# [Maxima] bugs, features?

Dieter Kaiser drdieterkaiser at web.de
Mon Jul 27 15:05:42 CDT 2009

```Am Montag, den 27.07.2009, 12:10 -0700 schrieb Richard Fateman:
> integrate(log(sin(x),x)  gives a Lisp error.

The error is no longer present with the current CVS version. Until
Maxima 5.17 we have got a noun form. Maxima 5.18.1 gives the reported
Lisp error. That is the new result:

(%i14) integrate(log(sin(x)),x);
(%o14) x*log(sin(x))-(x*log(sin(x)^2+cos(x)^2+2*cos(x)+1)
+x*log(sin(x)^2+cos(x)^2-2*cos(x)+1)
+2*%i*x*atan2(sin(x),cos(x)+1)
-2*%i*x*atan2(sin(x),1-cos(x))-2*%i*li[2](%e^(%
i*x))
-2*%i*li[2](-%e^(%i*x))-%i*x^2)
/2

But the result is not very well simplified. It contains sin^2+cos^2
terms and I think the atan2 terms should vanish too. More work can be
done.

> Comparing integration results in Mathematica, I get Ei(x)  exponential
> integral in Mathematica,
> and incomplete_gamma(0,-%e^x)  in maxima.  Same result?

Maxima at this time does not simplify the Incomplete Gamma function
automatically. But more simplifications or transformations can be done,
e.g.

(%i15) gamma_incomplete(0,-exp(x)),gamma_expand:true;
(%o15) -expintegral_ei(%e^x)-log(-%e^x)+x
(%i16) %,logexpand:all;
(%o16) -expintegral_ei(%e^x)-log(-1)
(%i21) %,rectform;
(%o21) -expintegral_ei(%e^x)-%i*%pi

If we change the sign of the argument to gamma_incomplete we get:

(%i22) gamma_incomplete(0,exp(x)),gamma_expand:true,logexpand:all;
(%o22) -expintegral_ei(-%e^x)

The question is what simplifications should happen automatically.

Dieter Kaiser

```