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Integrals!

\[ \large \int_0^\infty \dfrac{x e^{-11x}}{\sqrt{e^{2x} -1}} \, dx = - \dfrac{10!!}{11!!} \left( \ln 2 + \sum_{n=1}^{11} \dfrac{(-1)^n}n \right) \]

Prove the equation above.

Clarification: \( !!\) denotes the double factorial notation.

Note by Hummus A
1 year, 8 months ago

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\(\frac { 10! }{ 11! } =\frac { 1 }{ 11 } \)

Joel Yip - 1 year, 8 months ago

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it was supposed to be a double factorial

Hummus A - 1 year, 8 months ago

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Nowhere double factorial notation is used . hahaha

Aman Rajput - 1 year, 8 months ago

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it was used,but i guess someone edited it,it should be double factorial,shouldn't it? and yes,it's funny lol

Hummus A - 1 year, 8 months ago

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