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

[cragar]

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 .

 

[gabbagabbahey]

I'd start by multiplying both numerator and denominator by $e$...after that, just use the following trick:

$$\frac{e}{e^x+e}=\frac{e+e^x-e^x}{e^x+e}=1-\frac{e^x}{e^x+e}$$

 

[cragar]

thanks for you help , that is a really slick trick