wxMaxima version: 13.4.0
Maxima version: 5.31.1
Maxima build date: 2013-09-24 09:49:12
Host type: i686-pc-mingw32
Lisp implementation type: GNU Common Lisp (GCL)
Lisp implementation version: GCL 2.6.8
(assume(a>0,b>0), t1:integrate(exp(-a^2*x^2-b^2/x^2),x,0,inf), t2:integrate(exp(-a^2*x^2-b^2/x^2),x,-inf,0) , t3:integrate(exp(-a^2*x^2-b^2/x^2),x,-inf,inf),ldisp([t1,t2,t3]));
By symmetry of x and -x the first two results, t1 and t2 , should be same which they correctly are. But then obviously the 3rd result, t3, should just be twice t1 (or t2) but instead it adds a term with the the positive exponent in the exponential to t1 which is incorrect. Also maxima should be able to do closed form integrals of the form
integrate(x^(2*i)*exp(-a*x^2-b/x^2),x,0,inf) for any integer i by differentiating i times the closed form answer of
with respect to a for i>0 or b for i<0 but it does not do so.
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