Integral of this exponential function: analytical solution?

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, m < 0 (negative number so it converges).

I have tried to transform the denominator to cosh and integrate by parts,

among many others alternatives but I didn't suceed.

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.