Optimal. Leaf size=17 \[ x+\frac {1}{x}+2 \log (1-x)-\log (x) \]
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Rubi [A] time = 0.03, antiderivative size = 17, normalized size of antiderivative = 1.00, 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*}
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Mathematica [A] time = 0.00, size = 17, normalized size = 1.00 \[ x+\frac {1}{x}+2 \log (1-x)-\log (x) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.70, size = 21, normalized size = 1.24 \[ \frac {x^{2} + 2 \, x \log \left (x - 1\right ) - x \log \relax (x) + 1}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.32, size = 17, normalized size = 1.00 \[ x + \frac {1}{x} + 2 \, \log \left ({\left | x - 1 \right |}\right ) - \log \left ({\left | x \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 16, normalized size = 0.94 \[ x -\ln \relax (x )+2 \ln \left (x -1\right )+\frac {1}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.89, size = 15, normalized size = 0.88 \[ x + \frac {1}{x} + 2 \, \log \left (x - 1\right ) - \log \relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 15, normalized size = 0.88 \[ x+2\,\ln \left (x-1\right )-\ln \relax (x)+\frac {1}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.11, size = 14, normalized size = 0.82 \[ x - \log {\relax (x )} + 2 \log {\left (x - 1 \right )} + \frac {1}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
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