Optimal. Leaf size=17 \[ x+\frac{1}{x}+2 \log (1-x)-\log (x) \]
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Rubi [A] time = 0.0295838, antiderivative size = 17, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 17, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.118, Rules used = {1593, 1620} \[ x+\frac{1}{x}+2 \log (1-x)-\log (x) \]
Antiderivative was successfully verified.
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Rule 1593
Rule 1620
Rubi steps
\begin{align*} \int \frac{1+x^3}{-x^2+x^3} \, dx &=\int \frac{1+x^3}{(-1+x) x^2} \, dx\\ &=\int \left (1+\frac{2}{-1+x}-\frac{1}{x^2}-\frac{1}{x}\right ) \, dx\\ &=\frac{1}{x}+x+2 \log (1-x)-\log (x)\\ \end{align*}
Mathematica [A] time = 0.0035802, size = 17, normalized size = 1. \[ x+\frac{1}{x}+2 \log (1-x)-\log (x) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.006, size = 16, normalized size = 0.9 \begin{align*} x+2\,\ln \left ( x-1 \right ) +{x}^{-1}-\ln \left ( x \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.09659, size = 20, normalized size = 1.18 \begin{align*} x + \frac{1}{x} + 2 \, \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 = 1.72478, size = 55, normalized size = 3.24 \begin{align*} \frac{x^{2} + 2 \, x \log \left (x - 1\right ) - x \log \left (x\right ) + 1}{x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.09717, size = 14, normalized size = 0.82 \begin{align*} x - \log{\left (x \right )} + 2 \log{\left (x - 1 \right )} + \frac{1}{x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.11114, size = 23, normalized size = 1.35 \begin{align*} x + \frac{1}{x} + 2 \, \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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