Optimal. Leaf size=11 \[ 2 \log (x)-\log (x+1) \]
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Rubi [A] time = 0.0051985, antiderivative size = 11, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.091, Rules used = {631} \[ 2 \log (x)-\log (x+1) \]
Antiderivative was successfully verified.
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Rule 631
Rubi steps
\begin{align*} \int \frac{2+x}{x+x^2} \, dx &=\int \left (\frac{1}{-1-x}+\frac{2}{x}\right ) \, dx\\ &=2 \log (x)-\log (1+x)\\ \end{align*}
Mathematica [A] time = 0.001957, size = 11, normalized size = 1. \[ 2 \log (x)-\log (x+1) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.005, size = 12, normalized size = 1.1 \begin{align*} 2\,\ln \left ( x \right ) -\ln \left ( 1+x \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.932655, size = 15, normalized size = 1.36 \begin{align*} -\log \left (x + 1\right ) + 2 \, \log \left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 0.717003, size = 32, normalized size = 2.91 \begin{align*} -\log \left (x + 1\right ) + 2 \, \log \left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.086883, size = 8, normalized size = 0.73 \begin{align*} 2 \log{\left (x \right )} - \log{\left (x + 1 \right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.09685, size = 18, normalized size = 1.64 \begin{align*} -\log \left ({\left | x + 1 \right |}\right ) + 2 \, \log \left ({\left | x \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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