Integral Problem: Find Solution to 1/((e^(x-1)+1)) & (x)/((e^(x-1)+1))

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SUMMARY

The forum discussion focuses on the integration of the functions 1/((e^(x-1)+1)) and (x)/((e^(x-1)+1)). A user attempted to solve the problem using integration by parts and partial fractions but struggled to find a solution. Another participant suggested a method involving multiplying both the numerator and denominator by e, leading to the simplification of the integral using the identity \frac{e}{e^x+e}=\frac{e+e^x-e^x}{e^x+e}=1-\frac{e^x}{e^x+e}, which proved effective.

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Homework Statement


integrate 1/((e^(x-1)+1))
and (x)/((e^(x-1)+1))





The Attempt at a Solution


i tried using integration parts , and partial fractions but i am not really sure what to do
any help will be much appreciated .
 
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I'd start by multiplying both numerator and denominator by [itex]e[/itex]...after that, just use the following trick:

[tex]\frac{e}{e^x+e}=\frac{e+e^x-e^x}{e^x+e}=1-\frac{e^x}{e^x+e}[/tex]
 
thanks for you help , that is a really slick trick
 

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