Optimal. Leaf size=12 \[ x+\log (1-x)-\log (x) \]
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Rubi [A] time = 0.03, antiderivative size = 12, 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, 1802} \begin {gather*} x+\log (1-x)-\log (x) \end {gather*}
Antiderivative was successfully verified.
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Rule 1593
Rule 1802
Rubi steps
\begin {align*} \int \frac {1+x^3}{-x+x^3} \, dx &=\int \frac {1+x^3}{x \left (-1+x^2\right )} \, dx\\ &=\int \left (1+\frac {1}{-1+x}-\frac {1}{x}\right ) \, dx\\ &=x+\log (1-x)-\log (x)\\ \end {align*}
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Mathematica [A] time = 0.00, size = 12, normalized size = 1.00 \begin {gather*} x+\log (1-x)-\log (x) \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {1+x^3}{-x+x^3} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 1.56, size = 10, normalized size = 0.83 \begin {gather*} x + \log \left (x - 1\right ) - \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.37, size = 12, normalized size = 1.00 \begin {gather*} x + \log \left ({\left | x - 1 \right |}\right ) - \log \left ({\left | x \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 11, normalized size = 0.92 \begin {gather*} x -\ln \relax (x )+\ln \left (x -1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.01, size = 10, normalized size = 0.83 \begin {gather*} x + \log \left (x - 1\right ) - \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 2.14, size = 10, normalized size = 0.83 \begin {gather*} x-2\,\mathrm {atanh}\left (2\,x-1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.10, size = 8, normalized size = 0.67 \begin {gather*} x - \log {\relax (x )} + \log {\left (x - 1 \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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