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 = {712}
\begin {gather*} -\frac {9}{5 x^5}+\frac {6}{x^4}-\frac {22}{3 x^3}+\frac {4}{x^2}-\frac {1}{x} \end {gather*}
Antiderivative was successfully verified.
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Rule 712
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 \begin {gather*} -\frac {9}{5 x^5}+\frac {6}{x^4}-\frac {22}{3 x^3}+\frac {4}{x^2}-\frac {1}{x} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.66, size = 27, normalized size = 0.90
method | result | size |
norman | \(\frac {-x^{4}+4 x^{3}-\frac {22}{3} x^{2}+6 x -\frac {9}{5}}{x^{5}}\) | \(25\) |
risch | \(\frac {-x^{4}+4 x^{3}-\frac {22}{3} x^{2}+6 x -\frac {9}{5}}{x^{5}}\) | \(25\) |
gosper | \(-\frac {15 x^{4}-60 x^{3}+110 x^{2}-90 x +27}{15 x^{5}}\) | \(26\) |
default | \(-\frac {9}{5 x^{5}}+\frac {6}{x^{4}}-\frac {22}{3 x^{3}}+\frac {4}{x^{2}}-\frac {1}{x}\) | \(27\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.28, size = 25, normalized size = 0.83 \begin {gather*} -\frac {15 \, x^{4} - 60 \, x^{3} + 110 \, x^{2} - 90 \, x + 27}{15 \, x^{5}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 2.50, size = 25, normalized size = 0.83 \begin {gather*} -\frac {15 \, x^{4} - 60 \, x^{3} + 110 \, x^{2} - 90 \, x + 27}{15 \, x^{5}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.04, size = 24, normalized size = 0.80 \begin {gather*} \frac {- 15 x^{4} + 60 x^{3} - 110 x^{2} + 90 x - 27}{15 x^{5}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.09, size = 25, normalized size = 0.83 \begin {gather*} -\frac {15 \, x^{4} - 60 \, x^{3} + 110 \, x^{2} - 90 \, x + 27}{15 \, x^{5}} \end {gather*}
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 \begin {gather*} -\frac {x^4-4\,x^3+\frac {22\,x^2}{3}-6\,x+\frac {9}{5}}{x^5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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