My question is about an integral but not an ordinary one
$\int_{le^{-bt'}}^{l}s^{l-1}e^{-s}ds$
I have the idea of use the leibniz integral rule because I don't want to use the Generalized incomplete gamma function but when I used the integral becomes more difficult i think because the result of use the leibniz rule is:
$\int_{le^{-bt'}}^{l}s^{l-1}e^{-s}ds=l^{l-1}e^{-l}-\left(le^{-bt'}\right)^{l-1}e^{-le^{-bt'}}e^{-bt'}+\int_{le^{-bt'}}^{l}s^{l-1}e^{-s}ln(s)ds$
I hope someone can help my with the last integral