Integrand size = 14, antiderivative size = 27 \[ \int \frac {\left (3-4 x+x^2\right )^2}{x} \, dx=-24 x+11 x^2-\frac {8 x^3}{3}+\frac {x^4}{4}+9 \log (x) \]
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Time = 0.01 (sec) , antiderivative size = 27, 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} \[ \int \frac {\left (3-4 x+x^2\right )^2}{x} \, dx=\frac {x^4}{4}-\frac {8 x^3}{3}+11 x^2-24 x+9 \log (x) \]
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Rule 712
Rubi steps \begin{align*} \text {integral}& = \int \left (-24+\frac {9}{x}+22 x-8 x^2+x^3\right ) \, dx \\ & = -24 x+11 x^2-\frac {8 x^3}{3}+\frac {x^4}{4}+9 \log (x) \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 27, normalized size of antiderivative = 1.00 \[ \int \frac {\left (3-4 x+x^2\right )^2}{x} \, dx=-24 x+11 x^2-\frac {8 x^3}{3}+\frac {x^4}{4}+9 \log (x) \]
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Time = 16.89 (sec) , antiderivative size = 24, normalized size of antiderivative = 0.89
method | result | size |
default | \(-24 x +11 x^{2}-\frac {8 x^{3}}{3}+\frac {x^{4}}{4}+9 \ln \left (x \right )\) | \(24\) |
norman | \(-24 x +11 x^{2}-\frac {8 x^{3}}{3}+\frac {x^{4}}{4}+9 \ln \left (x \right )\) | \(24\) |
risch | \(-24 x +11 x^{2}-\frac {8 x^{3}}{3}+\frac {x^{4}}{4}+9 \ln \left (x \right )\) | \(24\) |
parallelrisch | \(-24 x +11 x^{2}-\frac {8 x^{3}}{3}+\frac {x^{4}}{4}+9 \ln \left (x \right )\) | \(24\) |
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none
Time = 0.26 (sec) , antiderivative size = 23, normalized size of antiderivative = 0.85 \[ \int \frac {\left (3-4 x+x^2\right )^2}{x} \, dx=\frac {1}{4} \, x^{4} - \frac {8}{3} \, x^{3} + 11 \, x^{2} - 24 \, x + 9 \, \log \left (x\right ) \]
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Time = 0.03 (sec) , antiderivative size = 24, normalized size of antiderivative = 0.89 \[ \int \frac {\left (3-4 x+x^2\right )^2}{x} \, dx=\frac {x^{4}}{4} - \frac {8 x^{3}}{3} + 11 x^{2} - 24 x + 9 \log {\left (x \right )} \]
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none
Time = 0.20 (sec) , antiderivative size = 23, normalized size of antiderivative = 0.85 \[ \int \frac {\left (3-4 x+x^2\right )^2}{x} \, dx=\frac {1}{4} \, x^{4} - \frac {8}{3} \, x^{3} + 11 \, x^{2} - 24 \, x + 9 \, \log \left (x\right ) \]
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none
Time = 0.26 (sec) , antiderivative size = 24, normalized size of antiderivative = 0.89 \[ \int \frac {\left (3-4 x+x^2\right )^2}{x} \, dx=\frac {1}{4} \, x^{4} - \frac {8}{3} \, x^{3} + 11 \, x^{2} - 24 \, x + 9 \, \log \left ({\left | x \right |}\right ) \]
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Time = 0.02 (sec) , antiderivative size = 23, normalized size of antiderivative = 0.85 \[ \int \frac {\left (3-4 x+x^2\right )^2}{x} \, dx=9\,\ln \left (x\right )-24\,x+11\,x^2-\frac {8\,x^3}{3}+\frac {x^4}{4} \]
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