Optimal. Leaf size=27 \[ \frac{x^4}{4}-\frac{8 x^3}{3}+11 x^2-24 x+9 \log (x) \]
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Rubi [A] time = 0.0092649, antiderivative size = 27, 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} \[ \frac{x^4}{4}-\frac{8 x^3}{3}+11 x^2-24 x+9 \log (x) \]
Antiderivative was successfully verified.
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Rule 698
Rubi steps
\begin{align*} \int \frac{\left (3-4 x+x^2\right )^2}{x} \, dx &=\int \left (-24+\frac{9}{x}+22 x-8 x^2+x^3\right ) \, dx\\ &=-24 x+11 x^2-\frac{8 x^3}{3}+\frac{x^4}{4}+9 \log (x)\\ \end{align*}
Mathematica [A] time = 0.0006272, size = 27, normalized size = 1. \[ \frac{x^4}{4}-\frac{8 x^3}{3}+11 x^2-24 x+9 \log (x) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.038, size = 24, normalized size = 0.9 \begin{align*} -24\,x+11\,{x}^{2}-{\frac{8\,{x}^{3}}{3}}+{\frac{{x}^{4}}{4}}+9\,\ln \left ( x \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.960832, size = 31, normalized size = 1.15 \begin{align*} \frac{1}{4} \, x^{4} - \frac{8}{3} \, x^{3} + 11 \, x^{2} - 24 \, x + 9 \, \log \left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.63101, size = 62, normalized size = 2.3 \begin{align*} \frac{1}{4} \, x^{4} - \frac{8}{3} \, x^{3} + 11 \, x^{2} - 24 \, x + 9 \, \log \left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.082447, size = 24, normalized size = 0.89 \begin{align*} \frac{x^{4}}{4} - \frac{8 x^{3}}{3} + 11 x^{2} - 24 x + 9 \log{\left (x \right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.14016, size = 32, normalized size = 1.19 \begin{align*} \frac{1}{4} \, x^{4} - \frac{8}{3} \, x^{3} + 11 \, x^{2} - 24 \, x + 9 \, \log \left ({\left | x \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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