I reopen the question with more context. I was unaware of the Stack Overflow directives. Please apologize.
Background: The sun is a star. Billions of stars (e.g. say $10^{12}$) make a galaxy. This integral might come out in the computation of how much light gets each star from the others (i.e., in the processes of the interstellar medium) that I'm playing with.
It doesn't require much more details to understand that having a closed form for this integral can be important for me, being it computed millions of times: even if I reduce the number of its computations, analytic will be always faster than numeric in the long runs.
$$\int_0^T {\frac{{{Exp[{ - \frac{a}{t} + bt]}}}}{{{t^{3/2}}}}dt}$$
I've tried with a change of variables in the exp... but not a good idea so far :/
Finally, it's astrophysics: a>0, b>0, T>0. All reals, all "easy" ;)
ThX in advance.
here is the steps to your integral you can use the website https://www.integral-calculator.com/ for further integral help