Integrand size = 156, antiderivative size = 24 \[ \int \frac {-100 x^5-750 x^6+\left (300 x^3+6750 x^4+45500 x^5+7500 x^6+300 x^7\right ) \log \left (\frac {2+30 x+3 x^2}{1+15 x+x^2}\right )+\left (-200 x-6000 x^2-45500 x^3-7500 x^4-300 x^5\right ) \log ^2\left (\frac {2+30 x+3 x^2}{1+15 x+x^2}\right )}{\left (2+60 x+455 x^2+75 x^3+3 x^4\right ) \log ^3\left (\frac {2+30 x+3 x^2}{1+15 x+x^2}\right )} \, dx=\left (-5+\frac {5 x^2}{\log \left (2+\frac {x}{15+\frac {1}{x}+x}\right )}\right )^2 \]
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\[ \int \frac {-100 x^5-750 x^6+\left (300 x^3+6750 x^4+45500 x^5+7500 x^6+300 x^7\right ) \log \left (\frac {2+30 x+3 x^2}{1+15 x+x^2}\right )+\left (-200 x-6000 x^2-45500 x^3-7500 x^4-300 x^5\right ) \log ^2\left (\frac {2+30 x+3 x^2}{1+15 x+x^2}\right )}{\left (2+60 x+455 x^2+75 x^3+3 x^4\right ) \log ^3\left (\frac {2+30 x+3 x^2}{1+15 x+x^2}\right )} \, dx=\int \frac {-100 x^5-750 x^6+\left (300 x^3+6750 x^4+45500 x^5+7500 x^6+300 x^7\right ) \log \left (\frac {2+30 x+3 x^2}{1+15 x+x^2}\right )+\left (-200 x-6000 x^2-45500 x^3-7500 x^4-300 x^5\right ) \log ^2\left (\frac {2+30 x+3 x^2}{1+15 x+x^2}\right )}{\left (2+60 x+455 x^2+75 x^3+3 x^4\right ) \log ^3\left (\frac {2+30 x+3 x^2}{1+15 x+x^2}\right )} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \left (-\frac {50 x^5 (2+15 x)}{\left (1+15 x+x^2\right ) \left (2+30 x+3 x^2\right ) \log ^3\left (\frac {2+30 x+3 x^2}{1+15 x+x^2}\right )}+\frac {50 x^3 \left (6+135 x+910 x^2+150 x^3+6 x^4\right )}{\left (1+15 x+x^2\right ) \left (2+30 x+3 x^2\right ) \log ^2\left (\frac {2+30 x+3 x^2}{1+15 x+x^2}\right )}-\frac {100 x}{\log \left (\frac {2+30 x+3 x^2}{1+15 x+x^2}\right )}\right ) \, dx \\ & = -\left (50 \int \frac {x^5 (2+15 x)}{\left (1+15 x+x^2\right ) \left (2+30 x+3 x^2\right ) \log ^3\left (\frac {2+30 x+3 x^2}{1+15 x+x^2}\right )} \, dx\right )+50 \int \frac {x^3 \left (6+135 x+910 x^2+150 x^3+6 x^4\right )}{\left (1+15 x+x^2\right ) \left (2+30 x+3 x^2\right ) \log ^2\left (\frac {2+30 x+3 x^2}{1+15 x+x^2}\right )} \, dx-100 \int \frac {x}{\log \left (\frac {2+30 x+3 x^2}{1+15 x+x^2}\right )} \, dx \\ & = -\left (50 \int \left (\frac {2350}{\log ^3\left (\frac {2+30 x+3 x^2}{1+15 x+x^2}\right )}-\frac {373 x}{3 \log ^3\left (\frac {2+30 x+3 x^2}{1+15 x+x^2}\right )}+\frac {5 x^2}{\log ^3\left (\frac {2+30 x+3 x^2}{1+15 x+x^2}\right )}+\frac {-3330-49727 x}{\left (1+15 x+x^2\right ) \log ^3\left (\frac {2+30 x+3 x^2}{1+15 x+x^2}\right )}+\frac {8 (735+10951 x)}{3 \left (2+30 x+3 x^2\right ) \log ^3\left (\frac {2+30 x+3 x^2}{1+15 x+x^2}\right )}\right ) \, dx\right )+50 \int \left (\frac {5}{\log ^2\left (\frac {2+30 x+3 x^2}{1+15 x+x^2}\right )}+\frac {2 x^3}{\log ^2\left (\frac {2+30 x+3 x^2}{1+15 x+x^2}\right )}+\frac {-15-223 x}{\left (1+15 x+x^2\right ) \log ^2\left (\frac {2+30 x+3 x^2}{1+15 x+x^2}\right )}+\frac {4 (5+74 x)}{\left (2+30 x+3 x^2\right ) \log ^2\left (\frac {2+30 x+3 x^2}{1+15 x+x^2}\right )}\right ) \, dx-100 \int \frac {x}{\log \left (\frac {2+30 x+3 x^2}{1+15 x+x^2}\right )} \, dx \\ & = -\left (50 \int \frac {-3330-49727 x}{\left (1+15 x+x^2\right ) \log ^3\left (\frac {2+30 x+3 x^2}{1+15 x+x^2}\right )} \, dx\right )+50 \int \frac {-15-223 x}{\left (1+15 x+x^2\right ) \log ^2\left (\frac {2+30 x+3 x^2}{1+15 x+x^2}\right )} \, dx+100 \int \frac {x^3}{\log ^2\left (\frac {2+30 x+3 x^2}{1+15 x+x^2}\right )} \, dx-100 \int \frac {x}{\log \left (\frac {2+30 x+3 x^2}{1+15 x+x^2}\right )} \, dx-\frac {400}{3} \int \frac {735+10951 x}{\left (2+30 x+3 x^2\right ) \log ^3\left (\frac {2+30 x+3 x^2}{1+15 x+x^2}\right )} \, dx+200 \int \frac {5+74 x}{\left (2+30 x+3 x^2\right ) \log ^2\left (\frac {2+30 x+3 x^2}{1+15 x+x^2}\right )} \, dx-250 \int \frac {x^2}{\log ^3\left (\frac {2+30 x+3 x^2}{1+15 x+x^2}\right )} \, dx+250 \int \frac {1}{\log ^2\left (\frac {2+30 x+3 x^2}{1+15 x+x^2}\right )} \, dx+\frac {18650}{3} \int \frac {x}{\log ^3\left (\frac {2+30 x+3 x^2}{1+15 x+x^2}\right )} \, dx-117500 \int \frac {1}{\log ^3\left (\frac {2+30 x+3 x^2}{1+15 x+x^2}\right )} \, dx \\ & = -\left (50 \int \left (-\frac {3330}{\left (1+15 x+x^2\right ) \log ^3\left (\frac {2+30 x+3 x^2}{1+15 x+x^2}\right )}-\frac {49727 x}{\left (1+15 x+x^2\right ) \log ^3\left (\frac {2+30 x+3 x^2}{1+15 x+x^2}\right )}\right ) \, dx\right )+50 \int \left (-\frac {15}{\left (1+15 x+x^2\right ) \log ^2\left (\frac {2+30 x+3 x^2}{1+15 x+x^2}\right )}-\frac {223 x}{\left (1+15 x+x^2\right ) \log ^2\left (\frac {2+30 x+3 x^2}{1+15 x+x^2}\right )}\right ) \, dx+100 \int \frac {x^3}{\log ^2\left (\frac {2+30 x+3 x^2}{1+15 x+x^2}\right )} \, dx-100 \int \frac {x}{\log \left (\frac {2+30 x+3 x^2}{1+15 x+x^2}\right )} \, dx-\frac {400}{3} \int \left (\frac {735}{\left (2+30 x+3 x^2\right ) \log ^3\left (\frac {2+30 x+3 x^2}{1+15 x+x^2}\right )}+\frac {10951 x}{\left (2+30 x+3 x^2\right ) \log ^3\left (\frac {2+30 x+3 x^2}{1+15 x+x^2}\right )}\right ) \, dx+200 \int \left (\frac {5}{\left (2+30 x+3 x^2\right ) \log ^2\left (\frac {2+30 x+3 x^2}{1+15 x+x^2}\right )}+\frac {74 x}{\left (2+30 x+3 x^2\right ) \log ^2\left (\frac {2+30 x+3 x^2}{1+15 x+x^2}\right )}\right ) \, dx-250 \int \frac {x^2}{\log ^3\left (\frac {2+30 x+3 x^2}{1+15 x+x^2}\right )} \, dx+250 \int \frac {1}{\log ^2\left (\frac {2+30 x+3 x^2}{1+15 x+x^2}\right )} \, dx+\frac {18650}{3} \int \frac {x}{\log ^3\left (\frac {2+30 x+3 x^2}{1+15 x+x^2}\right )} \, dx-117500 \int \frac {1}{\log ^3\left (\frac {2+30 x+3 x^2}{1+15 x+x^2}\right )} \, dx \\ & = 100 \int \frac {x^3}{\log ^2\left (\frac {2+30 x+3 x^2}{1+15 x+x^2}\right )} \, dx-100 \int \frac {x}{\log \left (\frac {2+30 x+3 x^2}{1+15 x+x^2}\right )} \, dx-250 \int \frac {x^2}{\log ^3\left (\frac {2+30 x+3 x^2}{1+15 x+x^2}\right )} \, dx+250 \int \frac {1}{\log ^2\left (\frac {2+30 x+3 x^2}{1+15 x+x^2}\right )} \, dx-750 \int \frac {1}{\left (1+15 x+x^2\right ) \log ^2\left (\frac {2+30 x+3 x^2}{1+15 x+x^2}\right )} \, dx+1000 \int \frac {1}{\left (2+30 x+3 x^2\right ) \log ^2\left (\frac {2+30 x+3 x^2}{1+15 x+x^2}\right )} \, dx+\frac {18650}{3} \int \frac {x}{\log ^3\left (\frac {2+30 x+3 x^2}{1+15 x+x^2}\right )} \, dx-11150 \int \frac {x}{\left (1+15 x+x^2\right ) \log ^2\left (\frac {2+30 x+3 x^2}{1+15 x+x^2}\right )} \, dx+14800 \int \frac {x}{\left (2+30 x+3 x^2\right ) \log ^2\left (\frac {2+30 x+3 x^2}{1+15 x+x^2}\right )} \, dx-98000 \int \frac {1}{\left (2+30 x+3 x^2\right ) \log ^3\left (\frac {2+30 x+3 x^2}{1+15 x+x^2}\right )} \, dx-117500 \int \frac {1}{\log ^3\left (\frac {2+30 x+3 x^2}{1+15 x+x^2}\right )} \, dx+166500 \int \frac {1}{\left (1+15 x+x^2\right ) \log ^3\left (\frac {2+30 x+3 x^2}{1+15 x+x^2}\right )} \, dx-\frac {4380400}{3} \int \frac {x}{\left (2+30 x+3 x^2\right ) \log ^3\left (\frac {2+30 x+3 x^2}{1+15 x+x^2}\right )} \, dx+2486350 \int \frac {x}{\left (1+15 x+x^2\right ) \log ^3\left (\frac {2+30 x+3 x^2}{1+15 x+x^2}\right )} \, dx \\ & = 100 \int \frac {x^3}{\log ^2\left (\frac {2+30 x+3 x^2}{1+15 x+x^2}\right )} \, dx-100 \int \frac {x}{\log \left (\frac {2+30 x+3 x^2}{1+15 x+x^2}\right )} \, dx-250 \int \frac {x^2}{\log ^3\left (\frac {2+30 x+3 x^2}{1+15 x+x^2}\right )} \, dx+250 \int \frac {1}{\log ^2\left (\frac {2+30 x+3 x^2}{1+15 x+x^2}\right )} \, dx-750 \int \left (-\frac {2}{\sqrt {221} \left (-15+\sqrt {221}-2 x\right ) \log ^2\left (\frac {2+30 x+3 x^2}{1+15 x+x^2}\right )}-\frac {2}{\sqrt {221} \left (15+\sqrt {221}+2 x\right ) \log ^2\left (\frac {2+30 x+3 x^2}{1+15 x+x^2}\right )}\right ) \, dx+1000 \int \left (-\frac {\sqrt {\frac {3}{73}}}{\left (-30+2 \sqrt {219}-6 x\right ) \log ^2\left (\frac {2+30 x+3 x^2}{1+15 x+x^2}\right )}-\frac {\sqrt {\frac {3}{73}}}{\left (30+2 \sqrt {219}+6 x\right ) \log ^2\left (\frac {2+30 x+3 x^2}{1+15 x+x^2}\right )}\right ) \, dx+\frac {18650}{3} \int \frac {x}{\log ^3\left (\frac {2+30 x+3 x^2}{1+15 x+x^2}\right )} \, dx-11150 \int \left (\frac {1-\frac {15}{\sqrt {221}}}{\left (15-\sqrt {221}+2 x\right ) \log ^2\left (\frac {2+30 x+3 x^2}{1+15 x+x^2}\right )}+\frac {1+\frac {15}{\sqrt {221}}}{\left (15+\sqrt {221}+2 x\right ) \log ^2\left (\frac {2+30 x+3 x^2}{1+15 x+x^2}\right )}\right ) \, dx+14800 \int \left (\frac {1-5 \sqrt {\frac {3}{73}}}{\left (30-2 \sqrt {219}+6 x\right ) \log ^2\left (\frac {2+30 x+3 x^2}{1+15 x+x^2}\right )}+\frac {1+5 \sqrt {\frac {3}{73}}}{\left (30+2 \sqrt {219}+6 x\right ) \log ^2\left (\frac {2+30 x+3 x^2}{1+15 x+x^2}\right )}\right ) \, dx-98000 \int \left (-\frac {\sqrt {\frac {3}{73}}}{\left (-30+2 \sqrt {219}-6 x\right ) \log ^3\left (\frac {2+30 x+3 x^2}{1+15 x+x^2}\right )}-\frac {\sqrt {\frac {3}{73}}}{\left (30+2 \sqrt {219}+6 x\right ) \log ^3\left (\frac {2+30 x+3 x^2}{1+15 x+x^2}\right )}\right ) \, dx-117500 \int \frac {1}{\log ^3\left (\frac {2+30 x+3 x^2}{1+15 x+x^2}\right )} \, dx+166500 \int \left (-\frac {2}{\sqrt {221} \left (-15+\sqrt {221}-2 x\right ) \log ^3\left (\frac {2+30 x+3 x^2}{1+15 x+x^2}\right )}-\frac {2}{\sqrt {221} \left (15+\sqrt {221}+2 x\right ) \log ^3\left (\frac {2+30 x+3 x^2}{1+15 x+x^2}\right )}\right ) \, dx-\frac {4380400}{3} \int \left (\frac {1-5 \sqrt {\frac {3}{73}}}{\left (30-2 \sqrt {219}+6 x\right ) \log ^3\left (\frac {2+30 x+3 x^2}{1+15 x+x^2}\right )}+\frac {1+5 \sqrt {\frac {3}{73}}}{\left (30+2 \sqrt {219}+6 x\right ) \log ^3\left (\frac {2+30 x+3 x^2}{1+15 x+x^2}\right )}\right ) \, dx+2486350 \int \left (\frac {1-\frac {15}{\sqrt {221}}}{\left (15-\sqrt {221}+2 x\right ) \log ^3\left (\frac {2+30 x+3 x^2}{1+15 x+x^2}\right )}+\frac {1+\frac {15}{\sqrt {221}}}{\left (15+\sqrt {221}+2 x\right ) \log ^3\left (\frac {2+30 x+3 x^2}{1+15 x+x^2}\right )}\right ) \, dx \\ & = 100 \int \frac {x^3}{\log ^2\left (\frac {2+30 x+3 x^2}{1+15 x+x^2}\right )} \, dx-100 \int \frac {x}{\log \left (\frac {2+30 x+3 x^2}{1+15 x+x^2}\right )} \, dx-250 \int \frac {x^2}{\log ^3\left (\frac {2+30 x+3 x^2}{1+15 x+x^2}\right )} \, dx+250 \int \frac {1}{\log ^2\left (\frac {2+30 x+3 x^2}{1+15 x+x^2}\right )} \, dx+\frac {18650}{3} \int \frac {x}{\log ^3\left (\frac {2+30 x+3 x^2}{1+15 x+x^2}\right )} \, dx-117500 \int \frac {1}{\log ^3\left (\frac {2+30 x+3 x^2}{1+15 x+x^2}\right )} \, dx-\left (1000 \sqrt {\frac {3}{73}}\right ) \int \frac {1}{\left (-30+2 \sqrt {219}-6 x\right ) \log ^2\left (\frac {2+30 x+3 x^2}{1+15 x+x^2}\right )} \, dx-\left (1000 \sqrt {\frac {3}{73}}\right ) \int \frac {1}{\left (30+2 \sqrt {219}+6 x\right ) \log ^2\left (\frac {2+30 x+3 x^2}{1+15 x+x^2}\right )} \, dx+\left (98000 \sqrt {\frac {3}{73}}\right ) \int \frac {1}{\left (-30+2 \sqrt {219}-6 x\right ) \log ^3\left (\frac {2+30 x+3 x^2}{1+15 x+x^2}\right )} \, dx+\left (98000 \sqrt {\frac {3}{73}}\right ) \int \frac {1}{\left (30+2 \sqrt {219}+6 x\right ) \log ^3\left (\frac {2+30 x+3 x^2}{1+15 x+x^2}\right )} \, dx+\frac {1500 \int \frac {1}{\left (-15+\sqrt {221}-2 x\right ) \log ^2\left (\frac {2+30 x+3 x^2}{1+15 x+x^2}\right )} \, dx}{\sqrt {221}}+\frac {1500 \int \frac {1}{\left (15+\sqrt {221}+2 x\right ) \log ^2\left (\frac {2+30 x+3 x^2}{1+15 x+x^2}\right )} \, dx}{\sqrt {221}}-\frac {333000 \int \frac {1}{\left (-15+\sqrt {221}-2 x\right ) \log ^3\left (\frac {2+30 x+3 x^2}{1+15 x+x^2}\right )} \, dx}{\sqrt {221}}-\frac {333000 \int \frac {1}{\left (15+\sqrt {221}+2 x\right ) \log ^3\left (\frac {2+30 x+3 x^2}{1+15 x+x^2}\right )} \, dx}{\sqrt {221}}+\frac {1}{73} \left (14800 \left (73-5 \sqrt {219}\right )\right ) \int \frac {1}{\left (30-2 \sqrt {219}+6 x\right ) \log ^2\left (\frac {2+30 x+3 x^2}{1+15 x+x^2}\right )} \, dx-\frac {1}{219} \left (4380400 \left (73-5 \sqrt {219}\right )\right ) \int \frac {1}{\left (30-2 \sqrt {219}+6 x\right ) \log ^3\left (\frac {2+30 x+3 x^2}{1+15 x+x^2}\right )} \, dx+\frac {1}{73} \left (14800 \left (73+5 \sqrt {219}\right )\right ) \int \frac {1}{\left (30+2 \sqrt {219}+6 x\right ) \log ^2\left (\frac {2+30 x+3 x^2}{1+15 x+x^2}\right )} \, dx-\frac {1}{219} \left (4380400 \left (73+5 \sqrt {219}\right )\right ) \int \frac {1}{\left (30+2 \sqrt {219}+6 x\right ) \log ^3\left (\frac {2+30 x+3 x^2}{1+15 x+x^2}\right )} \, dx-\frac {1}{221} \left (11150 \left (221-15 \sqrt {221}\right )\right ) \int \frac {1}{\left (15-\sqrt {221}+2 x\right ) \log ^2\left (\frac {2+30 x+3 x^2}{1+15 x+x^2}\right )} \, dx+\frac {1}{221} \left (2486350 \left (221-15 \sqrt {221}\right )\right ) \int \frac {1}{\left (15-\sqrt {221}+2 x\right ) \log ^3\left (\frac {2+30 x+3 x^2}{1+15 x+x^2}\right )} \, dx-\frac {1}{221} \left (11150 \left (221+15 \sqrt {221}\right )\right ) \int \frac {1}{\left (15+\sqrt {221}+2 x\right ) \log ^2\left (\frac {2+30 x+3 x^2}{1+15 x+x^2}\right )} \, dx+\frac {1}{221} \left (2486350 \left (221+15 \sqrt {221}\right )\right ) \int \frac {1}{\left (15+\sqrt {221}+2 x\right ) \log ^3\left (\frac {2+30 x+3 x^2}{1+15 x+x^2}\right )} \, dx \\ \end{align*}
Leaf count is larger than twice the leaf count of optimal. \(63\) vs. \(2(24)=48\).
Time = 0.08 (sec) , antiderivative size = 63, normalized size of antiderivative = 2.62 \[ \int \frac {-100 x^5-750 x^6+\left (300 x^3+6750 x^4+45500 x^5+7500 x^6+300 x^7\right ) \log \left (\frac {2+30 x+3 x^2}{1+15 x+x^2}\right )+\left (-200 x-6000 x^2-45500 x^3-7500 x^4-300 x^5\right ) \log ^2\left (\frac {2+30 x+3 x^2}{1+15 x+x^2}\right )}{\left (2+60 x+455 x^2+75 x^3+3 x^4\right ) \log ^3\left (\frac {2+30 x+3 x^2}{1+15 x+x^2}\right )} \, dx=50 \left (\frac {x^4}{2 \log ^2\left (\frac {2+30 x+3 x^2}{1+15 x+x^2}\right )}-\frac {x^2}{\log \left (\frac {2+30 x+3 x^2}{1+15 x+x^2}\right )}\right ) \]
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Leaf count of result is larger than twice the leaf count of optimal. \(57\) vs. \(2(24)=48\).
Time = 10.56 (sec) , antiderivative size = 58, normalized size of antiderivative = 2.42
method | result | size |
risch | \(\frac {25 \left (x^{2}-2 \ln \left (\frac {3 x^{2}+30 x +2}{x^{2}+15 x +1}\right )\right ) x^{2}}{\ln \left (\frac {3 x^{2}+30 x +2}{x^{2}+15 x +1}\right )^{2}}\) | \(58\) |
parallelrisch | \(-\frac {-225 x^{4}+450 x^{2} \ln \left (\frac {3 x^{2}+30 x +2}{x^{2}+15 x +1}\right )}{9 \ln \left (\frac {3 x^{2}+30 x +2}{x^{2}+15 x +1}\right )^{2}}\) | \(60\) |
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Leaf count of result is larger than twice the leaf count of optimal. 57 vs. \(2 (25) = 50\).
Time = 0.30 (sec) , antiderivative size = 57, normalized size of antiderivative = 2.38 \[ \int \frac {-100 x^5-750 x^6+\left (300 x^3+6750 x^4+45500 x^5+7500 x^6+300 x^7\right ) \log \left (\frac {2+30 x+3 x^2}{1+15 x+x^2}\right )+\left (-200 x-6000 x^2-45500 x^3-7500 x^4-300 x^5\right ) \log ^2\left (\frac {2+30 x+3 x^2}{1+15 x+x^2}\right )}{\left (2+60 x+455 x^2+75 x^3+3 x^4\right ) \log ^3\left (\frac {2+30 x+3 x^2}{1+15 x+x^2}\right )} \, dx=\frac {25 \, {\left (x^{4} - 2 \, x^{2} \log \left (\frac {3 \, x^{2} + 30 \, x + 2}{x^{2} + 15 \, x + 1}\right )\right )}}{\log \left (\frac {3 \, x^{2} + 30 \, x + 2}{x^{2} + 15 \, x + 1}\right )^{2}} \]
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Leaf count of result is larger than twice the leaf count of optimal. 51 vs. \(2 (19) = 38\).
Time = 0.10 (sec) , antiderivative size = 51, normalized size of antiderivative = 2.12 \[ \int \frac {-100 x^5-750 x^6+\left (300 x^3+6750 x^4+45500 x^5+7500 x^6+300 x^7\right ) \log \left (\frac {2+30 x+3 x^2}{1+15 x+x^2}\right )+\left (-200 x-6000 x^2-45500 x^3-7500 x^4-300 x^5\right ) \log ^2\left (\frac {2+30 x+3 x^2}{1+15 x+x^2}\right )}{\left (2+60 x+455 x^2+75 x^3+3 x^4\right ) \log ^3\left (\frac {2+30 x+3 x^2}{1+15 x+x^2}\right )} \, dx=\frac {25 x^{4} - 50 x^{2} \log {\left (\frac {3 x^{2} + 30 x + 2}{x^{2} + 15 x + 1} \right )}}{\log {\left (\frac {3 x^{2} + 30 x + 2}{x^{2} + 15 x + 1} \right )}^{2}} \]
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Leaf count of result is larger than twice the leaf count of optimal. 85 vs. \(2 (25) = 50\).
Time = 0.25 (sec) , antiderivative size = 85, normalized size of antiderivative = 3.54 \[ \int \frac {-100 x^5-750 x^6+\left (300 x^3+6750 x^4+45500 x^5+7500 x^6+300 x^7\right ) \log \left (\frac {2+30 x+3 x^2}{1+15 x+x^2}\right )+\left (-200 x-6000 x^2-45500 x^3-7500 x^4-300 x^5\right ) \log ^2\left (\frac {2+30 x+3 x^2}{1+15 x+x^2}\right )}{\left (2+60 x+455 x^2+75 x^3+3 x^4\right ) \log ^3\left (\frac {2+30 x+3 x^2}{1+15 x+x^2}\right )} \, dx=\frac {25 \, {\left (x^{4} - 2 \, x^{2} \log \left (3 \, x^{2} + 30 \, x + 2\right ) + 2 \, x^{2} \log \left (x^{2} + 15 \, x + 1\right )\right )}}{\log \left (3 \, x^{2} + 30 \, x + 2\right )^{2} - 2 \, \log \left (3 \, x^{2} + 30 \, x + 2\right ) \log \left (x^{2} + 15 \, x + 1\right ) + \log \left (x^{2} + 15 \, x + 1\right )^{2}} \]
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Leaf count of result is larger than twice the leaf count of optimal. 57 vs. \(2 (25) = 50\).
Time = 0.58 (sec) , antiderivative size = 57, normalized size of antiderivative = 2.38 \[ \int \frac {-100 x^5-750 x^6+\left (300 x^3+6750 x^4+45500 x^5+7500 x^6+300 x^7\right ) \log \left (\frac {2+30 x+3 x^2}{1+15 x+x^2}\right )+\left (-200 x-6000 x^2-45500 x^3-7500 x^4-300 x^5\right ) \log ^2\left (\frac {2+30 x+3 x^2}{1+15 x+x^2}\right )}{\left (2+60 x+455 x^2+75 x^3+3 x^4\right ) \log ^3\left (\frac {2+30 x+3 x^2}{1+15 x+x^2}\right )} \, dx=\frac {25 \, {\left (x^{4} - 2 \, x^{2} \log \left (\frac {3 \, x^{2} + 30 \, x + 2}{x^{2} + 15 \, x + 1}\right )\right )}}{\log \left (\frac {3 \, x^{2} + 30 \, x + 2}{x^{2} + 15 \, x + 1}\right )^{2}} \]
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Time = 15.25 (sec) , antiderivative size = 113, normalized size of antiderivative = 4.71 \[ \int \frac {-100 x^5-750 x^6+\left (300 x^3+6750 x^4+45500 x^5+7500 x^6+300 x^7\right ) \log \left (\frac {2+30 x+3 x^2}{1+15 x+x^2}\right )+\left (-200 x-6000 x^2-45500 x^3-7500 x^4-300 x^5\right ) \log ^2\left (\frac {2+30 x+3 x^2}{1+15 x+x^2}\right )}{\left (2+60 x+455 x^2+75 x^3+3 x^4\right ) \log ^3\left (\frac {2+30 x+3 x^2}{1+15 x+x^2}\right )} \, dx=\frac {2531672218\,\ln \left (\frac {3\,x^2+30\,x+2}{x^2+15\,x+1}\right )}{50625}+\frac {25\,x^4-50\,x^2\,\ln \left (\frac {3\,x^2+30\,x+2}{x^2+15\,x+1}\right )}{{\ln \left (\frac {3\,x^2+30\,x+2}{x^2+15\,x+1}\right )}^2}+\frac {\mathrm {atan}\left (\frac {x^2\,371{}\mathrm {i}+x\,2250{}\mathrm {i}+150{}\mathrm {i}}{955\,x^2+11010\,x+734}\right )\,5063344436{}\mathrm {i}}{50625} \]
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