Calculus/integral

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Expert: - 5/29/2008


Question
I'm in trouble integrating : S dx/(e^(x/2)+e^x). I tried to integrate it as sum but it wasn't successful (there is dx, but I need d(-x/2) to use formula) Hoping for sum peace of advice, Liva

Answer
Let t=1+e^(x/2), so 2 dt = e^x dx.
After this has been done, split the integral using A/u + B/(u-1) and find out what A and B are by combining the fractions.  Doing this give [A(u-1)+Bu]/[u(u-1)], so that now A and B can be found.
You will end up integrating is A/u and B/(u-1) to
A*ln(u) + B*(ln(u-1)) + C.  You know, C that elusive constant.

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