MATLAB: Does the INT function in the Symbolic Math Toolbox 3.2.3 (R2008a) return an expression with extra variables

Symbolic Math Toolbox

When I use the INT function to integrate a symbolic expression, I receive an expression that contains an extra variable _R. For example,
syms x y
y = int(1/(x^3+x+1),x);
returns,
y =
sum(1/(3*_R^2+1)*log(x-_R),_R = RootOf(_Z^3+_Z+1))

Best Answer

The _R variable is an index of iteration for a summation that is present in the output expression in "y". If you look closely at the output by executing the following command,
pretty(y)
you will see an expression with a summation over the variable _R. This variable is introduced by the INT function in the Maple kernel (which is used for all Symbolic computation in MATLAB) when the output of the function needs to contain a summation. The summation is typically over multiple roots of a polynomial which cannot be determined until the values of the variable are known.