FCIteratedIntegral[f,x,a,b]
is a special head indicating that the function f represents an iterated integral or a linear combination thereof and that it should be integrated in x from a to b. This notation is understood by the function FCIteratedIntegralEvaluate
that does the actual integration.
Notice that before applying FCIteratedIntegralEvaluate
all rational functions of x in f should be converted to the FCPartialFractionForm
representation.
Overview, FCIteratedIntegralEvaluate, ToFCPartialFractionForm
= 1/(1 + x) fun
\frac{1}{x+1}
= FCIteratedIntegral[ToFCPartialFractionForm[fun, x], x, a, b] int
\text{FCIteratedIntegral}\left(\text{FCPartialFractionForm}\left(0,\left( \begin{array}{cc} \{x+1,-1\} & 1 \\ \end{array} \right),x\right),x,a,b\right)
[int] FCIteratedIntegralEvaluate
G(-1; b)-G(-1; a)