Can someone help me solve this integral? (1/(1+e^x))dx

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Help W/ Integration--Calc 1

Hey everybody,
I have a problem that I don't know how to solve...can someone help me out:
Integral (1/(1+e^x))dx
 
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Try using substitution first for u=e^x which will give you

\int \frac{du}{u(1+u)}
and then use partial fractions to get some A,B where

\int \frac{A}{u}du + \int \frac{B}{1+u}du

and from there try and see if you can find a solution.
 


You can use the substitution jeffreydk said or use u=1+e^x. Both are fine.
 


Thanks guys, so much...answer wasn't too difficult after that.
 
Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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