№1720
\[\begin{array}{l}
{\text{Докажите}}{\text{, что}} \hfill \\
\int\limits_0^{ + \infty } {\frac{1}{{1 + {x^{2n}}}}dx} = \frac{\pi }{{2n \cdot \sin \frac{\pi }{{2n}}}}. \hfill \\
n \in \mathbb{N} \hfill \\
\end{array}\]
§
Euler's reflection formula
\[\Gamma \left( z \right)\Gamma \left( {1 - z} \right) = \frac{\pi }{{\sin \left( {\pi z} \right)}},{\text{ }}z \notin \mathbb{Z}\]
Your solution
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