# [Maxima] Endless loop during definte integral

Richard Hennessy rich.hennessy at verizon.net
Sun Mar 29 19:08:22 CDT 2009

```I get an endless loop in the definite integral but not the indefinite integral in the following case.  The answer should be integral
does not converge, I am pretty sure.  I don't know if anything like this has been reported before.

(%i1) f2(x):=(2*sigma^(3/2))/(%pi*x^4+2*%pi*sigma*x^2+%pi*sigma^2)\$
(%i2) integrate(f2(a*x-b)*x^3,x,minf,inf);
Is  sigma  positive, negative, or zero?
p;
Is  sigma  positive or negative?
p;
Is  a b  positive, negative, or zero?
p;
Maxima encountered a Lisp error:
Console interrupt.
Automatically continuing.
To reenable the Lisp debugger set *debugger-hook* to nil.
(%i3) display2d:false;

(%o3) false
(%i4) integrate(f2(a*x-b)*x^3,x);
Is  sigma  positive or negative?
p;
(%o4) 2*sigma^(3/2)
*(log(a^2*x^2-2*a*b*x+sigma+b^2)/(2*%pi*a^4)+(3*b*sigma+b^3)*atan((2*a^2*x-2*a*b)/(2*a*sqrt(sigma)))/(2*%pi*a^4*sigma^(3/2))
-((3*a*b*sigma-a*b^3)*x-sigma^2+b^4)
/(2*%pi*a^6*sigma*x^2-4*%pi*a^5*b*sigma*x+2*%pi*a^4*sigma^2+2*%pi*a^4*b^2*sigma))
(%i5) build_info();

Maxima version: 5.17.1
Maxima build date: 19:10 12/18/2008
host type: i686-pc-mingw32
lisp-implementation-type: GNU Common Lisp (GCL)
lisp-implementation-version: GCL 2.6.8

(%o5)
(%i6)

Rich

```