Integral of this exponential function: analytical solution?
I'm trying to solve the definite integral between 0 and inf of:
exp(a*x^2 + b*x + c)
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,