#12947: Bug in integrating x*cos(x^3)
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Reporter: kcrisman | Owner: burcin
Type: defect | Status: new
Priority: major | Milestone: sage-5.1
Component: calculus | Keywords:
Work issues: | Report Upstream: N/A
Reviewers: | Authors:
Merged in: | Dependencies:
Stopgaps: |
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From this [https://groups.google.com/forum/?fromgroups#!topic/sage-
support/-Dzaion3VrA sage-support thread]:
{{{
sage: numerical_integral(x*cos(x^3),0,.5)
(0.1247560409610376, 1.3850702913602309e-15)
sage: integrate(x*cos(x^3),(x,0,1/2)).n()
-0.0677842754623305
}}}
Given
{{{
sage: integrate(x*cos(x^3),x)
1/12*((-I*sqrt(3) - 1)*gamma(2/3, -I*x^3) + (I*sqrt(3) - 1)*gamma(2/3,
I*x^3))*(x^3)^(1/3)/x
sage: integrate(x*cos(x^3),(x,0,1/2))
-1/3*gamma(2/3) + 1/6*gamma(2/3, -1/8*I) + 1/6*gamma(2/3, 1/8*I)
}}}
this is probably something where Maxima is returning too many imaginary
things and something isn't cancelling right either there or in Sage
proper? We've had trouble with either side of this with incomplete gamma
functions before.
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/12947>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
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