integrate((x-1)^5 answer should be (x-1)^6/6
integrate((x-1)^5*log(x-1),x) answer should be
(x-1)^6*log(x-1)/6-(x-1)^6/36.
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
/* nicely, better than Maple */
(%i3) integrate((x-1)^6*log(x-1),x);
(%o3) ((x-1)^7*log(x-1))/7-(x-1)^7/49
How can this be corrected?