Integrand size = 48, antiderivative size = 19 \[ \int \frac {-432-144 x-864 x^2}{x^3+6 x^4+9 x^5+\left (6 x^2+18 x^3\right ) \log (x)+9 x \log ^2(x)} \, dx=\frac {144}{x \left (1+3 \left (x+\frac {\log (x)}{x}\right )\right )} \]
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Time = 0.09 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.79, number of steps used = 3, number of rules used = 3, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.062, Rules used = {6820, 12, 6818} \[ \int \frac {-432-144 x-864 x^2}{x^3+6 x^4+9 x^5+\left (6 x^2+18 x^3\right ) \log (x)+9 x \log ^2(x)} \, dx=\frac {144}{3 x^2+x+3 \log (x)} \]
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Rule 12
Rule 6818
Rule 6820
Rubi steps \begin{align*} \text {integral}& = \int \frac {144 \left (-3-x-6 x^2\right )}{x \left (x+3 x^2+3 \log (x)\right )^2} \, dx \\ & = 144 \int \frac {-3-x-6 x^2}{x \left (x+3 x^2+3 \log (x)\right )^2} \, dx \\ & = \frac {144}{x+3 x^2+3 \log (x)} \\ \end{align*}
Time = 0.02 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.79 \[ \int \frac {-432-144 x-864 x^2}{x^3+6 x^4+9 x^5+\left (6 x^2+18 x^3\right ) \log (x)+9 x \log ^2(x)} \, dx=\frac {144}{x+3 x^2+3 \log (x)} \]
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Time = 0.26 (sec) , antiderivative size = 16, normalized size of antiderivative = 0.84
method | result | size |
default | \(\frac {144}{3 x^{2}+3 \ln \left (x \right )+x}\) | \(16\) |
norman | \(\frac {144}{3 x^{2}+3 \ln \left (x \right )+x}\) | \(16\) |
risch | \(\frac {144}{3 x^{2}+3 \ln \left (x \right )+x}\) | \(16\) |
parallelrisch | \(\frac {144}{3 x^{2}+3 \ln \left (x \right )+x}\) | \(16\) |
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Time = 0.25 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.79 \[ \int \frac {-432-144 x-864 x^2}{x^3+6 x^4+9 x^5+\left (6 x^2+18 x^3\right ) \log (x)+9 x \log ^2(x)} \, dx=\frac {144}{3 \, x^{2} + x + 3 \, \log \left (x\right )} \]
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Time = 0.05 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.63 \[ \int \frac {-432-144 x-864 x^2}{x^3+6 x^4+9 x^5+\left (6 x^2+18 x^3\right ) \log (x)+9 x \log ^2(x)} \, dx=\frac {144}{3 x^{2} + x + 3 \log {\left (x \right )}} \]
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Time = 0.22 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.79 \[ \int \frac {-432-144 x-864 x^2}{x^3+6 x^4+9 x^5+\left (6 x^2+18 x^3\right ) \log (x)+9 x \log ^2(x)} \, dx=\frac {144}{3 \, x^{2} + x + 3 \, \log \left (x\right )} \]
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Time = 0.26 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.79 \[ \int \frac {-432-144 x-864 x^2}{x^3+6 x^4+9 x^5+\left (6 x^2+18 x^3\right ) \log (x)+9 x \log ^2(x)} \, dx=\frac {144}{3 \, x^{2} + x + 3 \, \log \left (x\right )} \]
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Time = 8.41 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.79 \[ \int \frac {-432-144 x-864 x^2}{x^3+6 x^4+9 x^5+\left (6 x^2+18 x^3\right ) \log (x)+9 x \log ^2(x)} \, dx=\frac {144}{x+3\,\ln \left (x\right )+3\,x^2} \]
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