Optimal. Leaf size=6 \[ \log (2-x) \]
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Rubi [A] time = 0.01, antiderivative size = 6, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.100, Rules used = {1586, 31} \[ \log (2-x) \]
Antiderivative was successfully verified.
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Rule 31
Rule 1586
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*}
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Mathematica [A] time = 0.00, size = 4, normalized size = 0.67 \[ \log (x-2) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.67, size = 4, normalized size = 0.67 \[ \log \left (x - 2\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.28, size = 5, normalized size = 0.83 \[ \log \left ({\left | x - 2 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 5, normalized size = 0.83 \[ \ln \left (x -2\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.57, size = 4, normalized size = 0.67 \[ \log \left (x - 2\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.02, size = 4, normalized size = 0.67 \[ \ln \left (x-2\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.06, size = 3, normalized size = 0.50 \[ \log {\left (x - 2 \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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