Optimal. Leaf size=4 \[ \log (x+2) \]
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Rubi [A] time = 0.0105952, antiderivative size = 4, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 26, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.077, Rules used = {1586, 31} \[ \log (x+2) \]
Antiderivative was successfully verified.
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Rule 1586
Rule 31
Rubi steps
\begin{align*} \int \frac{2-x-2 x^2+x^3}{4-5 x^2+x^4} \, dx &=\int \frac{1}{2+x} \, dx\\ &=\log (2+x)\\ \end{align*}
Mathematica [A] time = 0.0011245, size = 4, normalized size = 1. \[ \log (x+2) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.002, size = 5, normalized size = 1.3 \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 = 0.968118, size = 5, normalized size = 1.25 \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 = 1.98294, size = 16, normalized size = 4. \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 = 0.061844, size = 3, normalized size = 0.75 \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 = 1.06881, size = 7, normalized size = 1.75 \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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