See here:
Wolfram Mathematica Online Integrator
I'm tryng to solve the following integrals:
1) (x/t)*(e^(-x/t))*(1+e^(-x/t))^-2
2) ((x^2)/t)*(e^(-x/t))*(1+e^(-x/t))^-2
Both on negative infinity to positive infinity.
You can see that they are both expectations of functions of a weibull random variable with theta of t and beta of 1.
1) Y = X(1+e^(-X/t))^-2
2) Y = (X^2)(1+e^(-X/t))^-2
I'm not sure if you need to use that or if I just can't solve the integrals properly. Any help?
See here:
Wolfram Mathematica Online Integrator