Sort:  

ok sure, I changed a little bit the code ( I don't know why I make this stupid error ), defining dx as a fix number, so now it is a bit faster, but not so much. :)
And I add a function to calculate the time.
call.JPG

Now I arrived to the 7nt decimal digit correct. (below the approximation there is the time in seconds)

eses.JPG

And the "graph" is:

gra.JPG

x axis : correct digit
y axis : time

Obviously it has an exponential shape, and for sure Python is not indicate to make calculations.

That's me again :)
I made an improvement on my code, changing the method to calculate the integral.
I used the trapezoidal method, and now I got the precision to the 10nt digital digit in less time! (23 seconds)

Cattura.JPG

newes.JPG

fraphes.JPG

Now I wanna try another method.