Can anyone help me solve following indefinite integral? I've been trying to work this out for quite some time now. Not a math major myself and the last time I did any undergrad college level calculus was back in 2013. Hence it might seem easy for a lot of you but please do help. I'm trying to brush up my calculus again. The question is
Solve $$f(x) = \int e^{x^n}\, dx $$
With $t=-x^n$ and odd $n$, the integral becomes
$$\int e^{x^n}dx=-\frac1n\int t^{1/n-1}e^{-t}\,dt.$$
This is an incomplete Gamma integral, though it is usually not used with negative bounds.