Maxima calls inte to do integrate((sqrt(1-x^2)*(x^2+1))/(2-2*x^2),x,0,1). If I recall, inte is one of the last functions integrate tries. Some other method (not sure which one) handles integrate((x^2+1)/(2*sqrt(1-x^2)),x,0,1). integrate((sqrt(1-x^2)*(x^2+1))/(2-2*x^2),x,0,1) is in the testsuite. --Barton