ToFCPartialFractionForm[exp, x] converts sums of
rational functions of the form n +
\frac{f_1}{[x-r_1]^p_1} + \frac{f_2}{[x-r_2]^p_2} + \ldots to
FCPartialFractionForm[n, {{f1,x-r1,p1},{f2,x-r2,p2}, ...}, x].
This facilitates the handling of iterated integrals.
Overview, FCPartialFractionForm, FromFCPartialFractionForm.
x/(x + 1)
ToFCPartialFractionForm[%, x]\frac{x}{x+1}
\text{FCPartialFractionForm}\left(1,\left( \begin{array}{cc} \{x+1,-1\} & -1 \\ \end{array} \right),x\right)
1/(x^2 + 3)
ToFCPartialFractionForm[%, x]\frac{1}{x^2+3}
\text{FCPartialFractionForm}\left(0,\left( \begin{array}{cc} \left\{x-i \sqrt{3},-1\right\} & -\frac{i}{2 \sqrt{3}} \\ \left\{x+i \sqrt{3},-1\right\} & \frac{i}{2 \sqrt{3}} \\ \end{array} \right),x\right)
(-64*(-1 + z^2))/(15*(1 + z^2 + z^4))
ToFCPartialFractionForm[%, z]-\frac{64 \left(z^2-1\right)}{15 \left(z^4+z^2+1\right)}
\text{FCPartialFractionForm}\left(0,\left( \begin{array}{cc} \left\{z-\sqrt[3]{-1},-1\right\} & -\frac{32}{15} \\ \left\{z+\sqrt[3]{-1},-1\right\} & \frac{32}{15} \\ \left\{z-(-1)^{2/3},-1\right\} & \frac{32}{15} \\ \left\{z+(-1)^{2/3},-1\right\} & -\frac{32}{15} \\ \end{array} \right),z\right)