Optimal. Leaf size=19 \[ \frac{x^2}{2}+6 x+17 \log (2-x) \]
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Rubi [A] time = 0.009546, antiderivative size = 19, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 14, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.071, Rules used = {698} \[ \frac{x^2}{2}+6 x+17 \log (2-x) \]
Antiderivative was successfully verified.
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Rule 698
Rubi steps
\begin{align*} \int \frac{5+4 x+x^2}{-2+x} \, dx &=\int \left (6+\frac{17}{-2+x}+x\right ) \, dx\\ &=6 x+\frac{x^2}{2}+17 \log (2-x)\\ \end{align*}
Mathematica [A] time = 0.0033058, size = 18, normalized size = 0.95 \[ \frac{x^2}{2}+6 x+17 \log (x-2)-14 \]
Antiderivative was successfully verified.
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Maple [A] time = 0.04, size = 16, normalized size = 0.8 \begin{align*}{\frac{{x}^{2}}{2}}+6\,x+17\,\ln \left ( -2+x \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.959847, size = 20, normalized size = 1.05 \begin{align*} \frac{1}{2} \, x^{2} + 6 \, x + 17 \, \log \left (x - 2\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.92843, size = 42, normalized size = 2.21 \begin{align*} \frac{1}{2} \, x^{2} + 6 \, x + 17 \, \log \left (x - 2\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.076976, size = 14, normalized size = 0.74 \begin{align*} \frac{x^{2}}{2} + 6 x + 17 \log{\left (x - 2 \right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.13047, size = 22, normalized size = 1.16 \begin{align*} \frac{1}{2} \, x^{2} + 6 \, x + 17 \, \log \left ({\left | x - 2 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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