I was curious and started reading up about non-elementary functions, and their integrals and asked myself how one would integrate the function $x!$, as I can't even imagine integrating the $\pi$ function but I am curious as to how someone else may do it because how would someone integrate the integral sign in the function. I'm not even sure where I would start with such a function.
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7If you want to consider $x!$ for non-integer $x$, you might want to use the Gamma function suitably adjusted – Henry Jan 27 '23 at 10:11
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3I would not expect a closed form antiderivate. My guess is that we need numerical methods. – Peter Jan 27 '23 at 10:15
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https://www.wolframalpha.com/input/?i=integral%20of%20Gamma(x)&dataset= – joriki Jan 27 '23 at 11:32
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3Sorry, but does this answer your question? Integral of factorial function – Тyma Gaidash Jan 27 '23 at 12:05