Optimal. Leaf size=30 \[ -\frac {9}{5 x^5}+\frac {6}{x^4}-\frac {22}{3 x^3}+\frac {4}{x^2}-\frac {1}{x} \]
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Rubi [A] time = 0.01, antiderivative size = 30, 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} \[ \frac {4}{x^2}-\frac {22}{3 x^3}+\frac {6}{x^4}-\frac {9}{5 x^5}-\frac {1}{x} \]
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*}
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Mathematica [A] time = 0.00, size = 30, normalized size = 1.00 \[ -\frac {9}{5 x^5}+\frac {6}{x^4}-\frac {22}{3 x^3}+\frac {4}{x^2}-\frac {1}{x} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.79, size = 25, normalized size = 0.83 \[ -\frac {15 \, x^{4} - 60 \, x^{3} + 110 \, x^{2} - 90 \, x + 27}{15 \, x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 25, normalized size = 0.83 \[ -\frac {15 \, x^{4} - 60 \, x^{3} + 110 \, x^{2} - 90 \, x + 27}{15 \, x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.05, size = 27, normalized size = 0.90 \[ -\frac {1}{x}+\frac {4}{x^{2}}-\frac {22}{3 x^{3}}+\frac {6}{x^{4}}-\frac {9}{5 x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.02, size = 25, normalized size = 0.83 \[ -\frac {15 \, x^{4} - 60 \, x^{3} + 110 \, x^{2} - 90 \, x + 27}{15 \, x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.02, size = 23, normalized size = 0.77 \[ -\frac {x^4-4\,x^3+\frac {22\,x^2}{3}-6\,x+\frac {9}{5}}{x^5} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.11, size = 24, normalized size = 0.80 \[ \frac {- 15 x^{4} + 60 x^{3} - 110 x^{2} + 90 x - 27}{15 x^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
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