Optimal. Leaf size=36 \[ -\frac {3}{2 x^6}+\frac {24}{5 x^5}-\frac {11}{2 x^4}+\frac {8}{3 x^3}-\frac {1}{2 x^2} \]
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Rubi [A]
time = 0.01, antiderivative size = 36, 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 {3}{2 x^6}+\frac {24}{5 x^5}-\frac {11}{2 x^4}+\frac {8}{3 x^3}-\frac {1}{2 x^2} \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^7} \, dx &=\int \left (\frac {9}{x^7}-\frac {24}{x^6}+\frac {22}{x^5}-\frac {8}{x^4}+\frac {1}{x^3}\right ) \, dx\\ &=-\frac {3}{2 x^6}+\frac {24}{5 x^5}-\frac {11}{2 x^4}+\frac {8}{3 x^3}-\frac {1}{2 x^2}\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 36, normalized size = 1.00 \begin {gather*} -\frac {3}{2 x^6}+\frac {24}{5 x^5}-\frac {11}{2 x^4}+\frac {8}{3 x^3}-\frac {1}{2 x^2} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.74, size = 27, normalized size = 0.75
method | result | size |
norman | \(\frac {-\frac {1}{2} x^{4}+\frac {8}{3} x^{3}-\frac {11}{2} x^{2}+\frac {24}{5} x -\frac {3}{2}}{x^{6}}\) | \(25\) |
risch | \(\frac {-\frac {1}{2} x^{4}+\frac {8}{3} x^{3}-\frac {11}{2} x^{2}+\frac {24}{5} x -\frac {3}{2}}{x^{6}}\) | \(25\) |
gosper | \(-\frac {15 x^{4}-80 x^{3}+165 x^{2}-144 x +45}{30 x^{6}}\) | \(26\) |
default | \(-\frac {3}{2 x^{6}}+\frac {24}{5 x^{5}}-\frac {11}{2 x^{4}}+\frac {8}{3 x^{3}}-\frac {1}{2 x^{2}}\) | \(27\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.27, size = 25, normalized size = 0.69 \begin {gather*} -\frac {15 \, x^{4} - 80 \, x^{3} + 165 \, x^{2} - 144 \, x + 45}{30 \, x^{6}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 3.02, size = 25, normalized size = 0.69 \begin {gather*} -\frac {15 \, x^{4} - 80 \, x^{3} + 165 \, x^{2} - 144 \, x + 45}{30 \, x^{6}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.06, size = 24, normalized size = 0.67 \begin {gather*} \frac {- 15 x^{4} + 80 x^{3} - 165 x^{2} + 144 x - 45}{30 x^{6}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.18, size = 25, normalized size = 0.69 \begin {gather*} -\frac {15 \, x^{4} - 80 \, x^{3} + 165 \, x^{2} - 144 \, x + 45}{30 \, x^{6}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.02, size = 25, normalized size = 0.69 \begin {gather*} -\frac {15\,x^4-80\,x^3+165\,x^2-144\,x+45}{30\,x^6} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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