Integral of this exponential function: does it have a solution?

  1. Hi all,

    I'm trying to solve the definite integral between 0 and inf of:

    exp(a*x^2 + b*x + c)
    --------------------- dx
    1 + exp(m*x + n)

    with a,b,c,m,n real numbers and a < 0 (negative number so it converges).

    I've read in the forum's rules that I have to post the work that I have done to get an answer but I have nothing reasonable to post (I have tried many alternatives but I didn't suceed, sorry)

    A way to obtain the exact solution would be perfect but an approximate result, even an upper/lowerbound would be fine as well.

    Any idea or help, please?

    Thanks in advance,
    FC.
     
  2. jcsd
  3. Can you do the special case...
    [tex]
    \int _{0}^{\infty }\!{\frac {{{\rm e}^{-{x}^{2}}}}{1+{{\rm e}^{x}}}}{d
    x}
    [/tex]
     
  4. Mathematica can't...
     
  5. Gib Z

    Gib Z 3,348
    Homework Helper

    Maybe hes alluding to the idea that if you can't do one of the basic cases you wouldn't be able to do the general case either.
     
  6. Hi guys,

    thank you for your answers. I have found that if m<0 and n<0 then 1/(1 + exp(m*x + n)) can be expanded into Maclaurin series, which yields something like 1 + e^() - e^2*(). The terms can be multiplied by the numerator of the original integral, thus finally obtaining three integrals of the form exp^(a*x^2 + b*x + c), which have closed-form solutions in terms of the error function.

    Thank you for your interest!
     
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