Hmm. Mathematica
(integrals.wolfram.com<http://integrals.wolfram.com/index.jsp?expr=+sqrt(x^2%2B4)/(x^2%2B1)>)
gets
asin(x/2)+sqrt(3)*atan((sqrt(3)*x)/sqrt(4+x^2)), but that is not correct
according to Maxima:
ex0: sqrt(x^2+4)/(x^2+1)$
ex1: asin(x/2)+sqrt(3)*atan(sqrt(3)*x/sqrt(4+x^2))$
The difference d: diff(ex1,x)-ex0 is messy and hard to simplify to something
simple.
Plotting d shows that it is non-constant and taylor agrees that the
difference is non-constant:
taylor(diff(ex1,x)-ex0,x,0,10);
=> x^2/8+5*x^6/1024+63*x^10/262144
Have I made some blunder, or is the Mathematica result incorrect?
-s
On Fri, Feb 18, 2011 at 07:49, Jaime Villate <villate at fe.up.pt> wrote:
> sqrt(x^2+4)/(x^2+1)