Optimal. Leaf size=12 \[ \frac {1}{2} \log \left (x^2+2 x\right ) \]
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Rubi [A] time = 0.00, antiderivative size = 12, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.077, Rules used = {628} \begin {gather*} \frac {1}{2} \log \left (x^2+2 x\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 628
Rubi steps
\begin {align*} \int \frac {1+x}{2 x+x^2} \, dx &=\frac {1}{2} \log \left (2 x+x^2\right )\\ \end {align*}
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Mathematica [A] time = 0.00, size = 15, normalized size = 1.25 \begin {gather*} \frac {\log (x)}{2}+\frac {1}{2} \log (x+2) \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {1+x}{2 x+x^2} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 0.39, size = 10, normalized size = 0.83 \begin {gather*} \frac {1}{2} \, \log \left (x^{2} + 2 \, x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 13, normalized size = 1.08 \begin {gather*} \frac {1}{2} \, \log \left (2 \, {\left | \frac {1}{2} \, x^{2} + x \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 9, normalized size = 0.75 \begin {gather*} \frac {\ln \left (\left (x +2\right ) x \right )}{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.35, size = 10, normalized size = 0.83 \begin {gather*} \frac {1}{2} \, \log \left (x^{2} + 2 \, x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.18, size = 8, normalized size = 0.67 \begin {gather*} \frac {\ln \left (x\,\left (x+2\right )\right )}{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.09, size = 8, normalized size = 0.67 \begin {gather*} \frac {\log {\left (x^{2} + 2 x \right )}}{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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