Integrating 2/((e^(-x))+1): Solving the Unknown Integral

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Homework Statement





integral of 2/((e^(-x))+1)

Homework Equations



how do you do this?



The Attempt at a Solution



no freaking clue! this is the BS i came up with

2(x-ln(e^-x + 1) + C)
 
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You can rewrite the integrand and then use a simple substitution. Hint: multiply the numerator and denominator by e^x and then simplify.
 
Last edited:
Dunkle said:
You can rewrite the integrand and then use a simple substitution. Hint: multiply the numerator and denominator by e^x and then simplify.

so then...i want to find the integral of e^x/(e^x + 1)...and i think i want to use substitution? u = e^x + 1. but then i do something wrong somewhere...i'm getting retarded answers...
 
If u=e^x+1 then du=?
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

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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