Optimal. Leaf size=11 \[ 2 \log (x)-\log (x+1) \]
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Rubi [A] time = 0.01, antiderivative size = 11, normalized size of antiderivative = 1.00, 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*}
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Mathematica [A] time = 0.00, size = 11, normalized size = 1.00 \[ 2 \log (x)-\log (x+1) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.39, size = 11, normalized size = 1.00 \[ -\log \left (x + 1\right ) + 2 \, \log \relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.01, size = 13, normalized size = 1.18 \[ -\log \left ({\left | x + 1 \right |}\right ) + 2 \, \log \left ({\left | x \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 12, normalized size = 1.09 \[ 2 \ln \relax (x )-\ln \left (x +1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.49, size = 11, normalized size = 1.00 \[ -\log \left (x + 1\right ) + 2 \, \log \relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.10, size = 11, normalized size = 1.00 \[ 2\,\ln \relax (x)-\ln \left (x+1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.10, size = 8, normalized size = 0.73 \[ 2 \log {\relax (x )} - \log {\left (x + 1 \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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