#12947: Bug in integrating x*cos(x^3)
----------------------------+-----------------------------------------------
Reporter: kcrisman | Owner: burcin
Type: defect | Status: new
Priority: major | Milestone: sage-5.1
Component: calculus | Resolution:
Keywords: | Work issues:
Report Upstream: N/A | Reviewers:
Authors: | Merged in:
Dependencies: | Stopgaps:
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Comment (by kcrisman):
{{{
sage: assume(u>0)
sage: integrate(x*cos(x^3),x,0,u)
-1/3*gamma(2/3) + 1/6*gamma(2/3, -I*u^3) + 1/6*gamma(2/3, I*u^3)
}}}
To compare the "right" answer, do
{{{
sage: f(u) = integrate(x*cos(x^3),x,0,u)
sage: plot(f,(u,0,2*pi))
sage: plot(lambda u: numerical_integral(x*cos(x^3),0,u)[0],(u,0,2*pi))
}}}
Note how they don't really look quite similar, not really a branch cut
thing? Also, in Maxima
{{{
(%i2) display2d:false;
(%o2) false
(%i3) f:integrate(x*cos(x^3),x);
(%o3) (gamma_incomplete(2/3,%i*x^3)+gamma_incomplete(2/3,-%i*x^3))/6
(%i5) diff(f,x);
(%o5) (-3*%i*x*%e^(%i*x^3)/(-1)^(1/6)-3*%i*x*%e^-(%i*x^3)/(-1)^(1/6))/6
}}}
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/12947#comment:1>
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