Because I have only time in the evening hours and I use the time to look at the
code, I can not answer so fast.
I will open a bug report at the weekend.
Perhaps further results I have got are interessting for you:
1.
I have found a bug in the routine lt-exp and f35p147. This bug prevents the
calculation of integrals with e.g. sin(2*sqrt(a*t)). SPECINT gives the result 0.
Here the output of Maxima after correction:
(%i6) radcan(specint(%e^(-s*t)*sin(2*sqrt(a*t)),t));
(%o6) sqrt(%pi)*sqrt(a)*%e^-(a/s)/s^(3/2)
That is perfectly the tabulated expression and SPECINT now works for a lot of
other integrals too.
2.
To show how we can extend the algorithm of SPECINT to calculate further
integrals, I have added code to calculate integrals of the form
t^-1*(%e^(-a*t)-%e^(-b*t)). The code works also for integrals like
t^-1*sin(a*t). Here an example
(%i4) specint(%e^(-s*t)*t^-1*sin(a*t),t);
(%o4) %i*(log(s-%i*a)-log(s+%i*a))/2
That's equivalent with the tabulated answer: atan(a/s)
Dieter Kaiser