#2332 integrate gives complex area

[Richard Hennessy]

In evaluating integrate(exp(-signum(x-2)*x^3),x,-2,3); maxima gives complex result. Integrand is real valued and has well defined area under the curve. I would expect Maxima to give real number for result.

(%i2) load(abs_integrate);
(%o2) C:/Maxima-5.25.1/share/maxima/5.25.1/share/contrib/integration/abs_integrate.mac
(%i3) display2d:false;
(%o3) false
(%i4) integrate(exp(-signum(x-2)*x^3),x,-2,3);
(%o4) gamma_incomplete(1/3,-8)/3-gamma_incomplete(1/3,27)/3
(%i5) rectform(float(%));
(%o5) -239.7616342762335*%i-137.5334645791589
(%i6) build_info();
Maxima version: 5.25.1
Maxima build date: 10:2 9/6/2011
Host type: i686-pc-mingw32
Lisp implementation type: GNU Common Lisp (GCL)
Lisp implementation version: GCL 2.6.8
(%o6) ""
(%i7)

[Aleksas]

(%i1) f:exp(-signum(x-2)*x^3)$

By properties of definite integral
integrate(f,x,-2,3)=integrate(f,x,-2,0)+integrate(f,x,0,2)+integrate(f,x,2,3)

(%i2) integrate(f,x,-2,0)+integrate(f,x,0,2)+integrate(f,x,2,3)$
float(%), expand;
sol:realpart(%);

(%o3) 277.7458676930253-4.263256414560601*10^-14*%i
(%o4) 277.7458676930253

(%i5) /* test*/
first(quad_qags(exp(-signum(x-2)*x^3),x,-2,3));
(%o5) 277.7458676961945

Aleksas D.