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

by fchopin
Tags: exponential, function, integral, solution
 P: 9 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.
 P: 608 Can you do the special case... $$\int _{0}^{\infty }\!{\frac {{{\rm e}^{-{x}^{2}}}}{1+{{\rm e}^{x}}}}{d x}$$
P: 588
 Quote by g_edgar Can you do the special case... $$\int _{0}^{\infty }\!{\frac {{{\rm e}^{-{x}^{2}}}}{1+{{\rm e}^{x}}}}{d x}$$
Mathematica can't...

HW Helper
P: 3,353

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

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.
 P: 9 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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