Optimal. Leaf size=30 \[ \frac{4}{x^2}-\frac{22}{3 x^3}+\frac{6}{x^4}-\frac{9}{5 x^5}-\frac{1}{x} \]
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Rubi [A] time = 0.0116723, antiderivative size = 30, 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} \[ \frac{4}{x^2}-\frac{22}{3 x^3}+\frac{6}{x^4}-\frac{9}{5 x^5}-\frac{1}{x} \]
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^6} \, dx &=\int \left (\frac{9}{x^6}-\frac{24}{x^5}+\frac{22}{x^4}-\frac{8}{x^3}+\frac{1}{x^2}\right ) \, dx\\ &=-\frac{9}{5 x^5}+\frac{6}{x^4}-\frac{22}{3 x^3}+\frac{4}{x^2}-\frac{1}{x}\\ \end{align*}
Mathematica [A] time = 0.0006086, size = 30, normalized size = 1. \[ \frac{4}{x^2}-\frac{22}{3 x^3}+\frac{6}{x^4}-\frac{9}{5 x^5}-\frac{1}{x} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.043, size = 27, normalized size = 0.9 \begin{align*} -{\frac{9}{5\,{x}^{5}}}+6\,{x}^{-4}-{\frac{22}{3\,{x}^{3}}}+4\,{x}^{-2}-{x}^{-1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.00619, size = 34, normalized size = 1.13 \begin{align*} -\frac{15 \, x^{4} - 60 \, x^{3} + 110 \, x^{2} - 90 \, x + 27}{15 \, x^{5}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.88511, size = 69, normalized size = 2.3 \begin{align*} -\frac{15 \, x^{4} - 60 \, x^{3} + 110 \, x^{2} - 90 \, x + 27}{15 \, x^{5}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.105595, size = 26, normalized size = 0.87 \begin{align*} - \frac{15 x^{4} - 60 x^{3} + 110 x^{2} - 90 x + 27}{15 x^{5}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.11944, size = 34, normalized size = 1.13 \begin{align*} -\frac{15 \, x^{4} - 60 \, x^{3} + 110 \, x^{2} - 90 \, x + 27}{15 \, x^{5}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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