Optimal. Leaf size=6 \[ \log (2-x) \]
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Rubi [A] time = 0.0079106, antiderivative size = 6, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.1, Rules used = {1586, 31} \[ \log (2-x) \]
Antiderivative was successfully verified.
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Rule 1586
Rule 31
Rubi steps
\begin{align*} \int \frac{x+x^2}{-2 x-x^2+x^3} \, dx &=\int \frac{1}{-2+x} \, dx\\ &=\log (2-x)\\ \end{align*}
Mathematica [A] time = 0.0007617, size = 4, normalized size = 0.67 \[ \log (x-2) \]
Antiderivative was successfully verified.
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Maple [A] time = 0., size = 5, normalized size = 0.8 \begin{align*} \ln \left ( -2+x \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.00519, size = 5, normalized size = 0.83 \begin{align*} \log \left (x - 2\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 0.954969, size = 16, normalized size = 2.67 \begin{align*} \log \left (x - 2\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.058289, size = 3, normalized size = 0.5 \begin{align*} \log{\left (x - 2 \right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.104, size = 7, normalized size = 1.17 \begin{align*} \log \left ({\left | x - 2 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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