Re: [Maxima-discuss] Maxima 5.1.40 cannot integrate A&S integral 5.1.42

[Richard F. <fa...@be...>]

On 6/19/2017 7:10 AM, Soegtrop, Michael wrote:
>
> current Maxima cannot integrate Abramowitz and Stegun integral 5.1.42:
>
> (%i44) integrate(x*%e^(%i*x)/(a^2+x^2),x);
>
> (%o44) 
> integrate(((x^2-a^2)*%e^(%i*x))/(%i*x^4+2*%i*a^2*x^2+%i*a^4),x)+(x*%e^(%i*x))/(%i*x^2+%i*a^2)
>
Maxima also does not do the simpler exp(x)/(x^2+a2) either,
but since the answer involves the exponential integral Ei   (or some
other expression involving gamma or hypergeometric functions),
maybe it is not exactly a bug.  An unimplemented extension
maybe.

The solution to this and many other integrals may be found by
(eventually) incorporating Albert Rich's  Rubi  program into Maxima.
http://www.apmaths.uwo.ca/~arich/
which would be possible when the (promised) separation of Rubi
from its current rule-based / Mathematica syntax  is complete.


RJF