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

Prove the equation above.

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

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

Prove the equation above.

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

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## Comments

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TopNewest\(\frac { 10! }{ 11! } =\frac { 1 }{ 11 } \) – Joel Yip · 9 months, 1 week ago

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– Hummus A · 9 months, 1 week ago

it was supposed to be a double factorialLog in to reply

Nowhere double factorial notation is used . hahaha – Aman Rajput · 9 months, 1 week ago

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– Hummus A · 9 months, 1 week ago

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