Optimal. Leaf size=24 \[ \frac{x^3}{6}-\frac{3 x^2}{4}+4 x-12 \log (x+3) \]
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Rubi [A] time = 0.0188889, antiderivative size = 24, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.133, Rules used = {1593, 772} \[ \frac{x^3}{6}-\frac{3 x^2}{4}+4 x-12 \log (x+3) \]
Antiderivative was successfully verified.
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Rule 1593
Rule 772
Rubi steps
\begin{align*} \int \frac{-x+x^3}{6+2 x} \, dx &=\int \frac{x \left (-1+x^2\right )}{6+2 x} \, dx\\ &=\int \left (4-\frac{3 x}{2}+\frac{x^2}{2}-\frac{12}{3+x}\right ) \, dx\\ &=4 x-\frac{3 x^2}{4}+\frac{x^3}{6}-12 \log (3+x)\\ \end{align*}
Mathematica [A] time = 0.0058096, size = 31, normalized size = 1.29 \[ \frac{1}{2} \left (\frac{x^3}{3}-\frac{3 x^2}{2}+8 x-24 \log (x+3)+\frac{93}{2}\right ) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 21, normalized size = 0.9 \begin{align*} 4\,x-{\frac{3\,{x}^{2}}{4}}+{\frac{{x}^{3}}{6}}-12\,\ln \left ( 3+x \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.04315, size = 27, normalized size = 1.12 \begin{align*} \frac{1}{6} \, x^{3} - \frac{3}{4} \, x^{2} + 4 \, x - 12 \, \log \left (x + 3\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 0.965709, size = 55, normalized size = 2.29 \begin{align*} \frac{1}{6} \, x^{3} - \frac{3}{4} \, x^{2} + 4 \, x - 12 \, \log \left (x + 3\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.072741, size = 20, normalized size = 0.83 \begin{align*} \frac{x^{3}}{6} - \frac{3 x^{2}}{4} + 4 x - 12 \log{\left (x + 3 \right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.15991, size = 28, normalized size = 1.17 \begin{align*} \frac{1}{6} \, x^{3} - \frac{3}{4} \, x^{2} + 4 \, x - 12 \, \log \left ({\left | x + 3 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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