I'd like to compute the following integral. I've tried SAGE but it just runs for 15 minutes then stops.. not sure what that means. If anyone wants to take a crack with mathematica or anything, please feel free
qA = var('qA')
qB = var('qB')
qM = var('qM')
rA = var('rA')
rB = var('rB')
rM = var('rM')
c = var('c')
expression = exp(-(qA/qB*(c-rA)+rB))/(1+exp(-(qA/qB*(c-rA)+rB)))*exp(-(qA/qM*(c-rA)+rM))/(1+exp(-(qA/qM*(c-rA)+rM)))*(exp(-c))/(1+exp(-c))^2
integral = integrate(expression,c,0,infinity)
here it is in latex:
$$ \int_{0}^{\infty}\left(\frac{\exp\left\{ -\left(\frac{q_{A}}{q_{B}}(c-r_{A})+r_{B}\right)\right\} }{1+\exp\left\{ -\left(\frac{q_{A}}{q_{B}}(c-r_{A})+r_{B}\right)\right\} }\right)\left(\frac{\exp\left\{ -\left(\frac{q_{A}}{q_{M}}(c-r_{A})+r_{M}\right)\right\} }{1+\exp\left\{ -\left(\frac{q_{A}}{q_{M}}(c-r_{A})+r_{M}\right)\right\} }\right)\frac{\exp\left\{ -c\right\} }{\left(1+\exp\left\{ -c\right\} \right)^{2}}dc $$
I mean I guess first question..is it even doable?