Optimal. Leaf size=25 \[ -\frac{11}{x^2}+\frac{8}{x^3}-\frac{9}{4 x^4}+\frac{8}{x}+\log (x) \]
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Rubi [A] time = 0.0112481, 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} \[ -\frac{11}{x^2}+\frac{8}{x^3}-\frac{9}{4 x^4}+\frac{8}{x}+\log (x) \]
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^5} \, dx &=\int \left (\frac{9}{x^5}-\frac{24}{x^4}+\frac{22}{x^3}-\frac{8}{x^2}+\frac{1}{x}\right ) \, dx\\ &=-\frac{9}{4 x^4}+\frac{8}{x^3}-\frac{11}{x^2}+\frac{8}{x}+\log (x)\\ \end{align*}
Mathematica [A] time = 0.0006945, size = 25, normalized size = 1. \[ -\frac{11}{x^2}+\frac{8}{x^3}-\frac{9}{4 x^4}+\frac{8}{x}+\log (x) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.043, size = 24, normalized size = 1. \begin{align*} -{\frac{9}{4\,{x}^{4}}}+8\,{x}^{-3}-11\,{x}^{-2}+8\,{x}^{-1}+\ln \left ( x \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.995359, size = 31, normalized size = 1.24 \begin{align*} \frac{32 \, x^{3} - 44 \, x^{2} + 32 \, x - 9}{4 \, x^{4}} + \log \left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.85166, size = 72, normalized size = 2.88 \begin{align*} \frac{4 \, x^{4} \log \left (x\right ) + 32 \, x^{3} - 44 \, x^{2} + 32 \, x - 9}{4 \, x^{4}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.105897, size = 22, normalized size = 0.88 \begin{align*} \log{\left (x \right )} + \frac{32 x^{3} - 44 x^{2} + 32 x - 9}{4 x^{4}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.13567, size = 32, normalized size = 1.28 \begin{align*} \frac{32 \, x^{3} - 44 \, x^{2} + 32 \, x - 9}{4 \, x^{4}} + \log \left ({\left | x \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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