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 = 0.01, antiderivative size = 27, normalized size of antiderivative = 1.00, 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*}
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Mathematica [A] time = 0.00, size = 27, normalized size = 1.00 \[ \frac {x^2}{2}-\frac {9}{2 x^2}-8 x+\frac {24}{x}+22 \log (x) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.84, size = 25, normalized size = 0.93 \[ \frac {x^{4} - 16 \, x^{3} + 44 \, x^{2} \log \relax (x) + 48 \, x - 9}{2 \, x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 24, normalized size = 0.89 \[ \frac {1}{2} \, x^{2} - 8 \, x + \frac {3 \, {\left (16 \, x - 3\right )}}{2 \, x^{2}} + 22 \, \log \left ({\left | x \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.05, size = 24, normalized size = 0.89 \[ \frac {x^{2}}{2}-8 x +22 \ln \relax (x )+\frac {24}{x}-\frac {9}{2 x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.00, size = 23, normalized size = 0.85 \[ \frac {1}{2} \, x^{2} - 8 \, x + \frac {3 \, {\left (16 \, x - 3\right )}}{2 \, x^{2}} + 22 \, \log \relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 22, normalized size = 0.81 \[ 22\,\ln \relax (x)-8\,x+\frac {24\,x-\frac {9}{2}}{x^2}+\frac {x^2}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.10, size = 22, normalized size = 0.81 \[ \frac {x^{2}}{2} - 8 x + 22 \log {\relax (x )} + \frac {48 x - 9}{2 x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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