[Maxima-bugs] [ maxima-Bugs-3473860 ] integrate(x^(1/3)*sin(x), x, 0, 1)

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Bugs item #3473860, was opened at 2012-01-14 12:22
Message generated for change (Settings changed) made by dgildea
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Category: None
Group: None
>Status: Closed
>Resolution: Duplicate
Priority: 5
Private: No
Submitted By: Aleksas (aleksasd)
Assigned to: Nobody/Anonymous (nobody)
Summary: integrate(x^(1/3)*sin(x),x,0,1)

Initial Comment:
Wrong
(%i1) integrate(x^(1/3)*sin(x),x,0,1);
(%o1) -cos(1)+(%i*gamma_incomplete(1/3,%i))/12-(%i*gamma_incomplete(1/3,-%i))/12
(%i2) float(%),expand;
(%o2) -0.408634157339482

(%i3) /* test */
first(quad_qags(x^(1/3)*sin(x),x,0,1));
(%o3) 0.391402134720738

 Correct exact answer(compare with Mathematica or Maple solutions):
(%i4) ((%i-sqrt(3))*gamma_incomplete(4/3,%i))/4-((%i+sqrt(3))*gamma_incomplete(4/3,-%i))/4+gamma(1/3)/(2*sqrt(3))$
(%i5) float(%),expand;
(%o5) 0.391402134723405

(%i6) build_info()$
Maxima version: 5.25.1
Maxima build date: 9:23 9/6/2011
Host type: i686-pc-mingw32
Lisp implementation type: Clozure Common Lisp
Lisp implementation version: Version 1.7-r14925M  (WindowsX8632)

Aleksas D.

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