

$$\bullet A,B,....,K$$ all in positive integers.

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

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