This integral cannot be described in terms of simple functions.
You can select one integration method over another depending on what you need the integration for.
Integration via power series
Recall that is analytic on , so the following equality holds
and this means that
Now youcan integrate:
Integration via the Incomplete Gamma Function
First, substitute :
The function is continuous. This means that its primitive functions are such that
and this is well defined because the function is such that for it holds , so that the improper integral is finite (I call ).
So you have that
Remark that . This means that for we get that , so that . So following improper integral of is finite:
We can write:
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