Integrand size = 52, antiderivative size = 19 \[ \int \frac {-4 x^2-6 x^3-2 x^4+\left (10 x+16 x^2+6 x^3\right ) \log (8)+\left (-6-10 x-4 x^2\right ) \log ^2(8)}{x^7} \, dx=\frac {\left (1+\frac {1}{x}\right )^2 (x-\log (8))^2}{x^4} \]
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Leaf count is larger than twice the leaf count of optimal. \(50\) vs. \(2(19)=38\).
Time = 0.04 (sec) , antiderivative size = 50, normalized size of antiderivative = 2.63, number of steps used = 2, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.019, Rules used = {14} \[ \int \frac {-4 x^2-6 x^3-2 x^4+\left (10 x+16 x^2+6 x^3\right ) \log (8)+\left (-6-10 x-4 x^2\right ) \log ^2(8)}{x^7} \, dx=\frac {\log ^2(8)}{x^6}-\frac {2 (1-\log (8)) \log (8)}{x^5}+\frac {1+\log ^2(8)-4 \log (8)}{x^4}+\frac {2 (1-\log (8))}{x^3}+\frac {1}{x^2} \]
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Rule 14
Rubi steps \begin{align*} \text {integral}& = \int \left (-\frac {2}{x^3}+\frac {6 (-1+\log (8))}{x^4}-\frac {10 (-1+\log (8)) \log (8)}{x^6}-\frac {6 \log ^2(8)}{x^7}-\frac {4 \left (1-4 \log (8)+\log ^2(8)\right )}{x^5}\right ) \, dx \\ & = \frac {1}{x^2}+\frac {2 (1-\log (8))}{x^3}-\frac {2 (1-\log (8)) \log (8)}{x^5}+\frac {\log ^2(8)}{x^6}+\frac {1-4 \log (8)+\log ^2(8)}{x^4} \\ \end{align*}
Leaf count is larger than twice the leaf count of optimal. \(51\) vs. \(2(19)=38\).
Time = 0.03 (sec) , antiderivative size = 51, normalized size of antiderivative = 2.68 \[ \int \frac {-4 x^2-6 x^3-2 x^4+\left (10 x+16 x^2+6 x^3\right ) \log (8)+\left (-6-10 x-4 x^2\right ) \log ^2(8)}{x^7} \, dx=\frac {10 x^4-20 x^3 (-1+\log (8))+10 \log ^2(8)+5 x^2 (2+\log (8) (-8+\log (64)))+4 x \log (8) (-5+\log (32768))}{10 x^6} \]
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Time = 0.04 (sec) , antiderivative size = 25, normalized size of antiderivative = 1.32
method | result | size |
gosper | \(\frac {\left (3 x \ln \left (2\right )-x^{2}+3 \ln \left (2\right )-x \right )^{2}}{x^{6}}\) | \(25\) |
norman | \(\frac {x^{4}+\left (18 \ln \left (2\right )^{2}-6 \ln \left (2\right )\right ) x +\left (-6 \ln \left (2\right )+2\right ) x^{3}+\left (1+9 \ln \left (2\right )^{2}-12 \ln \left (2\right )\right ) x^{2}+9 \ln \left (2\right )^{2}}{x^{6}}\) | \(54\) |
risch | \(\frac {x^{4}+\left (18 \ln \left (2\right )^{2}-6 \ln \left (2\right )\right ) x +\left (-6 \ln \left (2\right )+2\right ) x^{3}+\left (1+9 \ln \left (2\right )^{2}-12 \ln \left (2\right )\right ) x^{2}+9 \ln \left (2\right )^{2}}{x^{6}}\) | \(54\) |
default | \(-\frac {-18 \ln \left (2\right )^{2}+24 \ln \left (2\right )-2}{2 x^{4}}+\frac {6 \ln \left (2\right ) \left (3 \ln \left (2\right )-1\right )}{x^{5}}+\frac {9 \ln \left (2\right )^{2}}{x^{6}}+\frac {1}{x^{2}}-\frac {2 \left (9 \ln \left (2\right )-3\right )}{3 x^{3}}\) | \(55\) |
parallelrisch | \(\frac {9 x^{2} \ln \left (2\right )^{2}-6 x^{3} \ln \left (2\right )+x^{4}+18 x \ln \left (2\right )^{2}-12 x^{2} \ln \left (2\right )+2 x^{3}+9 \ln \left (2\right )^{2}-6 x \ln \left (2\right )+x^{2}}{x^{6}}\) | \(58\) |
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Leaf count of result is larger than twice the leaf count of optimal. 44 vs. \(2 (19) = 38\).
Time = 0.25 (sec) , antiderivative size = 44, normalized size of antiderivative = 2.32 \[ \int \frac {-4 x^2-6 x^3-2 x^4+\left (10 x+16 x^2+6 x^3\right ) \log (8)+\left (-6-10 x-4 x^2\right ) \log ^2(8)}{x^7} \, dx=\frac {x^{4} + 2 \, x^{3} + 9 \, {\left (x^{2} + 2 \, x + 1\right )} \log \left (2\right )^{2} + x^{2} - 6 \, {\left (x^{3} + 2 \, x^{2} + x\right )} \log \left (2\right )}{x^{6}} \]
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Leaf count of result is larger than twice the leaf count of optimal. 54 vs. \(2 (17) = 34\).
Time = 0.88 (sec) , antiderivative size = 54, normalized size of antiderivative = 2.84 \[ \int \frac {-4 x^2-6 x^3-2 x^4+\left (10 x+16 x^2+6 x^3\right ) \log (8)+\left (-6-10 x-4 x^2\right ) \log ^2(8)}{x^7} \, dx=- \frac {- x^{4} + x^{3} \left (-2 + 6 \log {\left (2 \right )}\right ) + x^{2} \left (- 9 \log {\left (2 \right )}^{2} - 1 + 12 \log {\left (2 \right )}\right ) + x \left (- 18 \log {\left (2 \right )}^{2} + 6 \log {\left (2 \right )}\right ) - 9 \log {\left (2 \right )}^{2}}{x^{6}} \]
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Leaf count of result is larger than twice the leaf count of optimal. 55 vs. \(2 (19) = 38\).
Time = 0.18 (sec) , antiderivative size = 55, normalized size of antiderivative = 2.89 \[ \int \frac {-4 x^2-6 x^3-2 x^4+\left (10 x+16 x^2+6 x^3\right ) \log (8)+\left (-6-10 x-4 x^2\right ) \log ^2(8)}{x^7} \, dx=\frac {x^{4} - 2 \, x^{3} {\left (3 \, \log \left (2\right ) - 1\right )} + {\left (9 \, \log \left (2\right )^{2} - 12 \, \log \left (2\right ) + 1\right )} x^{2} + 6 \, {\left (3 \, \log \left (2\right )^{2} - \log \left (2\right )\right )} x + 9 \, \log \left (2\right )^{2}}{x^{6}} \]
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Leaf count of result is larger than twice the leaf count of optimal. 57 vs. \(2 (19) = 38\).
Time = 0.28 (sec) , antiderivative size = 57, normalized size of antiderivative = 3.00 \[ \int \frac {-4 x^2-6 x^3-2 x^4+\left (10 x+16 x^2+6 x^3\right ) \log (8)+\left (-6-10 x-4 x^2\right ) \log ^2(8)}{x^7} \, dx=\frac {x^{4} - 6 \, x^{3} \log \left (2\right ) + 9 \, x^{2} \log \left (2\right )^{2} + 2 \, x^{3} - 12 \, x^{2} \log \left (2\right ) + 18 \, x \log \left (2\right )^{2} + x^{2} - 6 \, x \log \left (2\right ) + 9 \, \log \left (2\right )^{2}}{x^{6}} \]
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Time = 0.09 (sec) , antiderivative size = 51, normalized size of antiderivative = 2.68 \[ \int \frac {-4 x^2-6 x^3-2 x^4+\left (10 x+16 x^2+6 x^3\right ) \log (8)+\left (-6-10 x-4 x^2\right ) \log ^2(8)}{x^7} \, dx=\frac {x^4+\left (2-\ln \left (64\right )\right )\,x^3+\left (9\,{\ln \left (2\right )}^2-\ln \left (4096\right )+1\right )\,x^2+\left (18\,{\ln \left (2\right )}^2-\ln \left (64\right )\right )\,x+9\,{\ln \left (2\right )}^2}{x^6} \]
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