Optimal. Leaf size=13 \[ 2 \log (x+2)-\log (x+1) \]
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Rubi [A] time = 0.0034389, antiderivative size = 13, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 12, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.167, Rules used = {632, 31} \[ 2 \log (x+2)-\log (x+1) \]
Antiderivative was successfully verified.
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Rule 632
Rule 31
Rubi steps
\begin{align*} \int \frac{x}{2+3 x+x^2} \, dx &=2 \int \frac{1}{2+x} \, dx-\int \frac{1}{1+x} \, dx\\ &=-\log (1+x)+2 \log (2+x)\\ \end{align*}
Mathematica [A] time = 0.0034576, size = 13, normalized size = 1. \[ 2 \log (x+2)-\log (x+1) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.001, size = 14, normalized size = 1.1 \begin{align*} -\ln \left ( 1+x \right ) +2\,\ln \left ( 2+x \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.948218, size = 18, normalized size = 1.38 \begin{align*} 2 \, \log \left (x + 2\right ) - \log \left (x + 1\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.70567, size = 36, normalized size = 2.77 \begin{align*} 2 \, \log \left (x + 2\right ) - \log \left (x + 1\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.088606, size = 10, normalized size = 0.77 \begin{align*} - \log{\left (x + 1 \right )} + 2 \log{\left (x + 2 \right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.08687, size = 20, normalized size = 1.54 \begin{align*} 2 \, \log \left ({\left | x + 2 \right |}\right ) - \log \left ({\left | x + 1 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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