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