Integrand size = 116, antiderivative size = 30 \[ \int \frac {7454200-2564100 x+1823674 x^2-532140 x^3+66501 x^4-3780 x^5+81 x^6+\left (-12220-4798 x^2+840 x^3-36 x^4\right ) \log (x)+4 x^2 \log ^2(x)}{1493284 x^2-513240 x^3+66096 x^4-3780 x^5+81 x^6+\left (-4888 x^2+840 x^3-36 x^4\right ) \log (x)+4 x^2 \log ^2(x)} \, dx=x+\frac {5}{x \left (-1+\frac {2 \log (x)}{-3+(5+3 (10-x))^2}\right )} \]
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\[ \int \frac {7454200-2564100 x+1823674 x^2-532140 x^3+66501 x^4-3780 x^5+81 x^6+\left (-12220-4798 x^2+840 x^3-36 x^4\right ) \log (x)+4 x^2 \log ^2(x)}{1493284 x^2-513240 x^3+66096 x^4-3780 x^5+81 x^6+\left (-4888 x^2+840 x^3-36 x^4\right ) \log (x)+4 x^2 \log ^2(x)} \, dx=\int \frac {7454200-2564100 x+1823674 x^2-532140 x^3+66501 x^4-3780 x^5+81 x^6+\left (-12220-4798 x^2+840 x^3-36 x^4\right ) \log (x)+4 x^2 \log ^2(x)}{1493284 x^2-513240 x^3+66096 x^4-3780 x^5+81 x^6+\left (-4888 x^2+840 x^3-36 x^4\right ) \log (x)+4 x^2 \log ^2(x)} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {7454200-2564100 x+1823674 x^2-532140 x^3+66501 x^4-3780 x^5+81 x^6-2 \left (6110+2399 x^2-420 x^3+18 x^4\right ) \log (x)+4 x^2 \log ^2(x)}{x^2 \left (1222-210 x+9 x^2-2 \log (x)\right )^2} \, dx \\ & = \int \left (1+\frac {10 \left (-1222-128100 x+33039 x^2-2835 x^3+81 x^4\right )}{x^2 \left (1222-210 x+9 x^2-2 \log (x)\right )^2}-\frac {5 \left (-1222+9 x^2\right )}{x^2 \left (1222-210 x+9 x^2-2 \log (x)\right )}\right ) \, dx \\ & = x-5 \int \frac {-1222+9 x^2}{x^2 \left (1222-210 x+9 x^2-2 \log (x)\right )} \, dx+10 \int \frac {-1222-128100 x+33039 x^2-2835 x^3+81 x^4}{x^2 \left (1222-210 x+9 x^2-2 \log (x)\right )^2} \, dx \\ & = x-5 \int \left (\frac {9}{1222-210 x+9 x^2-2 \log (x)}-\frac {1222}{x^2 \left (1222-210 x+9 x^2-2 \log (x)\right )}\right ) \, dx+10 \int \left (\frac {33039}{\left (1222-210 x+9 x^2-2 \log (x)\right )^2}-\frac {1222}{x^2 \left (1222-210 x+9 x^2-2 \log (x)\right )^2}-\frac {128100}{x \left (1222-210 x+9 x^2-2 \log (x)\right )^2}-\frac {2835 x}{\left (1222-210 x+9 x^2-2 \log (x)\right )^2}+\frac {81 x^2}{\left (1222-210 x+9 x^2-2 \log (x)\right )^2}\right ) \, dx \\ & = x-45 \int \frac {1}{1222-210 x+9 x^2-2 \log (x)} \, dx+810 \int \frac {x^2}{\left (1222-210 x+9 x^2-2 \log (x)\right )^2} \, dx+6110 \int \frac {1}{x^2 \left (1222-210 x+9 x^2-2 \log (x)\right )} \, dx-12220 \int \frac {1}{x^2 \left (1222-210 x+9 x^2-2 \log (x)\right )^2} \, dx-28350 \int \frac {x}{\left (1222-210 x+9 x^2-2 \log (x)\right )^2} \, dx+330390 \int \frac {1}{\left (1222-210 x+9 x^2-2 \log (x)\right )^2} \, dx-1281000 \int \frac {1}{x \left (1222-210 x+9 x^2-2 \log (x)\right )^2} \, dx \\ \end{align*}
Time = 0.05 (sec) , antiderivative size = 33, normalized size of antiderivative = 1.10 \[ \int \frac {7454200-2564100 x+1823674 x^2-532140 x^3+66501 x^4-3780 x^5+81 x^6+\left (-12220-4798 x^2+840 x^3-36 x^4\right ) \log (x)+4 x^2 \log ^2(x)}{1493284 x^2-513240 x^3+66096 x^4-3780 x^5+81 x^6+\left (-4888 x^2+840 x^3-36 x^4\right ) \log (x)+4 x^2 \log ^2(x)} \, dx=x+\frac {5 \left (1222-210 x+9 x^2\right )}{x \left (-1222+210 x-9 x^2+2 \log (x)\right )} \]
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Time = 0.44 (sec) , antiderivative size = 34, normalized size of antiderivative = 1.13
method | result | size |
risch | \(x -\frac {5 \left (9 x^{2}-210 x +1222\right )}{x \left (9 x^{2}-210 x -2 \ln \left (x \right )+1222\right )}\) | \(34\) |
default | \(\frac {6110-1177 x^{2}-1050 x +210 x^{3}-9 x^{4}+2 x^{2} \ln \left (x \right )}{x \left (-9 x^{2}+2 \ln \left (x \right )+210 x -1222\right )}\) | \(48\) |
norman | \(\frac {-6110-3723 x^{2}+\frac {88690 x}{3}-2 x^{2} \ln \left (x \right )-\frac {140 x \ln \left (x \right )}{3}+9 x^{4}}{x \left (9 x^{2}-210 x -2 \ln \left (x \right )+1222\right )}\) | \(48\) |
parallelrisch | \(\frac {18 x^{4}-12220-420 x^{3}-4 x^{2} \ln \left (x \right )+2354 x^{2}+2100 x}{2 x \left (9 x^{2}-210 x -2 \ln \left (x \right )+1222\right )}\) | \(49\) |
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Time = 0.25 (sec) , antiderivative size = 49, normalized size of antiderivative = 1.63 \[ \int \frac {7454200-2564100 x+1823674 x^2-532140 x^3+66501 x^4-3780 x^5+81 x^6+\left (-12220-4798 x^2+840 x^3-36 x^4\right ) \log (x)+4 x^2 \log ^2(x)}{1493284 x^2-513240 x^3+66096 x^4-3780 x^5+81 x^6+\left (-4888 x^2+840 x^3-36 x^4\right ) \log (x)+4 x^2 \log ^2(x)} \, dx=\frac {9 \, x^{4} - 210 \, x^{3} - 2 \, x^{2} \log \left (x\right ) + 1177 \, x^{2} + 1050 \, x - 6110}{9 \, x^{3} - 210 \, x^{2} - 2 \, x \log \left (x\right ) + 1222 \, x} \]
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Time = 0.08 (sec) , antiderivative size = 31, normalized size of antiderivative = 1.03 \[ \int \frac {7454200-2564100 x+1823674 x^2-532140 x^3+66501 x^4-3780 x^5+81 x^6+\left (-12220-4798 x^2+840 x^3-36 x^4\right ) \log (x)+4 x^2 \log ^2(x)}{1493284 x^2-513240 x^3+66096 x^4-3780 x^5+81 x^6+\left (-4888 x^2+840 x^3-36 x^4\right ) \log (x)+4 x^2 \log ^2(x)} \, dx=x + \frac {45 x^{2} - 1050 x + 6110}{- 9 x^{3} + 210 x^{2} + 2 x \log {\left (x \right )} - 1222 x} \]
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Time = 0.23 (sec) , antiderivative size = 49, normalized size of antiderivative = 1.63 \[ \int \frac {7454200-2564100 x+1823674 x^2-532140 x^3+66501 x^4-3780 x^5+81 x^6+\left (-12220-4798 x^2+840 x^3-36 x^4\right ) \log (x)+4 x^2 \log ^2(x)}{1493284 x^2-513240 x^3+66096 x^4-3780 x^5+81 x^6+\left (-4888 x^2+840 x^3-36 x^4\right ) \log (x)+4 x^2 \log ^2(x)} \, dx=\frac {9 \, x^{4} - 210 \, x^{3} - 2 \, x^{2} \log \left (x\right ) + 1177 \, x^{2} + 1050 \, x - 6110}{9 \, x^{3} - 210 \, x^{2} - 2 \, x \log \left (x\right ) + 1222 \, x} \]
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Time = 0.26 (sec) , antiderivative size = 35, normalized size of antiderivative = 1.17 \[ \int \frac {7454200-2564100 x+1823674 x^2-532140 x^3+66501 x^4-3780 x^5+81 x^6+\left (-12220-4798 x^2+840 x^3-36 x^4\right ) \log (x)+4 x^2 \log ^2(x)}{1493284 x^2-513240 x^3+66096 x^4-3780 x^5+81 x^6+\left (-4888 x^2+840 x^3-36 x^4\right ) \log (x)+4 x^2 \log ^2(x)} \, dx=x - \frac {5 \, {\left (9 \, x^{2} - 210 \, x + 1222\right )}}{9 \, x^{3} - 210 \, x^{2} - 2 \, x \log \left (x\right ) + 1222 \, x} \]
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Time = 9.13 (sec) , antiderivative size = 32, normalized size of antiderivative = 1.07 \[ \int \frac {7454200-2564100 x+1823674 x^2-532140 x^3+66501 x^4-3780 x^5+81 x^6+\left (-12220-4798 x^2+840 x^3-36 x^4\right ) \log (x)+4 x^2 \log ^2(x)}{1493284 x^2-513240 x^3+66096 x^4-3780 x^5+81 x^6+\left (-4888 x^2+840 x^3-36 x^4\right ) \log (x)+4 x^2 \log ^2(x)} \, dx=x+\frac {45\,x^2-1050\,x+6110}{x\,\left (210\,x+2\,\ln \left (x\right )-9\,x^2-1222\right )} \]
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