Integrand size = 358, antiderivative size = 25 \[ \int \frac {\left (27 x-27 x^3+9 x^5-x^7\right ) \log ^5(2)+\left (135 x^2-135 x^4+45 x^6-5 x^8\right ) \log ^4(2) \log (x)+\left (270 x^3-270 x^5+90 x^7-10 x^9\right ) \log ^3(2) \log ^2(x)+\left (\left (-108+36 x^2\right ) \log (2)+\left (270 x^4-270 x^6+90 x^8-10 x^{10}\right ) \log ^2(2)\right ) \log ^3(x)+\left (-36 x^2+135 x^5-135 x^7+45 x^9-5 x^{11}\right ) \log (2) \log ^4(x)+\left (108 x-72 x^3+27 x^6-27 x^8+9 x^{10}-x^{12}\right ) \log ^5(x)}{\left (-27 x+27 x^3-9 x^5+x^7\right ) \log ^5(2)+\left (-135 x^2+135 x^4-45 x^6+5 x^8\right ) \log ^4(2) \log (x)+\left (-270 x^3+270 x^5-90 x^7+10 x^9\right ) \log ^3(2) \log ^2(x)+\left (-270 x^4+270 x^6-90 x^8+10 x^{10}\right ) \log ^2(2) \log ^3(x)+\left (-135 x^5+135 x^7-45 x^9+5 x^{11}\right ) \log (2) \log ^4(x)+\left (-27 x^6+27 x^8-9 x^{10}+x^{12}\right ) \log ^5(x)} \, dx=4-x+\frac {9}{\left (-3+x^2\right )^2 \left (x+\frac {\log (2)}{\log (x)}\right )^4} \]
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\[ \int \frac {\left (27 x-27 x^3+9 x^5-x^7\right ) \log ^5(2)+\left (135 x^2-135 x^4+45 x^6-5 x^8\right ) \log ^4(2) \log (x)+\left (270 x^3-270 x^5+90 x^7-10 x^9\right ) \log ^3(2) \log ^2(x)+\left (\left (-108+36 x^2\right ) \log (2)+\left (270 x^4-270 x^6+90 x^8-10 x^{10}\right ) \log ^2(2)\right ) \log ^3(x)+\left (-36 x^2+135 x^5-135 x^7+45 x^9-5 x^{11}\right ) \log (2) \log ^4(x)+\left (108 x-72 x^3+27 x^6-27 x^8+9 x^{10}-x^{12}\right ) \log ^5(x)}{\left (-27 x+27 x^3-9 x^5+x^7\right ) \log ^5(2)+\left (-135 x^2+135 x^4-45 x^6+5 x^8\right ) \log ^4(2) \log (x)+\left (-270 x^3+270 x^5-90 x^7+10 x^9\right ) \log ^3(2) \log ^2(x)+\left (-270 x^4+270 x^6-90 x^8+10 x^{10}\right ) \log ^2(2) \log ^3(x)+\left (-135 x^5+135 x^7-45 x^9+5 x^{11}\right ) \log (2) \log ^4(x)+\left (-27 x^6+27 x^8-9 x^{10}+x^{12}\right ) \log ^5(x)} \, dx=\int \frac {\left (27 x-27 x^3+9 x^5-x^7\right ) \log ^5(2)+\left (135 x^2-135 x^4+45 x^6-5 x^8\right ) \log ^4(2) \log (x)+\left (270 x^3-270 x^5+90 x^7-10 x^9\right ) \log ^3(2) \log ^2(x)+\left (\left (-108+36 x^2\right ) \log (2)+\left (270 x^4-270 x^6+90 x^8-10 x^{10}\right ) \log ^2(2)\right ) \log ^3(x)+\left (-36 x^2+135 x^5-135 x^7+45 x^9-5 x^{11}\right ) \log (2) \log ^4(x)+\left (108 x-72 x^3+27 x^6-27 x^8+9 x^{10}-x^{12}\right ) \log ^5(x)}{\left (-27 x+27 x^3-9 x^5+x^7\right ) \log ^5(2)+\left (-135 x^2+135 x^4-45 x^6+5 x^8\right ) \log ^4(2) \log (x)+\left (-270 x^3+270 x^5-90 x^7+10 x^9\right ) \log ^3(2) \log ^2(x)+\left (-270 x^4+270 x^6-90 x^8+10 x^{10}\right ) \log ^2(2) \log ^3(x)+\left (-135 x^5+135 x^7-45 x^9+5 x^{11}\right ) \log (2) \log ^4(x)+\left (-27 x^6+27 x^8-9 x^{10}+x^{12}\right ) \log ^5(x)} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {x \left (-3+x^2\right )^3 \log ^5(2)+5 x^2 \left (-3+x^2\right )^3 \log ^4(2) \log (x)+10 x^3 \left (-3+x^2\right )^3 \log ^3(2) \log ^2(x)+2 \left (-3+x^2\right ) \log (2) \left (-18+45 x^4 \log (2)-30 x^6 \log (2)+x^8 \log (32)\right ) \log ^3(x)+x^2 \left (36-135 x^3+135 x^5-45 x^7+5 x^9\right ) \log (2) \log ^4(x)+x \left (-108+72 x^2-27 x^5+27 x^7-9 x^9+x^{11}\right ) \log ^5(x)}{x \left (3-x^2\right )^3 (\log (2)+x \log (x))^5} \, dx \\ & = \int \left (\frac {108-72 x^2+27 x^5-27 x^7+9 x^9-x^{11}}{x^5 \left (-3+x^2\right )^3}-\frac {2 \log ^4(2) (18 x-\log (262144))}{x^5 \left (-3+x^2\right )^2 (\log (2)+x \log (x))^5}+\frac {18 \log ^3(2) \left (-18 x+6 x^3-x^2 \log (4096)+\log (1073741824)\right )}{x^5 \left (-3+x^2\right )^3 (\log (2)+x \log (x))^4}-\frac {36 \log ^2(2) \left (-9 x+3 x^3+30 \log (2)-14 x^2 \log (2)\right )}{x^5 \left (-3+x^2\right )^3 (\log (2)+x \log (x))^3}+\frac {36 \log (2) \left (-3 x+x^3+30 \log (2)-16 x^2 \log (2)\right )}{x^5 \left (-3+x^2\right )^3 (\log (2)+x \log (x))^2}+\frac {108 \left (-5+3 x^2\right ) \log (2)}{x^5 \left (-3+x^2\right )^3 (\log (2)+x \log (x))}\right ) \, dx \\ & = (36 \log (2)) \int \frac {-3 x+x^3+30 \log (2)-16 x^2 \log (2)}{x^5 \left (-3+x^2\right )^3 (\log (2)+x \log (x))^2} \, dx+(108 \log (2)) \int \frac {-5+3 x^2}{x^5 \left (-3+x^2\right )^3 (\log (2)+x \log (x))} \, dx-\left (36 \log ^2(2)\right ) \int \frac {-9 x+3 x^3+30 \log (2)-14 x^2 \log (2)}{x^5 \left (-3+x^2\right )^3 (\log (2)+x \log (x))^3} \, dx+\left (18 \log ^3(2)\right ) \int \frac {-18 x+6 x^3-x^2 \log (4096)+\log (1073741824)}{x^5 \left (-3+x^2\right )^3 (\log (2)+x \log (x))^4} \, dx-\left (2 \log ^4(2)\right ) \int \frac {18 x-\log (262144)}{x^5 \left (-3+x^2\right )^2 (\log (2)+x \log (x))^5} \, dx+\int \frac {108-72 x^2+27 x^5-27 x^7+9 x^9-x^{11}}{x^5 \left (-3+x^2\right )^3} \, dx \\ & = \frac {1}{\left (-3+x^2\right )^2}+\frac {1}{12} \int \frac {-432+144 x^2+48 x^4-108 x^5+72 x^7-12 x^9}{x^5 \left (-3+x^2\right )^2} \, dx+(36 \log (2)) \int \left (\frac {1}{9 x^4 (\log (2)+x \log (x))^2}+\frac {2}{27 x^2 (\log (2)+x \log (x))^2}-\frac {10 \log (2)}{9 x^5 (\log (2)+x \log (x))^2}-\frac {14 \log (2)}{27 x^3 (\log (2)+x \log (x))^2}-\frac {4 \log (2)}{27 x (\log (2)+x \log (x))^2}-\frac {2 x \log (2)}{3 \left (-3+x^2\right )^3 (\log (2)+x \log (x))^2}+\frac {2 (-1+x \log (4))}{27 \left (-3+x^2\right ) (\log (2)+x \log (x))^2}+\frac {3+x \log (4)}{27 \left (-3+x^2\right )^2 (\log (2)+x \log (x))^2}\right ) \, dx+(108 \log (2)) \int \left (\frac {5}{27 x^5 (\log (2)+x \log (x))}+\frac {2}{27 x^3 (\log (2)+x \log (x))}+\frac {1}{81 x (\log (2)+x \log (x))}+\frac {4 x}{27 \left (-3+x^2\right )^3 (\log (2)+x \log (x))}-\frac {x}{27 \left (-3+x^2\right )^2 (\log (2)+x \log (x))}-\frac {x}{81 \left (-3+x^2\right ) (\log (2)+x \log (x))}\right ) \, dx-\left (36 \log ^2(2)\right ) \int \left (\frac {1}{3 x^4 (\log (2)+x \log (x))^3}+\frac {2}{9 x^2 (\log (2)+x \log (x))^3}-\frac {10 \log (2)}{9 x^5 (\log (2)+x \log (x))^3}-\frac {16 \log (2)}{27 x^3 (\log (2)+x \log (x))^3}-\frac {2 \log (2)}{9 x (\log (2)+x \log (x))^3}-\frac {4 x \log (2)}{9 \left (-3+x^2\right )^3 (\log (2)+x \log (x))^3}+\frac {2 (-1+x \log (2))}{9 \left (-3+x^2\right ) (\log (2)+x \log (x))^3}+\frac {9-x \log (4)}{27 \left (-3+x^2\right )^2 (\log (2)+x \log (x))^3}\right ) \, dx+\left (18 \log ^3(2)\right ) \int \left (\frac {2}{3 x^4 (\log (2)+x \log (x))^4}+\frac {4}{9 x^2 (\log (2)+x \log (x))^4}-\frac {x \log (64)}{27 \left (-3+x^2\right )^3 (\log (2)+x \log (x))^4}+\frac {18-x \log (64)}{27 \left (-3+x^2\right )^2 (\log (2)+x \log (x))^4}-\frac {\log (262144)}{27 x^3 (\log (2)+x \log (x))^4}-\frac {\log (16777216)}{81 x (\log (2)+x \log (x))^4}+\frac {-36+x \log (16777216)}{81 \left (-3+x^2\right ) (\log (2)+x \log (x))^4}-\frac {\log (1073741824)}{27 x^5 (\log (2)+x \log (x))^4}\right ) \, dx-\left (2 \log ^4(2)\right ) \int \left (\frac {2}{x^4 (\log (2)+x \log (x))^5}+\frac {4}{3 x^2 (\log (2)+x \log (x))^5}-\frac {\log (262144)}{9 x^5 (\log (2)+x \log (x))^5}-\frac {2 \log (262144)}{27 x^3 (\log (2)+x \log (x))^5}-\frac {\log (262144)}{27 x (\log (2)+x \log (x))^5}+\frac {54-x \log (262144)}{27 \left (-3+x^2\right )^2 (\log (2)+x \log (x))^5}+\frac {-36+x \log (262144)}{27 \left (-3+x^2\right ) (\log (2)+x \log (x))^5}\right ) \, dx \\ & = \text {Too large to display} \\ \end{align*}
Leaf count is larger than twice the leaf count of optimal. \(628\) vs. \(2(25)=50\).
Time = 0.78 (sec) , antiderivative size = 628, normalized size of antiderivative = 25.12 \[ \int \frac {\left (27 x-27 x^3+9 x^5-x^7\right ) \log ^5(2)+\left (135 x^2-135 x^4+45 x^6-5 x^8\right ) \log ^4(2) \log (x)+\left (270 x^3-270 x^5+90 x^7-10 x^9\right ) \log ^3(2) \log ^2(x)+\left (\left (-108+36 x^2\right ) \log (2)+\left (270 x^4-270 x^6+90 x^8-10 x^{10}\right ) \log ^2(2)\right ) \log ^3(x)+\left (-36 x^2+135 x^5-135 x^7+45 x^9-5 x^{11}\right ) \log (2) \log ^4(x)+\left (108 x-72 x^3+27 x^6-27 x^8+9 x^{10}-x^{12}\right ) \log ^5(x)}{\left (-27 x+27 x^3-9 x^5+x^7\right ) \log ^5(2)+\left (-135 x^2+135 x^4-45 x^6+5 x^8\right ) \log ^4(2) \log (x)+\left (-270 x^3+270 x^5-90 x^7+10 x^9\right ) \log ^3(2) \log ^2(x)+\left (-270 x^4+270 x^6-90 x^8+10 x^{10}\right ) \log ^2(2) \log ^3(x)+\left (-135 x^5+135 x^7-45 x^9+5 x^{11}\right ) \log (2) \log ^4(x)+\left (-27 x^6+27 x^8-9 x^{10}+x^{12}\right ) \log ^5(x)} \, dx=\frac {1}{x^4}+\frac {2}{3 x^2}-x+\frac {1}{\left (-3+x^2\right )^2}-\frac {2}{3 \left (-3+x^2\right )}+\frac {9 \log ^4(2)}{x^4 \left (-3+x^2\right )^2 (\log (2)+x \log (x))^4}-\frac {36 \log ^3(2)}{x^4 \left (-3+x^2\right )^2 (\log (2)+x \log (x))^3}-\frac {3 \log ^2(2) \left (180 x^8 \log (2)-1620 x \log ^4(2)+324 \log ^5(2)-216 x^2 \log ^3(2) \left (-15+\log ^2(2)\right )+1080 x^3 \log ^2(2) \left (-3+\log ^2(2)\right )-72 x^7 \left (-3+5 \log ^2(2)\right )+36 x^4 \log (2) \left (45-60 \log ^2(2)+\log ^4(2)\right )-36 x^5 \left (9-60 \log ^2(2)+5 \log ^4(2)\right )+360 x^6 \left (\log ^3(2)-\log (8)\right )+x^9 \left (-36-155 \log ^5(2)+31 \log ^4(2) \log (32)\right )\right )}{2 x^4 \left (-3+x^2\right )^4 (x-\log (2))^5 (\log (2)+x \log (x))^2}-\frac {3 \log (2) \left (-9072 x \log ^6(2)+1296 \log ^7(2)-1296 x^2 \log ^5(2) \left (-21+\log ^2(2)\right )+9072 x^3 \log ^4(2) \left (-5+\log ^2(2)\right )+432 x^4 \log ^3(2) \left (105-63 \log ^2(2)+\log ^4(2)\right )-3024 x^5 \log ^2(2) \left (9-15 \log ^2(2)+\log ^4(2)\right )-48 x^6 \log (2) \left (-189+945 \log ^2(2)-189 \log ^4(2)+\log ^6(2)\right )+48 x^7 \left (-27+567 \log ^2(2)-315 \log ^4(2)+7 \log ^6(2)\right )-4 x^{12} \log (2) \left (84-5310 \log ^3(2)+505 \log ^5(2)+1062 \log ^2(2) \log (32)-101 \log ^4(2) \log (32)\right )+48 x^{10} \log (2) \left (63-35 \log ^2(2)+260 \log ^5(2)-52 \log ^4(2) \log (32)\right )-6 x^9 \left (-216+1512 \log ^2(2)-280 \log ^4(2)+525 \log ^7(2)-105 \log ^6(2) \log (32)\right )+3 x^{11} \left (-144+336 \log ^2(2)-7385 \log ^5(2)+70 \log ^7(2)+1477 \log ^4(2) \log (32)-14 \log ^6(2) \log (32)\right )+x^{13} \left (48-11520 \log ^3(2)+6635 \log ^5(2)-50 \log ^7(2)+2304 \log ^2(2) \log (32)-1327 \log ^4(2) \log (32)+10 \log ^6(2) \log (32)\right )-1008 x^8 \left (-15 \log ^3(2)+\log ^5(2)+\log (512)\right )\right )}{4 x^4 \left (-3+x^2\right )^5 (x-\log (2))^7 (\log (2)+x \log (x))} \]
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Time = 6.42 (sec) , antiderivative size = 27, normalized size of antiderivative = 1.08
method | result | size |
default | \(-x +\frac {9 \ln \left (x \right )^{4}}{\left (x \ln \left (x \right )+\ln \left (2\right )\right )^{4} \left (x^{2}-3\right )^{2}}\) | \(27\) |
risch | \(-\frac {x^{9}-6 x^{7}+9 x^{5}-9}{x^{4} \left (x^{4}-6 x^{2}+9\right )}-\frac {9 \ln \left (2\right ) \left (4 x^{3} \ln \left (x \right )^{3}+6 x^{2} \ln \left (2\right ) \ln \left (x \right )^{2}+4 \ln \left (x \right ) \ln \left (2\right )^{2} x +\ln \left (2\right )^{3}\right )}{x^{4} \left (x^{4}-6 x^{2}+9\right ) \left (x \ln \left (x \right )+\ln \left (2\right )\right )^{4}}\) | \(96\) |
parallelrisch | \(\frac {-x^{9} \ln \left (x \right )^{4}+6 x^{7} \ln \left (x \right )^{4}-x^{5} \ln \left (2\right )^{4}+6 x^{3} \ln \left (2\right )^{4}-9 x \ln \left (2\right )^{4}-9 x^{5} \ln \left (x \right )^{4}+9 \ln \left (x \right )^{4}-36 x^{4} \ln \left (2\right ) \ln \left (x \right )^{3}+24 \ln \left (x \right ) \ln \left (2\right )^{3} x^{4}-36 x^{2} \ln \left (2\right )^{3} \ln \left (x \right )-4 \ln \left (x \right )^{3} \ln \left (2\right ) x^{8}-6 \ln \left (x \right )^{2} \ln \left (2\right )^{2} x^{7}+24 \ln \left (x \right )^{3} \ln \left (2\right ) x^{6}-4 \ln \left (x \right ) \ln \left (2\right )^{3} x^{6}+36 \ln \left (x \right )^{2} \ln \left (2\right )^{2} x^{5}-54 \ln \left (2\right )^{2} x^{3} \ln \left (x \right )^{2}}{x^{8} \ln \left (x \right )^{4}+4 \ln \left (x \right )^{3} \ln \left (2\right ) x^{7}+6 \ln \left (x \right )^{2} \ln \left (2\right )^{2} x^{6}-6 x^{6} \ln \left (x \right )^{4}+4 \ln \left (x \right ) \ln \left (2\right )^{3} x^{5}-24 \ln \left (x \right )^{3} \ln \left (2\right ) x^{5}+\ln \left (2\right )^{4} x^{4}-36 x^{4} \ln \left (2\right )^{2} \ln \left (x \right )^{2}+9 x^{4} \ln \left (x \right )^{4}-24 \ln \left (x \right ) \ln \left (2\right )^{3} x^{3}+36 \ln \left (x \right )^{3} \ln \left (2\right ) x^{3}-6 x^{2} \ln \left (2\right )^{4}+54 \ln \left (x \right )^{2} \ln \left (2\right )^{2} x^{2}+36 x \ln \left (2\right )^{3} \ln \left (x \right )+9 \ln \left (2\right )^{4}}\) | \(321\) |
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Leaf count of result is larger than twice the leaf count of optimal. 211 vs. \(2 (25) = 50\).
Time = 0.26 (sec) , antiderivative size = 211, normalized size of antiderivative = 8.44 \[ \int \frac {\left (27 x-27 x^3+9 x^5-x^7\right ) \log ^5(2)+\left (135 x^2-135 x^4+45 x^6-5 x^8\right ) \log ^4(2) \log (x)+\left (270 x^3-270 x^5+90 x^7-10 x^9\right ) \log ^3(2) \log ^2(x)+\left (\left (-108+36 x^2\right ) \log (2)+\left (270 x^4-270 x^6+90 x^8-10 x^{10}\right ) \log ^2(2)\right ) \log ^3(x)+\left (-36 x^2+135 x^5-135 x^7+45 x^9-5 x^{11}\right ) \log (2) \log ^4(x)+\left (108 x-72 x^3+27 x^6-27 x^8+9 x^{10}-x^{12}\right ) \log ^5(x)}{\left (-27 x+27 x^3-9 x^5+x^7\right ) \log ^5(2)+\left (-135 x^2+135 x^4-45 x^6+5 x^8\right ) \log ^4(2) \log (x)+\left (-270 x^3+270 x^5-90 x^7+10 x^9\right ) \log ^3(2) \log ^2(x)+\left (-270 x^4+270 x^6-90 x^8+10 x^{10}\right ) \log ^2(2) \log ^3(x)+\left (-135 x^5+135 x^7-45 x^9+5 x^{11}\right ) \log (2) \log ^4(x)+\left (-27 x^6+27 x^8-9 x^{10}+x^{12}\right ) \log ^5(x)} \, dx=-\frac {{\left (x^{5} - 6 \, x^{3} + 9 \, x\right )} \log \left (2\right )^{4} + 4 \, {\left (x^{6} - 6 \, x^{4} + 9 \, x^{2}\right )} \log \left (2\right )^{3} \log \left (x\right ) + 6 \, {\left (x^{7} - 6 \, x^{5} + 9 \, x^{3}\right )} \log \left (2\right )^{2} \log \left (x\right )^{2} + 4 \, {\left (x^{8} - 6 \, x^{6} + 9 \, x^{4}\right )} \log \left (2\right ) \log \left (x\right )^{3} + {\left (x^{9} - 6 \, x^{7} + 9 \, x^{5} - 9\right )} \log \left (x\right )^{4}}{{\left (x^{4} - 6 \, x^{2} + 9\right )} \log \left (2\right )^{4} + 4 \, {\left (x^{5} - 6 \, x^{3} + 9 \, x\right )} \log \left (2\right )^{3} \log \left (x\right ) + 6 \, {\left (x^{6} - 6 \, x^{4} + 9 \, x^{2}\right )} \log \left (2\right )^{2} \log \left (x\right )^{2} + 4 \, {\left (x^{7} - 6 \, x^{5} + 9 \, x^{3}\right )} \log \left (2\right ) \log \left (x\right )^{3} + {\left (x^{8} - 6 \, x^{6} + 9 \, x^{4}\right )} \log \left (x\right )^{4}} \]
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Leaf count of result is larger than twice the leaf count of optimal. 212 vs. \(2 (20) = 40\).
Time = 0.31 (sec) , antiderivative size = 212, normalized size of antiderivative = 8.48 \[ \int \frac {\left (27 x-27 x^3+9 x^5-x^7\right ) \log ^5(2)+\left (135 x^2-135 x^4+45 x^6-5 x^8\right ) \log ^4(2) \log (x)+\left (270 x^3-270 x^5+90 x^7-10 x^9\right ) \log ^3(2) \log ^2(x)+\left (\left (-108+36 x^2\right ) \log (2)+\left (270 x^4-270 x^6+90 x^8-10 x^{10}\right ) \log ^2(2)\right ) \log ^3(x)+\left (-36 x^2+135 x^5-135 x^7+45 x^9-5 x^{11}\right ) \log (2) \log ^4(x)+\left (108 x-72 x^3+27 x^6-27 x^8+9 x^{10}-x^{12}\right ) \log ^5(x)}{\left (-27 x+27 x^3-9 x^5+x^7\right ) \log ^5(2)+\left (-135 x^2+135 x^4-45 x^6+5 x^8\right ) \log ^4(2) \log (x)+\left (-270 x^3+270 x^5-90 x^7+10 x^9\right ) \log ^3(2) \log ^2(x)+\left (-270 x^4+270 x^6-90 x^8+10 x^{10}\right ) \log ^2(2) \log ^3(x)+\left (-135 x^5+135 x^7-45 x^9+5 x^{11}\right ) \log (2) \log ^4(x)+\left (-27 x^6+27 x^8-9 x^{10}+x^{12}\right ) \log ^5(x)} \, dx=- x + \frac {- 36 x^{3} \log {\left (2 \right )} \log {\left (x \right )}^{3} - 54 x^{2} \log {\left (2 \right )}^{2} \log {\left (x \right )}^{2} - 36 x \log {\left (2 \right )}^{3} \log {\left (x \right )} - 9 \log {\left (2 \right )}^{4}}{x^{8} \log {\left (2 \right )}^{4} - 6 x^{6} \log {\left (2 \right )}^{4} + 9 x^{4} \log {\left (2 \right )}^{4} + \left (x^{12} - 6 x^{10} + 9 x^{8}\right ) \log {\left (x \right )}^{4} + \left (4 x^{9} \log {\left (2 \right )}^{3} - 24 x^{7} \log {\left (2 \right )}^{3} + 36 x^{5} \log {\left (2 \right )}^{3}\right ) \log {\left (x \right )} + \left (6 x^{10} \log {\left (2 \right )}^{2} - 36 x^{8} \log {\left (2 \right )}^{2} + 54 x^{6} \log {\left (2 \right )}^{2}\right ) \log {\left (x \right )}^{2} + \left (4 x^{11} \log {\left (2 \right )} - 24 x^{9} \log {\left (2 \right )} + 36 x^{7} \log {\left (2 \right )}\right ) \log {\left (x \right )}^{3}} + \frac {9}{x^{8} - 6 x^{6} + 9 x^{4}} \]
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Leaf count of result is larger than twice the leaf count of optimal. 272 vs. \(2 (25) = 50\).
Time = 0.47 (sec) , antiderivative size = 272, normalized size of antiderivative = 10.88 \[ \int \frac {\left (27 x-27 x^3+9 x^5-x^7\right ) \log ^5(2)+\left (135 x^2-135 x^4+45 x^6-5 x^8\right ) \log ^4(2) \log (x)+\left (270 x^3-270 x^5+90 x^7-10 x^9\right ) \log ^3(2) \log ^2(x)+\left (\left (-108+36 x^2\right ) \log (2)+\left (270 x^4-270 x^6+90 x^8-10 x^{10}\right ) \log ^2(2)\right ) \log ^3(x)+\left (-36 x^2+135 x^5-135 x^7+45 x^9-5 x^{11}\right ) \log (2) \log ^4(x)+\left (108 x-72 x^3+27 x^6-27 x^8+9 x^{10}-x^{12}\right ) \log ^5(x)}{\left (-27 x+27 x^3-9 x^5+x^7\right ) \log ^5(2)+\left (-135 x^2+135 x^4-45 x^6+5 x^8\right ) \log ^4(2) \log (x)+\left (-270 x^3+270 x^5-90 x^7+10 x^9\right ) \log ^3(2) \log ^2(x)+\left (-270 x^4+270 x^6-90 x^8+10 x^{10}\right ) \log ^2(2) \log ^3(x)+\left (-135 x^5+135 x^7-45 x^9+5 x^{11}\right ) \log (2) \log ^4(x)+\left (-27 x^6+27 x^8-9 x^{10}+x^{12}\right ) \log ^5(x)} \, dx=-\frac {x^{5} \log \left (2\right )^{4} - 6 \, x^{3} \log \left (2\right )^{4} + 9 \, x \log \left (2\right )^{4} + {\left (x^{9} - 6 \, x^{7} + 9 \, x^{5} - 9\right )} \log \left (x\right )^{4} + 4 \, {\left (x^{8} \log \left (2\right ) - 6 \, x^{6} \log \left (2\right ) + 9 \, x^{4} \log \left (2\right )\right )} \log \left (x\right )^{3} + 6 \, {\left (x^{7} \log \left (2\right )^{2} - 6 \, x^{5} \log \left (2\right )^{2} + 9 \, x^{3} \log \left (2\right )^{2}\right )} \log \left (x\right )^{2} + 4 \, {\left (x^{6} \log \left (2\right )^{3} - 6 \, x^{4} \log \left (2\right )^{3} + 9 \, x^{2} \log \left (2\right )^{3}\right )} \log \left (x\right )}{x^{4} \log \left (2\right )^{4} - 6 \, x^{2} \log \left (2\right )^{4} + {\left (x^{8} - 6 \, x^{6} + 9 \, x^{4}\right )} \log \left (x\right )^{4} + 9 \, \log \left (2\right )^{4} + 4 \, {\left (x^{7} \log \left (2\right ) - 6 \, x^{5} \log \left (2\right ) + 9 \, x^{3} \log \left (2\right )\right )} \log \left (x\right )^{3} + 6 \, {\left (x^{6} \log \left (2\right )^{2} - 6 \, x^{4} \log \left (2\right )^{2} + 9 \, x^{2} \log \left (2\right )^{2}\right )} \log \left (x\right )^{2} + 4 \, {\left (x^{5} \log \left (2\right )^{3} - 6 \, x^{3} \log \left (2\right )^{3} + 9 \, x \log \left (2\right )^{3}\right )} \log \left (x\right )} \]
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Leaf count of result is larger than twice the leaf count of optimal. 237 vs. \(2 (25) = 50\).
Time = 0.60 (sec) , antiderivative size = 237, normalized size of antiderivative = 9.48 \[ \int \frac {\left (27 x-27 x^3+9 x^5-x^7\right ) \log ^5(2)+\left (135 x^2-135 x^4+45 x^6-5 x^8\right ) \log ^4(2) \log (x)+\left (270 x^3-270 x^5+90 x^7-10 x^9\right ) \log ^3(2) \log ^2(x)+\left (\left (-108+36 x^2\right ) \log (2)+\left (270 x^4-270 x^6+90 x^8-10 x^{10}\right ) \log ^2(2)\right ) \log ^3(x)+\left (-36 x^2+135 x^5-135 x^7+45 x^9-5 x^{11}\right ) \log (2) \log ^4(x)+\left (108 x-72 x^3+27 x^6-27 x^8+9 x^{10}-x^{12}\right ) \log ^5(x)}{\left (-27 x+27 x^3-9 x^5+x^7\right ) \log ^5(2)+\left (-135 x^2+135 x^4-45 x^6+5 x^8\right ) \log ^4(2) \log (x)+\left (-270 x^3+270 x^5-90 x^7+10 x^9\right ) \log ^3(2) \log ^2(x)+\left (-270 x^4+270 x^6-90 x^8+10 x^{10}\right ) \log ^2(2) \log ^3(x)+\left (-135 x^5+135 x^7-45 x^9+5 x^{11}\right ) \log (2) \log ^4(x)+\left (-27 x^6+27 x^8-9 x^{10}+x^{12}\right ) \log ^5(x)} \, dx=-x - \frac {9 \, {\left (4 \, x^{3} \log \left (2\right ) \log \left (x\right )^{3} + 6 \, x^{2} \log \left (2\right )^{2} \log \left (x\right )^{2} + 4 \, x \log \left (2\right )^{3} \log \left (x\right ) + \log \left (2\right )^{4}\right )}}{x^{12} \log \left (x\right )^{4} + 4 \, x^{11} \log \left (2\right ) \log \left (x\right )^{3} + 6 \, x^{10} \log \left (2\right )^{2} \log \left (x\right )^{2} - 6 \, x^{10} \log \left (x\right )^{4} + 4 \, x^{9} \log \left (2\right )^{3} \log \left (x\right ) - 24 \, x^{9} \log \left (2\right ) \log \left (x\right )^{3} + x^{8} \log \left (2\right )^{4} - 36 \, x^{8} \log \left (2\right )^{2} \log \left (x\right )^{2} + 9 \, x^{8} \log \left (x\right )^{4} - 24 \, x^{7} \log \left (2\right )^{3} \log \left (x\right ) + 36 \, x^{7} \log \left (2\right ) \log \left (x\right )^{3} - 6 \, x^{6} \log \left (2\right )^{4} + 54 \, x^{6} \log \left (2\right )^{2} \log \left (x\right )^{2} + 36 \, x^{5} \log \left (2\right )^{3} \log \left (x\right ) + 9 \, x^{4} \log \left (2\right )^{4}} - \frac {2 \, x^{2} - 9}{3 \, {\left (x^{4} - 6 \, x^{2} + 9\right )}} + \frac {2 \, x^{2} + 3}{3 \, x^{4}} \]
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Timed out. \[ \int \frac {\left (27 x-27 x^3+9 x^5-x^7\right ) \log ^5(2)+\left (135 x^2-135 x^4+45 x^6-5 x^8\right ) \log ^4(2) \log (x)+\left (270 x^3-270 x^5+90 x^7-10 x^9\right ) \log ^3(2) \log ^2(x)+\left (\left (-108+36 x^2\right ) \log (2)+\left (270 x^4-270 x^6+90 x^8-10 x^{10}\right ) \log ^2(2)\right ) \log ^3(x)+\left (-36 x^2+135 x^5-135 x^7+45 x^9-5 x^{11}\right ) \log (2) \log ^4(x)+\left (108 x-72 x^3+27 x^6-27 x^8+9 x^{10}-x^{12}\right ) \log ^5(x)}{\left (-27 x+27 x^3-9 x^5+x^7\right ) \log ^5(2)+\left (-135 x^2+135 x^4-45 x^6+5 x^8\right ) \log ^4(2) \log (x)+\left (-270 x^3+270 x^5-90 x^7+10 x^9\right ) \log ^3(2) \log ^2(x)+\left (-270 x^4+270 x^6-90 x^8+10 x^{10}\right ) \log ^2(2) \log ^3(x)+\left (-135 x^5+135 x^7-45 x^9+5 x^{11}\right ) \log (2) \log ^4(x)+\left (-27 x^6+27 x^8-9 x^{10}+x^{12}\right ) \log ^5(x)} \, dx=-\int \frac {\left (-x^{12}+9\,x^{10}-27\,x^8+27\,x^6-72\,x^3+108\,x\right )\,{\ln \left (x\right )}^5-\ln \left (2\right )\,\left (5\,x^{11}-45\,x^9+135\,x^7-135\,x^5+36\,x^2\right )\,{\ln \left (x\right )}^4+\left (\ln \left (2\right )\,\left (36\,x^2-108\right )+{\ln \left (2\right )}^2\,\left (-10\,x^{10}+90\,x^8-270\,x^6+270\,x^4\right )\right )\,{\ln \left (x\right )}^3+{\ln \left (2\right )}^3\,\left (-10\,x^9+90\,x^7-270\,x^5+270\,x^3\right )\,{\ln \left (x\right )}^2+{\ln \left (2\right )}^4\,\left (-5\,x^8+45\,x^6-135\,x^4+135\,x^2\right )\,\ln \left (x\right )+{\ln \left (2\right )}^5\,\left (-x^7+9\,x^5-27\,x^3+27\,x\right )}{\left (-x^{12}+9\,x^{10}-27\,x^8+27\,x^6\right )\,{\ln \left (x\right )}^5+\ln \left (2\right )\,\left (-5\,x^{11}+45\,x^9-135\,x^7+135\,x^5\right )\,{\ln \left (x\right )}^4+{\ln \left (2\right )}^2\,\left (-10\,x^{10}+90\,x^8-270\,x^6+270\,x^4\right )\,{\ln \left (x\right )}^3+{\ln \left (2\right )}^3\,\left (-10\,x^9+90\,x^7-270\,x^5+270\,x^3\right )\,{\ln \left (x\right )}^2+{\ln \left (2\right )}^4\,\left (-5\,x^8+45\,x^6-135\,x^4+135\,x^2\right )\,\ln \left (x\right )+{\ln \left (2\right )}^5\,\left (-x^7+9\,x^5-27\,x^3+27\,x\right )} \,d x \]
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