I was only able to find integral tables that solve
$$f(t)=\int t^c e^{kt}dt$$
but the integral I'm trying to solve has a function, not a constant, for the exponent:
$$f(t)=\int t^c e^{g(t)}dt$$
Is there a general analytic solution to this form?
The actual integral I'm trying to solve is
$$f(t)=\int t^{a-1} e^{\frac{\ln2}{\lambda}t-\frac{1}{b}t^a}dt$$
where $a$, $b$, and $\lambda$ are all constants.