Optimal. Leaf size=25 \[ \frac{x^3}{3}-4 x^2+22 x-\frac{9}{x}-24 \log (x) \]
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Rubi [A] time = 0.01157, antiderivative size = 25, 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} \[ \frac{x^3}{3}-4 x^2+22 x-\frac{9}{x}-24 \log (x) \]
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^2} \, dx &=\int \left (22+\frac{9}{x^2}-\frac{24}{x}-8 x+x^2\right ) \, dx\\ &=-\frac{9}{x}+22 x-4 x^2+\frac{x^3}{3}-24 \log (x)\\ \end{align*}
Mathematica [A] time = 0.00066, size = 25, normalized size = 1. \[ \frac{x^3}{3}-4 x^2+22 x-\frac{9}{x}-24 \log (x) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.044, size = 24, normalized size = 1. \begin{align*} -9\,{x}^{-1}+22\,x-4\,{x}^{2}+{\frac{{x}^{3}}{3}}-24\,\ln \left ( x \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.954974, size = 31, normalized size = 1.24 \begin{align*} \frac{1}{3} \, x^{3} - 4 \, x^{2} + 22 \, x - \frac{9}{x} - 24 \, \log \left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.68577, size = 68, normalized size = 2.72 \begin{align*} \frac{x^{4} - 12 \, x^{3} + 66 \, x^{2} - 72 \, x \log \left (x\right ) - 27}{3 \, x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.087531, size = 20, normalized size = 0.8 \begin{align*} \frac{x^{3}}{3} - 4 x^{2} + 22 x - 24 \log{\left (x \right )} - \frac{9}{x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.10401, size = 32, normalized size = 1.28 \begin{align*} \frac{1}{3} \, x^{3} - 4 \, x^{2} + 22 \, x - \frac{9}{x} - 24 \, \log \left ({\left | x \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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