Integrand size = 14, antiderivative size = 23 \[ \int \left (-1-8 \log ^2(x)+3 \log ^3(x)\right ) \, dx=-35 x+34 x \log (x)-17 x \log ^2(x)+3 x \log ^3(x) \]
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Time = 0.01 (sec) , antiderivative size = 23, normalized size of antiderivative = 1.00, number of steps used = 6, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.143, Rules used = {2333, 2332} \[ \int \left (-1-8 \log ^2(x)+3 \log ^3(x)\right ) \, dx=-35 x+3 x \log ^3(x)-17 x \log ^2(x)+34 x \log (x) \]
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Rule 2332
Rule 2333
Rubi steps \begin{align*} \text {integral}& = -x+3 \int \log ^3(x) \, dx-8 \int \log ^2(x) \, dx \\ & = -x-8 x \log ^2(x)+3 x \log ^3(x)-9 \int \log ^2(x) \, dx+16 \int \log (x) \, dx \\ & = -17 x+16 x \log (x)-17 x \log ^2(x)+3 x \log ^3(x)+18 \int \log (x) \, dx \\ & = -35 x+34 x \log (x)-17 x \log ^2(x)+3 x \log ^3(x) \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 23, normalized size of antiderivative = 1.00 \[ \int \left (-1-8 \log ^2(x)+3 \log ^3(x)\right ) \, dx=-35 x+34 x \log (x)-17 x \log ^2(x)+3 x \log ^3(x) \]
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Time = 0.02 (sec) , antiderivative size = 24, normalized size of antiderivative = 1.04
method | result | size |
default | \(-35 x +34 x \ln \left (x \right )-17 x \ln \left (x \right )^{2}+3 x \ln \left (x \right )^{3}\) | \(24\) |
norman | \(-35 x +34 x \ln \left (x \right )-17 x \ln \left (x \right )^{2}+3 x \ln \left (x \right )^{3}\) | \(24\) |
risch | \(-35 x +34 x \ln \left (x \right )-17 x \ln \left (x \right )^{2}+3 x \ln \left (x \right )^{3}\) | \(24\) |
parallelrisch | \(-35 x +34 x \ln \left (x \right )-17 x \ln \left (x \right )^{2}+3 x \ln \left (x \right )^{3}\) | \(24\) |
parts | \(-35 x +34 x \ln \left (x \right )-17 x \ln \left (x \right )^{2}+3 x \ln \left (x \right )^{3}\) | \(24\) |
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none
Time = 0.24 (sec) , antiderivative size = 23, normalized size of antiderivative = 1.00 \[ \int \left (-1-8 \log ^2(x)+3 \log ^3(x)\right ) \, dx=3 \, x \log \left (x\right )^{3} - 17 \, x \log \left (x\right )^{2} + 34 \, x \log \left (x\right ) - 35 \, x \]
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Time = 0.05 (sec) , antiderivative size = 26, normalized size of antiderivative = 1.13 \[ \int \left (-1-8 \log ^2(x)+3 \log ^3(x)\right ) \, dx=3 x \log {\left (x \right )}^{3} - 17 x \log {\left (x \right )}^{2} + 34 x \log {\left (x \right )} - 35 x \]
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none
Time = 0.21 (sec) , antiderivative size = 36, normalized size of antiderivative = 1.57 \[ \int \left (-1-8 \log ^2(x)+3 \log ^3(x)\right ) \, dx=3 \, {\left (\log \left (x\right )^{3} - 3 \, \log \left (x\right )^{2} + 6 \, \log \left (x\right ) - 6\right )} x - 8 \, {\left (\log \left (x\right )^{2} - 2 \, \log \left (x\right ) + 2\right )} x - x \]
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none
Time = 0.28 (sec) , antiderivative size = 23, normalized size of antiderivative = 1.00 \[ \int \left (-1-8 \log ^2(x)+3 \log ^3(x)\right ) \, dx=3 \, x \log \left (x\right )^{3} - 17 \, x \log \left (x\right )^{2} + 34 \, x \log \left (x\right ) - 35 \, x \]
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Time = 0.42 (sec) , antiderivative size = 20, normalized size of antiderivative = 0.87 \[ \int \left (-1-8 \log ^2(x)+3 \log ^3(x)\right ) \, dx=x\,\left (3\,{\ln \left (x\right )}^3-17\,{\ln \left (x\right )}^2+34\,\ln \left (x\right )-35\right ) \]
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