I want to make sense of the expression
The denominator vanishes at t=1. The singularity at t=1 is not integrable. I want to see whether the integral is defined in the sense of Cauchy principal value. Thus, I let
K := Int(t^2/ln(t)*exp(-t), t=0..1-a) + Int(t^2/ln(t)*exp(-t), t=1+a..infinity);
and wish to see whether the following limit exists:
limit(K, a=0, right);
Maple cannot evaluate this. Nor can I. Alternatively, we may try:
series(K, a=0) assuming a>0, a<1;
In both cases Maple says that it is unable to compute the series.
So my question is: Does the Cauchy principal value exist, and can Maple help one to determine that?