Optimal. Leaf size=21 \[ \frac{12}{x^2}-\frac{3}{x^3}+x-\frac{22}{x}-8 \log (x) \]
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Rubi [A] time = 0.0107885, antiderivative size = 21, 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} \[ \frac{12}{x^2}-\frac{3}{x^3}+x-\frac{22}{x}-8 \log (x) \]
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^4} \, dx &=\int \left (1+\frac{9}{x^4}-\frac{24}{x^3}+\frac{22}{x^2}-\frac{8}{x}\right ) \, dx\\ &=-\frac{3}{x^3}+\frac{12}{x^2}-\frac{22}{x}+x-8 \log (x)\\ \end{align*}
Mathematica [A] time = 0.0006489, size = 21, normalized size = 1. \[ \frac{12}{x^2}-\frac{3}{x^3}+x-\frac{22}{x}-8 \log (x) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.045, size = 22, normalized size = 1.1 \begin{align*} -3\,{x}^{-3}+12\,{x}^{-2}-22\,{x}^{-1}+x-8\,\ln \left ( x \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.985285, size = 28, normalized size = 1.33 \begin{align*} x - \frac{22 \, x^{2} - 12 \, x + 3}{x^{3}} - 8 \, \log \left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.6889, size = 62, normalized size = 2.95 \begin{align*} \frac{x^{4} - 8 \, x^{3} \log \left (x\right ) - 22 \, x^{2} + 12 \, x - 3}{x^{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.100731, size = 19, normalized size = 0.9 \begin{align*} x - 8 \log{\left (x \right )} - \frac{22 x^{2} - 12 x + 3}{x^{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.13196, size = 30, normalized size = 1.43 \begin{align*} x - \frac{22 \, x^{2} - 12 \, x + 3}{x^{3}} - 8 \, \log \left ({\left | x \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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