Evaluate

$\displaystyle \int \frac{1}{e^x + 1} dx$.

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- Apr 12th 2010, 04:55 PMicemanfanUnusual Integral
Evaluate

$\displaystyle \int \frac{1}{e^x + 1} dx$. - Apr 12th 2010, 05:03 PMdwsmith
$\displaystyle -ln(e^x+1)+x$

- Apr 12th 2010, 05:04 PMpickslides
$\displaystyle \frac{1}{e^x + 1} \times \frac{e^{-x}}{e^{-x}}= \frac{e^{-x}}{1 + e^{-x}}$

Can you go from here? - Apr 12th 2010, 05:06 PMDeadstar
- Apr 12th 2010, 05:12 PMicemanfan
$\displaystyle \int \frac{1}{1 + e^x}dx = \int \frac{e^{-x}}{1 + e^{-x}} dx = -\ln(1 + e^{-x}) + C$

Correct? - Apr 12th 2010, 05:15 PMdwsmith
- Apr 12th 2010, 05:17 PMDeadstar
- Apr 12th 2010, 05:38 PMdwsmith
- Apr 12th 2010, 05:53 PMsa-ri-ga-ma