Optimal. Leaf size=12 \[ x+\log (1-x)-\log (x) \]
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Rubi [A] time = 0.0293969, antiderivative size = 12, 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, 1802} \[ x+\log (1-x)-\log (x) \]
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*}
Mathematica [A] time = 0.0044697, size = 12, normalized size = 1. \[ x+\log (1-x)-\log (x) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.005, size = 11, normalized size = 0.9 \begin{align*} x+\ln \left ( x-1 \right ) -\ln \left ( x \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.05532, size = 14, normalized size = 1.17 \begin{align*} x + \log \left (x - 1\right ) - \log \left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.71472, size = 34, normalized size = 2.83 \begin{align*} x + \log \left (x - 1\right ) - \log \left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.089337, size = 8, normalized size = 0.67 \begin{align*} x - \log{\left (x \right )} + \log{\left (x - 1 \right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.12206, size = 16, normalized size = 1.33 \begin{align*} x + \log \left ({\left | x - 1 \right |}\right ) - \log \left ({\left | x \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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