Help with improper integral calculation

  • #1
I'm supposed to find the integral of f(x) = (e^5x) / (1+(e^10x)) from negative infinity to 0. I know how to set up the integral as the limit as t approaches -∞ of ∫f(x) from t to 0, but I'm stuck on how to actually solve the integral. I've tried by parts and u-sub but I just can't seem to get it.
Any help would be appreciated, thanks in advance!
 

Answers and Replies

  • #2
arildno
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Well, if you set u=e^(5x), u^2=e^(10x).
Furthermore, you have:
du/dx=5u, that is dx=du/(5u)
Negative infinity in "x" goes to 0 in "u", whereas 0 in "x" goes to 1 in "u"
Your new integrand becomes 1/5*(1/(1+u^2)), which you should know how to integrate.
 

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