How to integrate a fraction of sums of exponentials?

  1. Is it possible to have an solution to this sort of integral? And if not, why not?

    [tex] \int_0^\infty \frac{e^{-ax}}{e^{-bx}+e^{-cx}}dx [/tex]

    Is a Taylor expansion the only way forward?

    Many thanks
    Last edited: Dec 21, 2011
  2. jcsd
  3. dextercioby

    dextercioby 12,324
    Science Advisor
    Homework Helper

    Use [tex ] instead of inline tex if you're not writing a formula on the same line with words.

    [tex]\int_0^\infty \frac{e^{-ax}}{e^{-bx}+e^{-cx}}dx[/tex]

    looks better and is easier to read.

    As for your question, before jumping to series expansions and substitutions, specify if the arbitrary constants are positive or negative. This makes a huge difference on the final result.
    Then try to get rid of as many exponentials as possible. You can make the substitution (a,b,c >0) [itex] \displaystyle{e^{-ax}} = t [/itex] and see what you get.
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