Optimal. Leaf size=17 \[ \log (1-x)+2 \log (x)-3 \log (x+1) \]
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Rubi [A] time = 0.02, antiderivative size = 17, normalized size of antiderivative = 1.00, 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 801
Rule 1593
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*}
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Mathematica [A] time = 0.01, size = 17, normalized size = 1.00 \[ \log (1-x)+2 \log (x)-3 \log (x+1) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.69, size = 15, normalized size = 0.88 \[ -3 \, \log \left (x + 1\right ) + \log \left (x - 1\right ) + 2 \, \log \relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.36, size = 18, normalized size = 1.06 \[ -3 \, \log \left ({\left | x + 1 \right |}\right ) + \log \left ({\left | x - 1 \right |}\right ) + 2 \, \log \left ({\left | x \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 16, normalized size = 0.94 \[ 2 \ln \relax (x )+\ln \left (x -1\right )-3 \ln \left (x +1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.61, size = 15, normalized size = 0.88 \[ -3 \, \log \left (x + 1\right ) + \log \left (x - 1\right ) + 2 \, \log \relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.06, size = 15, normalized size = 0.88 \[ \ln \left (x-1\right )-3\,\ln \left (x+1\right )+2\,\ln \relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.13, size = 15, normalized size = 0.88 \[ 2 \log {\relax (x )} + \log {\left (x - 1 \right )} - 3 \log {\left (x + 1 \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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