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Display information for equation id:math.2555.50 on revision:2555

* Page found: Das ideale Fermigas (eq math.2555.50)

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Das ideale Fermigas Eq: math.2555.50

Hash: 9426e6878a764f9381f6e4770a6f7203

TeX (original user input):

\begin{align}

& \int_{-\infty }^{\infty }{{}}dx\frac{{{e}^{x}}}{{{\left( {{e}^{x}}+1 \right)}^{2}}}=\left[ \frac{-1}{\left( {{e}^{x}}+1 \right)} \right]_{-\infty }^{\infty }=1 \\

& \int_{-\infty }^{\infty }{{}}dx\frac{x{{e}^{x}}}{{{\left( {{e}^{x}}+1 \right)}^{2}}}=0\quad da\ Integrand\ ungerade \\

& \int_{-\infty }^{\infty }{{}}dx{{x}^{2}}\frac{{{e}^{x}}}{{{\left( {{e}^{x}}+1 \right)}^{2}}}:=I \\

\end{align}

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\begin{aligned} \int_{- \infty}^{\infty} d x \frac{e^{x}}{{(e^{x} + 1)}^{2}} = {[\frac{- 1}{(e^{x} + 1)}]}_{- \infty}^{\infty} = 1 \\ \int_{- \infty}^{\infty} d x \frac{x e^{x}}{{(e^{x} + 1)}^{2}} = 0 d a I n t e g r a n d u n g e r a d e \\ \int_{- \infty}^{\infty} d x x^{2} \frac{e^{x}}{{(e^{x} + 1)}^{2}} : = I \end{aligned}

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