Integrand size = 82, antiderivative size = 24 \[ \int \frac {-80-800 x-3320 x^2-7400 x^3-9605 x^4-7360 x^5-3320 x^6-800 x^7-80 x^8+\left (400+3200 x+9960 x^2+14800 x^3+9605 x^4-3320 x^6-1600 x^7-240 x^8\right ) \log (x)}{x^6} \, dx=5 \left (9-\frac {x+\left (5+2 \left (\frac {1}{x}+x\right )\right )^4}{x}\right ) \log (x) \]
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Leaf count is larger than twice the leaf count of optimal. \(59\) vs. \(2(24)=48\).
Time = 0.14 (sec) , antiderivative size = 59, normalized size of antiderivative = 2.46, number of steps used = 14, number of rules used = 4, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.049, Rules used = {14, 2404, 2332, 2341} \[ \int \frac {-80-800 x-3320 x^2-7400 x^3-9605 x^4-7360 x^5-3320 x^6-800 x^7-80 x^8+\left (400+3200 x+9960 x^2+14800 x^3+9605 x^4-3320 x^6-1600 x^7-240 x^8\right ) \log (x)}{x^6} \, dx=-\frac {80 \log (x)}{x^5}-\frac {800 \log (x)}{x^4}-80 x^3 \log (x)-\frac {3320 \log (x)}{x^3}-800 x^2 \log (x)-\frac {7400 \log (x)}{x^2}-3320 x \log (x)-7360 \log (x)-\frac {9605 \log (x)}{x} \]
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Rule 14
Rule 2332
Rule 2341
Rule 2404
Rubi steps \begin{align*} \text {integral}& = \int \left (-\frac {5 \left (16+160 x+664 x^2+1480 x^3+1921 x^4+1472 x^5+664 x^6+160 x^7+16 x^8\right )}{x^6}-\frac {5 (2+x)^3 (1+2 x)^3 \left (-10-5 x+6 x^2\right ) \log (x)}{x^6}\right ) \, dx \\ & = -\left (5 \int \frac {16+160 x+664 x^2+1480 x^3+1921 x^4+1472 x^5+664 x^6+160 x^7+16 x^8}{x^6} \, dx\right )-5 \int \frac {(2+x)^3 (1+2 x)^3 \left (-10-5 x+6 x^2\right ) \log (x)}{x^6} \, dx \\ & = -\left (5 \int \left (664+\frac {16}{x^6}+\frac {160}{x^5}+\frac {664}{x^4}+\frac {1480}{x^3}+\frac {1921}{x^2}+\frac {1472}{x}+160 x+16 x^2\right ) \, dx\right )-5 \int \left (664 \log (x)-\frac {80 \log (x)}{x^6}-\frac {640 \log (x)}{x^5}-\frac {1992 \log (x)}{x^4}-\frac {2960 \log (x)}{x^3}-\frac {1921 \log (x)}{x^2}+320 x \log (x)+48 x^2 \log (x)\right ) \, dx \\ & = \frac {16}{x^5}+\frac {200}{x^4}+\frac {3320}{3 x^3}+\frac {3700}{x^2}+\frac {9605}{x}-3320 x-400 x^2-\frac {80 x^3}{3}-7360 \log (x)-240 \int x^2 \log (x) \, dx+400 \int \frac {\log (x)}{x^6} \, dx-1600 \int x \log (x) \, dx+3200 \int \frac {\log (x)}{x^5} \, dx-3320 \int \log (x) \, dx+9605 \int \frac {\log (x)}{x^2} \, dx+9960 \int \frac {\log (x)}{x^4} \, dx+14800 \int \frac {\log (x)}{x^3} \, dx \\ & = -7360 \log (x)-\frac {80 \log (x)}{x^5}-\frac {800 \log (x)}{x^4}-\frac {3320 \log (x)}{x^3}-\frac {7400 \log (x)}{x^2}-\frac {9605 \log (x)}{x}-3320 x \log (x)-800 x^2 \log (x)-80 x^3 \log (x) \\ \end{align*}
Leaf count is larger than twice the leaf count of optimal. \(59\) vs. \(2(24)=48\).
Time = 0.03 (sec) , antiderivative size = 59, normalized size of antiderivative = 2.46 \[ \int \frac {-80-800 x-3320 x^2-7400 x^3-9605 x^4-7360 x^5-3320 x^6-800 x^7-80 x^8+\left (400+3200 x+9960 x^2+14800 x^3+9605 x^4-3320 x^6-1600 x^7-240 x^8\right ) \log (x)}{x^6} \, dx=-7360 \log (x)-\frac {80 \log (x)}{x^5}-\frac {800 \log (x)}{x^4}-\frac {3320 \log (x)}{x^3}-\frac {7400 \log (x)}{x^2}-\frac {9605 \log (x)}{x}-3320 x \log (x)-800 x^2 \log (x)-80 x^3 \log (x) \]
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Time = 0.12 (sec) , antiderivative size = 48, normalized size of antiderivative = 2.00
method | result | size |
risch | \(-\frac {5 \left (16 x^{8}+160 x^{7}+664 x^{6}+1921 x^{4}+1480 x^{3}+664 x^{2}+160 x +16\right ) \ln \left (x \right )}{x^{5}}-7360 \ln \left (x \right )\) | \(48\) |
default | \(-\frac {7400 \ln \left (x \right )}{x^{2}}-3320 x \ln \left (x \right )-\frac {3320 \ln \left (x \right )}{x^{3}}-\frac {9605 \ln \left (x \right )}{x}-7360 \ln \left (x \right )-80 x^{3} \ln \left (x \right )-800 x^{2} \ln \left (x \right )-\frac {800 \ln \left (x \right )}{x^{4}}-\frac {80 \ln \left (x \right )}{x^{5}}\) | \(60\) |
parts | \(-\frac {7400 \ln \left (x \right )}{x^{2}}-3320 x \ln \left (x \right )-\frac {3320 \ln \left (x \right )}{x^{3}}-\frac {9605 \ln \left (x \right )}{x}-7360 \ln \left (x \right )-80 x^{3} \ln \left (x \right )-800 x^{2} \ln \left (x \right )-\frac {800 \ln \left (x \right )}{x^{4}}-\frac {80 \ln \left (x \right )}{x^{5}}\) | \(60\) |
norman | \(\frac {-7360 x^{5} \ln \left (x \right )-800 x \ln \left (x \right )-3320 x^{2} \ln \left (x \right )-7400 x^{3} \ln \left (x \right )-9605 x^{4} \ln \left (x \right )-3320 x^{6} \ln \left (x \right )-800 x^{7} \ln \left (x \right )-80 x^{8} \ln \left (x \right )-80 \ln \left (x \right )}{x^{5}}\) | \(64\) |
parallelrisch | \(-\frac {80 x^{8} \ln \left (x \right )+800 x^{7} \ln \left (x \right )+3320 x^{6} \ln \left (x \right )+7360 x^{5} \ln \left (x \right )+9605 x^{4} \ln \left (x \right )+7400 x^{3} \ln \left (x \right )+3320 x^{2} \ln \left (x \right )+800 x \ln \left (x \right )+80 \ln \left (x \right )}{x^{5}}\) | \(65\) |
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Time = 0.27 (sec) , antiderivative size = 47, normalized size of antiderivative = 1.96 \[ \int \frac {-80-800 x-3320 x^2-7400 x^3-9605 x^4-7360 x^5-3320 x^6-800 x^7-80 x^8+\left (400+3200 x+9960 x^2+14800 x^3+9605 x^4-3320 x^6-1600 x^7-240 x^8\right ) \log (x)}{x^6} \, dx=-\frac {5 \, {\left (16 \, x^{8} + 160 \, x^{7} + 664 \, x^{6} + 1472 \, x^{5} + 1921 \, x^{4} + 1480 \, x^{3} + 664 \, x^{2} + 160 \, x + 16\right )} \log \left (x\right )}{x^{5}} \]
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Leaf count of result is larger than twice the leaf count of optimal. 48 vs. \(2 (20) = 40\).
Time = 0.09 (sec) , antiderivative size = 48, normalized size of antiderivative = 2.00 \[ \int \frac {-80-800 x-3320 x^2-7400 x^3-9605 x^4-7360 x^5-3320 x^6-800 x^7-80 x^8+\left (400+3200 x+9960 x^2+14800 x^3+9605 x^4-3320 x^6-1600 x^7-240 x^8\right ) \log (x)}{x^6} \, dx=- 7360 \log {\left (x \right )} + \frac {\left (- 80 x^{8} - 800 x^{7} - 3320 x^{6} - 9605 x^{4} - 7400 x^{3} - 3320 x^{2} - 800 x - 80\right ) \log {\left (x \right )}}{x^{5}} \]
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Leaf count of result is larger than twice the leaf count of optimal. 59 vs. \(2 (24) = 48\).
Time = 0.19 (sec) , antiderivative size = 59, normalized size of antiderivative = 2.46 \[ \int \frac {-80-800 x-3320 x^2-7400 x^3-9605 x^4-7360 x^5-3320 x^6-800 x^7-80 x^8+\left (400+3200 x+9960 x^2+14800 x^3+9605 x^4-3320 x^6-1600 x^7-240 x^8\right ) \log (x)}{x^6} \, dx=-80 \, x^{3} \log \left (x\right ) - 800 \, x^{2} \log \left (x\right ) - 3320 \, x \log \left (x\right ) - \frac {9605 \, \log \left (x\right )}{x} - \frac {7400 \, \log \left (x\right )}{x^{2}} - \frac {3320 \, \log \left (x\right )}{x^{3}} - \frac {800 \, \log \left (x\right )}{x^{4}} - \frac {80 \, \log \left (x\right )}{x^{5}} - 7360 \, \log \left (x\right ) \]
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Time = 0.27 (sec) , antiderivative size = 47, normalized size of antiderivative = 1.96 \[ \int \frac {-80-800 x-3320 x^2-7400 x^3-9605 x^4-7360 x^5-3320 x^6-800 x^7-80 x^8+\left (400+3200 x+9960 x^2+14800 x^3+9605 x^4-3320 x^6-1600 x^7-240 x^8\right ) \log (x)}{x^6} \, dx=-5 \, {\left (16 \, x^{3} + 160 \, x^{2} + 664 \, x + \frac {1921 \, x^{4} + 1480 \, x^{3} + 664 \, x^{2} + 160 \, x + 16}{x^{5}}\right )} \log \left (x\right ) - 7360 \, \log \left (x\right ) \]
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Time = 13.20 (sec) , antiderivative size = 67, normalized size of antiderivative = 2.79 \[ \int \frac {-80-800 x-3320 x^2-7400 x^3-9605 x^4-7360 x^5-3320 x^6-800 x^7-80 x^8+\left (400+3200 x+9960 x^2+14800 x^3+9605 x^4-3320 x^6-1600 x^7-240 x^8\right ) \log (x)}{x^6} \, dx=-\frac {800\,x^2\,\ln \left (x\right )+3320\,x^3\,\ln \left (x\right )+7400\,x^4\,\ln \left (x\right )+9605\,x^5\,\ln \left (x\right )+7360\,x^6\,\ln \left (x\right )+3320\,x^7\,\ln \left (x\right )+800\,x^8\,\ln \left (x\right )+80\,x^9\,\ln \left (x\right )+80\,x\,\ln \left (x\right )}{x^6} \]
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