Integrand size = 14, antiderivative size = 30 \[ \int \frac {\left (3-4 x+x^2\right )^2}{x^6} \, dx=-\frac {9}{5 x^5}+\frac {6}{x^4}-\frac {22}{3 x^3}+\frac {4}{x^2}-\frac {1}{x} \]
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Time = 0.01 (sec) , antiderivative size = 30, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.071, Rules used = {712} \[ \int \frac {\left (3-4 x+x^2\right )^2}{x^6} \, dx=-\frac {9}{5 x^5}+\frac {6}{x^4}-\frac {22}{3 x^3}+\frac {4}{x^2}-\frac {1}{x} \]
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Rule 712
Rubi steps \begin{align*} \text {integral}& = \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*}
Time = 0.00 (sec) , antiderivative size = 30, normalized size of antiderivative = 1.00 \[ \int \frac {\left (3-4 x+x^2\right )^2}{x^6} \, dx=-\frac {9}{5 x^5}+\frac {6}{x^4}-\frac {22}{3 x^3}+\frac {4}{x^2}-\frac {1}{x} \]
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Time = 16.55 (sec) , antiderivative size = 25, normalized size of antiderivative = 0.83
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 | \(-\frac {15 x^{4}-60 x^{3}+110 x^{2}-90 x +27}{15 x^{5}}\) | \(26\) |
parallelrisch | \(\frac {-15 x^{4}+60 x^{3}-110 x^{2}+90 x -27}{15 x^{5}}\) | \(26\) |
default | \(-\frac {9}{5 x^{5}}+\frac {6}{x^{4}}-\frac {22}{3 x^{3}}+\frac {4}{x^{2}}-\frac {1}{x}\) | \(27\) |
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Time = 0.34 (sec) , antiderivative size = 25, normalized size of antiderivative = 0.83 \[ \int \frac {\left (3-4 x+x^2\right )^2}{x^6} \, dx=-\frac {15 \, x^{4} - 60 \, x^{3} + 110 \, x^{2} - 90 \, x + 27}{15 \, x^{5}} \]
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Time = 0.04 (sec) , antiderivative size = 24, normalized size of antiderivative = 0.80 \[ \int \frac {\left (3-4 x+x^2\right )^2}{x^6} \, dx=\frac {- 15 x^{4} + 60 x^{3} - 110 x^{2} + 90 x - 27}{15 x^{5}} \]
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Time = 0.19 (sec) , antiderivative size = 25, normalized size of antiderivative = 0.83 \[ \int \frac {\left (3-4 x+x^2\right )^2}{x^6} \, dx=-\frac {15 \, x^{4} - 60 \, x^{3} + 110 \, x^{2} - 90 \, x + 27}{15 \, x^{5}} \]
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Time = 0.27 (sec) , antiderivative size = 25, normalized size of antiderivative = 0.83 \[ \int \frac {\left (3-4 x+x^2\right )^2}{x^6} \, dx=-\frac {15 \, x^{4} - 60 \, x^{3} + 110 \, x^{2} - 90 \, x + 27}{15 \, x^{5}} \]
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Time = 0.02 (sec) , antiderivative size = 23, normalized size of antiderivative = 0.77 \[ \int \frac {\left (3-4 x+x^2\right )^2}{x^6} \, dx=-\frac {x^4-4\,x^3+\frac {22\,x^2}{3}-6\,x+\frac {9}{5}}{x^5} \]
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