This seems to be a bug, though it can integrate it fine after simplification:
(%i1) i2 : (x^2-4)*asin(sqrt(16-4*x^2)*sqrt(4-x^2)/(2*x^2-8)) $
(%i2) i3 : 8 * integrate (i2, x, 0, 2);
expt: undefined: 0 to a negative exponent.
Anonymous
2012-06-27
Also, that was reproduced in sage 5.0 and Maxima 5.27 + patches (from Git).
Aleksas
2012-06-27
(%i1) i2 : (x^2-4)*asin(sqrt(16-4*x^2)*sqrt(4-x^2)/(2*x^2-8));
(%o1) (x^2-4)*asin((sqrt(16-4*x^2)*sqrt(4-x^2))/(2*x^2-8))
(%i2) i3:8*'integrate(i2,x,0,2);
(%o2) 8*integrate((x^2-4)*asin((sqrt(16-4*x^2)*sqrt(4-x^2))/(2*x^2-8)),x,0,2)
(%i3) radcan((sqrt(16-4*x^2)*sqrt(4-x^2))/(2*x^2-8));
(%o3) -1
(%i4) radcan(i3);
(%o4) -4*integrate(%pi*x^2-4*%pi,x,0,2)
(%i5) ev(%, nouns);
(%o5) (64*%pi)/3
not bug
best
Aleksas D