OK:
(%i1) integrate(x^mu * atan(x),x); "Is "mu+1" zero or nonzero?"zero; (%o1) -(%pi*log(x^2+1)+2*%i*li[2](%i*x+1)-2*%i*li[2](1-%i*x)-4*atan(x)*log(x))/4
Not OK--the antiderivative isn't valid when mu + 1 = 0
(%i2) integrate(x^mu * acos(x),x); "Is "mu+1" zero or nonzero?"zero; (%o2) -((mu+1)*integrate((sqrt(1-x)*x*sqrt(x+1)*%e^(mu*log(x)))/((mu+1)*x^2-mu-1),x)-x*%e^(mu*log(x))*atan2(sqrt(1-x)*sqrt(x+1),x))/(mu+1)
Diff:
I put leading and trailing tildes (~~~~) around Maxima i/o, and assigned labels.