Optimal. Leaf size=27 \[ \frac{x^2}{2}-\frac{9}{2 x^2}-8 x+\frac{24}{x}+22 \log (x) \]
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Rubi [A] time = 0.0113032, 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} \[ \frac{x^2}{2}-\frac{9}{2 x^2}-8 x+\frac{24}{x}+22 \log (x) \]
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^3} \, dx &=\int \left (-8+\frac{9}{x^3}-\frac{24}{x^2}+\frac{22}{x}+x\right ) \, dx\\ &=-\frac{9}{2 x^2}+\frac{24}{x}-8 x+\frac{x^2}{2}+22 \log (x)\\ \end{align*}
Mathematica [A] time = 0.0007447, size = 27, normalized size = 1. \[ \frac{x^2}{2}-\frac{9}{2 x^2}-8 x+\frac{24}{x}+22 \log (x) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.043, size = 24, normalized size = 0.9 \begin{align*} -{\frac{9}{2\,{x}^{2}}}+24\,{x}^{-1}-8\,x+{\frac{{x}^{2}}{2}}+22\,\ln \left ( x \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.06307, size = 31, normalized size = 1.15 \begin{align*} \frac{1}{2} \, x^{2} - 8 \, x + \frac{3 \,{\left (16 \, x - 3\right )}}{2 \, x^{2}} + 22 \, \log \left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.72387, size = 69, normalized size = 2.56 \begin{align*} \frac{x^{4} - 16 \, x^{3} + 44 \, x^{2} \log \left (x\right ) + 48 \, x - 9}{2 \, x^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.09643, size = 22, normalized size = 0.81 \begin{align*} \frac{x^{2}}{2} - 8 x + 22 \log{\left (x \right )} + \frac{48 x - 9}{2 x^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.14068, size = 32, normalized size = 1.19 \begin{align*} \frac{1}{2} \, x^{2} - 8 \, x + \frac{3 \,{\left (16 \, x - 3\right )}}{2 \, x^{2}} + 22 \, \log \left ({\left | x \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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