Subject: integrate ( exp (x^3), x, 0, 1) still wrong
From: Barton Willis
Date: Sat, 12 May 2012 11:43:54 +0000
A workaround is to set the domain to complex:
(%i23) integrate(exp(x^3),x,0,1), domain : 'complex;
(%o23) ((-1)^(2/3)*gamma_incomplete(1/3,-1)-(-1)^(2/3)*gamma(1/3))/3
(%i24) expand(float(rectform(%)));
(%o24) 1.34190441797742-1.4802973661668753*10^-16*%i
When domain is real, (-1)^(2/3) simplifies to 1. As for the tiny spurious imaginary part of (%o24), I don't have a cure.
The option variable m1pbranch has something to do with this too.
--bw
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> (%i2) integrate(exp(x^3),x,0,1);
> (%o2) (gamma_incomplete(1/3,-1)-gamma(1/3))/3
>
> (%i3) float(%);
> (%o3) 0.333333*(-3.4863699*%i-2.0128566)