integration constant problem



----maxima-bounces at math.utexas.edu wrote: -----

>Maxima?5.24.0?gives(right,?but?not?nice):
>(%i1)?integrate((x-1)^5,x);
>(%o1)?x^6/6-x^5+(5*x^4)/2-(10*x^3)/3+(5*x^2)/2-x
>(%i2)?integrate((x-1)^5*log(x-1),x);
>(%o2)
>(x^6/6-x^5+(5*x^4)/2-(10*x^3)/3+(5*x^2)/2-x)*log(x-1)+log(x-1)/6-(x^6-6*x^
>5+15*x^4-20*x^3+15*x^2-6*x)/36

A method that requires trial and error and (mild) cleverness:

 (%i80) factor(integrate((x-1)^5,x,1,z));
 (%o80) (z-1)^6/6

 (%i81) facsum(integrate((x-1)^5*log(x-1),x,1,z),log(z-1));
 "Is  "z-1"  positive, negative, or zero?"pos;
 (%o81) (6*(z-1)^6*log(z-1)-(z-1)^6)/36

If you search the mailing list, you might be able to find other methods for doing 
things like this.

--Barton