Question: How to integrate this expression?



f := beta/(2*sigma*GAMMA(1/beta))*exp(-(abs(x-mu)/sigma)^beta);

where mu::real, beta > 0, sigma > 0.
How can we obtain the expression of F?

F := int(f, x=-infinity..s)

Reverse problem (a priori simpler):
It's known that 

F := 1/2+signum(x-mu)/(2*GAMMA(1/beta))*(GAMMA(1/beta)-GAMMA(1/beta, abs((x-mu)/sigma)^beta))

How can we check that diff(F, x)=f?
Even with the assumptions on beta, mu and sigma and additional assumptions x>0 or x<0, I can't verify that diff(F, x)=f.


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