Optimal. Leaf size=17 \[ \log (1-x)+2 \log (x)-3 \log (x+1) \]
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Rubi [A] time = 0.0181711, antiderivative size = 17, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.133, Rules used = {1593, 801} \[ \log (1-x)+2 \log (x)-3 \log (x+1) \]
Antiderivative was successfully verified.
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Rule 1593
Rule 801
Rubi steps
\begin{align*} \int \frac{-2+4 x}{-x+x^3} \, dx &=\int \frac{-2+4 x}{x \left (-1+x^2\right )} \, dx\\ &=\int \left (\frac{1}{-1+x}+\frac{2}{x}-\frac{3}{1+x}\right ) \, dx\\ &=\log (1-x)+2 \log (x)-3 \log (1+x)\\ \end{align*}
Mathematica [A] time = 0.0055575, size = 17, normalized size = 1. \[ \log (1-x)+2 \log (x)-3 \log (x+1) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.004, size = 16, normalized size = 0.9 \begin{align*} \ln \left ( x-1 \right ) +2\,\ln \left ( x \right ) -3\,\ln \left ( 1+x \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.97238, size = 20, normalized size = 1.18 \begin{align*} -3 \, \log \left (x + 1\right ) + \log \left (x - 1\right ) + 2 \, \log \left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 0.999472, size = 53, normalized size = 3.12 \begin{align*} -3 \, \log \left (x + 1\right ) + \log \left (x - 1\right ) + 2 \, \log \left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.110978, size = 15, normalized size = 0.88 \begin{align*} 2 \log{\left (x \right )} + \log{\left (x - 1 \right )} - 3 \log{\left (x + 1 \right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.18553, size = 24, normalized size = 1.41 \begin{align*} -3 \, \log \left ({\left | x + 1 \right |}\right ) + \log \left ({\left | x - 1 \right |}\right ) + 2 \, \log \left ({\left | x \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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