Optimal. Leaf size=17 \[ \frac {x^2}{2}-2 x+6 \log (x+2) \]
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Rubi [A] time = 0.01, antiderivative size = 17, 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 = {697} \[ \frac {x^2}{2}-2 x+6 \log (x+2) \]
Antiderivative was successfully verified.
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Rule 697
Rubi steps
\begin {align*} \int \frac {2+x^2}{2+x} \, dx &=\int \left (-2+x+\frac {6}{2+x}\right ) \, dx\\ &=-2 x+\frac {x^2}{2}+6 \log (2+x)\\ \end {align*}
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Mathematica [A] time = 0.00, size = 18, normalized size = 1.06 \[ \frac {x^2}{2}-2 x+6 \log (x+2)-6 \]
Antiderivative was successfully verified.
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fricas [A] time = 0.58, size = 15, normalized size = 0.88 \[ \frac {1}{2} \, x^{2} - 2 \, x + 6 \, \log \left (x + 2\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.37, size = 16, normalized size = 0.94 \[ \frac {1}{2} \, x^{2} - 2 \, x + 6 \, \log \left ({\left | x + 2 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 16, normalized size = 0.94 \[ \frac {x^{2}}{2}-2 x +6 \ln \left (x +2\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.44, size = 15, normalized size = 0.88 \[ \frac {1}{2} \, x^{2} - 2 \, x + 6 \, \log \left (x + 2\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 15, normalized size = 0.88 \[ 6\,\ln \left (x+2\right )-2\,x+\frac {x^2}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.07, size = 14, normalized size = 0.82 \[ \frac {x^{2}}{2} - 2 x + 6 \log {\left (x + 2 \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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