# Who's up to the challenge? 70

Calculus Level 5

$\large \int _{ 0 }^{ \infty }{ \dfrac { x\ln { x } }{ 1+{ e }^{ x } } \, dx } =\dfrac { 1 }{ B } \pi ^{ C }-{ \pi }^{ D }\ln { A } +\dfrac { { \pi }^{ E }\ln { F } }{ G } +\dfrac { { \pi }^{ H }\ln { \pi } }{ I }$

The equation above holds true for positive integers $$B,C,D,F,G,H$$ and $$I$$ such that $$F$$ is minimized.

Find $$B+C+D+E+F+G+H+I$$.

Notation: $$A$$ denotes the Glaisher–Kinkelin constant, $$A \approx 1.2824$$.

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