Optimal. Leaf size=12 \[ \frac{1}{x}+3 \log (1-x) \]
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Rubi [A] time = 0.0213736, antiderivative size = 12, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 22, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.091, Rules used = {1593, 893} \[ \frac{1}{x}+3 \log (1-x) \]
Antiderivative was successfully verified.
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Rule 1593
Rule 893
Rubi steps
\begin{align*} \int \frac{1-x+3 x^2}{-x^2+x^3} \, dx &=\int \frac{1-x+3 x^2}{(-1+x) x^2} \, dx\\ &=\int \left (\frac{3}{-1+x}-\frac{1}{x^2}\right ) \, dx\\ &=\frac{1}{x}+3 \log (1-x)\\ \end{align*}
Mathematica [A] time = 0.0033556, size = 12, normalized size = 1. \[ \frac{1}{x}+3 \log (1-x) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.006, size = 11, normalized size = 0.9 \begin{align*} 3\,\ln \left ( x-1 \right ) +{x}^{-1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.10043, size = 14, normalized size = 1.17 \begin{align*} \frac{1}{x} + 3 \, \log \left (x - 1\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.45993, size = 32, normalized size = 2.67 \begin{align*} \frac{3 \, x \log \left (x - 1\right ) + 1}{x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.083881, size = 8, normalized size = 0.67 \begin{align*} 3 \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 = 1.1625, size = 15, normalized size = 1.25 \begin{align*} \frac{1}{x} + 3 \, \log \left ({\left | x - 1 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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