###Bug in Sage Integral Computations?###
Value = "FriCAS 2014-12-18 compiled at Tue May 5 18:13:01 UTC 2015"
All user variables and function definitions have been cleared.
All )browse facility databases have been cleared.
Internally cached functions and constructors have been cleared.
)clear completely is finished.
FriCAS agrees with Sage that the value of the integral is 0.
Type: Expression(Integer)
Type: Union(f1: OrderedCompletion(Expression(Integer)),...)
Consider the indefinite integral
Type: Union(Expression(Integer),...)
There is a pole at and the branch becomes complex after that point.
Type: Expression(Float)
Type: Expression(Integer)
Type: Complex(Float)
Both and for are "multi-valued functions". In the case of log, the branches for negative numbers differ by , so we can choose a branch that is real-valued.
Type: Expression(Complex(Integer))
Type: Expression(Complex(Integer))
Type: Complex(Float)
We expect the derivative of the indefinite integral to be equal to the original expression.
Type: Expression(Integer)
In FriCAS normalize
rewites an expression "using the least possible number of algebraically independent kernels".
Type: Expression(Integer)
The conclusion is that although these results are not identical they are nonetheless algebraically dependent.