Integral that Mathematica will not solve: -1/(4a) int [(s+b)^2]/[ln(1+e^{2s})+ln(1+e^

[gadelke]

I have an integral that Mathematica will not solve:

. . . . .\(\displaystyle \displaystyle \dfrac{-1}{4\alpha}\, \int\, \dfrac{(s\, +\, \beta)^2}{\ln\left(1\, +\, e^{2s}\right)\, +\, \ln\left(1\, +\, e^{s - \beta}\right)}\, ds\)

Does anyone have any ideas on ways I can re-express this equation so that Mathematica can solve it?

Aside: As background, I wanted to map all real numbers to positive real numbers (or an interval in positive numbers) - and I achieved this using the logit function. However, using the logit function gives me difficult integrals like this. Are there any other mappings from all real numbers to some interval in positive numbers that is simpler than the logit?

Thank you

 

[Deleted member 4993]

I have an integral that Mathematica will not solve:

. . . . .\(\displaystyle \displaystyle \dfrac{-1}{4\alpha}\, \int\, \dfrac{(s\, +\, \beta)^2}{\ln\left(1\, +\, e^{2s}\right)\, +\, \ln\left(1\, +\, e^{s - \beta}\right)}\, ds\)

Does anyone have any ideas on ways I can re-express this equation so that Mathematica can solve it?

Aside: As background, I wanted to map all real numbers to positive real numbers (or an interval in positive numbers) - and I achieved this using the logit function. However, using the logit function gives me difficult integrals like this. Are there any other mappings from all real numbers to some interval in positive numbers that is simpler than the logit?

Thank you

If my uncle "Wolfram" cannot solve it - I cannot even cry uncle......