Integrand size = 190, antiderivative size = 28 \[ \int \frac {1250 x^4-200 x^6+6 x^8+\left (1000 x^3-40 x^5\right ) \log (x) \log (12 x)+\left (500 x^3-20 x^5+\left (500 x^3-60 x^5\right ) \log (x)\right ) \log ^2(12 x)+\left (600 x^2-8 x^4\right ) \log ^2(x) \log ^3(12 x)+\left (\left (300 x^2-4 x^4\right ) \log (x)-4 x^4 \log ^2(x)\right ) \log ^4(12 x)+120 x \log ^3(x) \log ^5(12 x)+\left (60 x \log ^2(x)-20 x \log ^3(x)\right ) \log ^6(12 x)+8 \log ^4(x) \log ^7(12 x)+\left (4 \log ^3(x)-2 \log ^4(x)\right ) \log ^8(12 x)}{x^3} \, dx=x^2 \left (-x^2+\left (5+\frac {\log (x) \log ^2(12 x)}{x}\right )^2\right )^2 \]
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\[ \int \frac {1250 x^4-200 x^6+6 x^8+\left (1000 x^3-40 x^5\right ) \log (x) \log (12 x)+\left (500 x^3-20 x^5+\left (500 x^3-60 x^5\right ) \log (x)\right ) \log ^2(12 x)+\left (600 x^2-8 x^4\right ) \log ^2(x) \log ^3(12 x)+\left (\left (300 x^2-4 x^4\right ) \log (x)-4 x^4 \log ^2(x)\right ) \log ^4(12 x)+120 x \log ^3(x) \log ^5(12 x)+\left (60 x \log ^2(x)-20 x \log ^3(x)\right ) \log ^6(12 x)+8 \log ^4(x) \log ^7(12 x)+\left (4 \log ^3(x)-2 \log ^4(x)\right ) \log ^8(12 x)}{x^3} \, dx=\int \frac {1250 x^4-200 x^6+6 x^8+\left (1000 x^3-40 x^5\right ) \log (x) \log (12 x)+\left (500 x^3-20 x^5+\left (500 x^3-60 x^5\right ) \log (x)\right ) \log ^2(12 x)+\left (600 x^2-8 x^4\right ) \log ^2(x) \log ^3(12 x)+\left (\left (300 x^2-4 x^4\right ) \log (x)-4 x^4 \log ^2(x)\right ) \log ^4(12 x)+120 x \log ^3(x) \log ^5(12 x)+\left (60 x \log ^2(x)-20 x \log ^3(x)\right ) \log ^6(12 x)+8 \log ^4(x) \log ^7(12 x)+\left (4 \log ^3(x)-2 \log ^4(x)\right ) \log ^8(12 x)}{x^3} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \left (2 x \left (625-100 x^2+3 x^4\right )-40 (-5+x) (5+x) \log (x) \log (12 x)-20 \left (-25+x^2-25 \log (x)+3 x^2 \log (x)\right ) \log ^2(12 x)-\frac {8 \left (-75+x^2\right ) \log ^2(x) \log ^3(12 x)}{x}-\frac {4 \log (x) \left (-75+x^2+x^2 \log (x)\right ) \log ^4(12 x)}{x}+\frac {120 \log ^3(x) \log ^5(12 x)}{x^2}-\frac {20 (-3+\log (x)) \log ^2(x) \log ^6(12 x)}{x^2}+\frac {8 \log ^4(x) \log ^7(12 x)}{x^3}-\frac {2 (-2+\log (x)) \log ^3(x) \log ^8(12 x)}{x^3}\right ) \, dx \\ & = 2 \int x \left (625-100 x^2+3 x^4\right ) \, dx-2 \int \frac {(-2+\log (x)) \log ^3(x) \log ^8(12 x)}{x^3} \, dx-4 \int \frac {\log (x) \left (-75+x^2+x^2 \log (x)\right ) \log ^4(12 x)}{x} \, dx-8 \int \frac {\left (-75+x^2\right ) \log ^2(x) \log ^3(12 x)}{x} \, dx+8 \int \frac {\log ^4(x) \log ^7(12 x)}{x^3} \, dx-20 \int \left (-25+x^2-25 \log (x)+3 x^2 \log (x)\right ) \log ^2(12 x) \, dx-20 \int \frac {(-3+\log (x)) \log ^2(x) \log ^6(12 x)}{x^2} \, dx-40 \int (-5+x) (5+x) \log (x) \log (12 x) \, dx+120 \int \frac {\log ^3(x) \log ^5(12 x)}{x^2} \, dx \\ & = 1000 x \log (x) \log (12 x)-\frac {40}{3} x^3 \log (x) \log (12 x)-\frac {120 \log ^3(x) \log ^5(12 x)}{x}-\frac {4 \log ^4(x) \log ^7(12 x)}{x^2}+2 \int \left (625 x-100 x^3+3 x^5\right ) \, dx-2 \int \left (-\frac {2 \log ^3(x) \log ^8(12 x)}{x^3}+\frac {\log ^4(x) \log ^8(12 x)}{x^3}\right ) \, dx-4 \int \left (-\frac {75 \log (x) \log ^4(12 x)}{x}+x \log (x) \log ^4(12 x)+x \log ^2(x) \log ^4(12 x)\right ) \, dx-8 \int \left (-\frac {75 \log ^2(x) \log ^3(12 x)}{x}+x \log ^2(x) \log ^3(12 x)\right ) \, dx+16 \int \frac {\log ^3(x) \log ^7(12 x)}{x^3} \, dx-20 \int \left (-25 \log ^2(12 x)+x^2 \log ^2(12 x)-25 \log (x) \log ^2(12 x)+3 x^2 \log (x) \log ^2(12 x)\right ) \, dx-20 \int \left (-\frac {3 \log ^2(x) \log ^6(12 x)}{x^2}+\frac {\log ^3(x) \log ^6(12 x)}{x^2}\right ) \, dx+28 \int \frac {\log ^4(x) \log ^6(12 x)}{x^3} \, dx+40 \int \frac {1}{3} \left (-75+x^2\right ) \log (x) \, dx+40 \int \frac {1}{3} \left (-75+x^2\right ) \log (12 x) \, dx+360 \int \frac {\log ^2(x) \log ^5(12 x)}{x^2} \, dx+600 \int \frac {\log ^3(x) \log ^4(12 x)}{x^2} \, dx \\ & = 625 x^2-50 x^4+x^6+1000 x \log (x) \log (12 x)-\frac {40}{3} x^3 \log (x) \log (12 x)-\frac {600 \log ^3(x) \log ^4(12 x)}{x}-\frac {360 \log ^2(x) \log ^5(12 x)}{x}-\frac {120 \log ^3(x) \log ^5(12 x)}{x}-\frac {14 \log ^4(x) \log ^6(12 x)}{x^2}-\frac {8 \log ^3(x) \log ^7(12 x)}{x^2}-\frac {4 \log ^4(x) \log ^7(12 x)}{x^2}-2 \int \frac {\log ^4(x) \log ^8(12 x)}{x^3} \, dx-4 \int x \log (x) \log ^4(12 x) \, dx-4 \int x \log ^2(x) \log ^4(12 x) \, dx+4 \int \frac {\log ^3(x) \log ^8(12 x)}{x^3} \, dx-8 \int x \log ^2(x) \log ^3(12 x) \, dx+\frac {40}{3} \int \left (-75+x^2\right ) \log (x) \, dx+\frac {40}{3} \int \left (-75+x^2\right ) \log (12 x) \, dx-20 \int x^2 \log ^2(12 x) \, dx-20 \int \frac {\log ^3(x) \log ^6(12 x)}{x^2} \, dx+24 \int \frac {\log ^2(x) \log ^7(12 x)}{x^3} \, dx+2 \left (56 \int \frac {\log ^3(x) \log ^6(12 x)}{x^3} \, dx\right )-60 \int x^2 \log (x) \log ^2(12 x) \, dx+60 \int \frac {\log ^2(x) \log ^6(12 x)}{x^2} \, dx+84 \int \frac {\log ^4(x) \log ^5(12 x)}{x^3} \, dx+300 \int \frac {\log (x) \log ^4(12 x)}{x} \, dx+500 \int \log ^2(12 x) \, dx+500 \int \log (x) \log ^2(12 x) \, dx+600 \int \frac {\log ^2(x) \log ^3(12 x)}{x} \, dx+720 \int \frac {\log (x) \log ^5(12 x)}{x^2} \, dx+2 \left (1800 \int \frac {\log ^2(x) \log ^4(12 x)}{x^2} \, dx\right )+2400 \int \frac {\log ^3(x) \log ^3(12 x)}{x^2} \, dx \\ & = 625 x^2-50 x^4+x^6-\frac {86400 \log (x)}{x}-3 x^2 \log (x)-1000 x \log (12 x)+\frac {40}{9} x^3 \log (12 x)-\frac {86400 \log (x) \log (12 x)}{x}+6 x^2 \log (x) \log (12 x)+500 x \log ^2(12 x)-\frac {20}{3} x^3 \log ^2(12 x)-\frac {43200 \log (x) \log ^2(12 x)}{x}+500 x \log (x) \log ^2(12 x)-6 x^2 \log (x) \log ^2(12 x)-20 x^3 \log (x) \log ^2(12 x)-\frac {14400 \log (x) \log ^3(12 x)}{x}+4 x^2 \log (x) \log ^3(12 x)-4 x^2 \log ^2(x) \log ^3(12 x)-\frac {2400 \log ^3(x) \log ^3(12 x)}{x}-\frac {3600 \log (x) \log ^4(12 x)}{x}-2 x^2 \log (x) \log ^4(12 x)-2 x^2 \log ^2(x) \log ^4(12 x)-\frac {600 \log ^3(x) \log ^4(12 x)}{x}+60 \log (x) \log ^5(12 x)-\frac {720 \log (x) \log ^5(12 x)}{x}-\frac {360 \log ^2(x) \log ^5(12 x)}{x}-\frac {120 \log ^3(x) \log ^5(12 x)}{x}-\frac {42 \log ^4(x) \log ^5(12 x)}{x^2}-\frac {60 \log ^2(x) \log ^6(12 x)}{x}+\frac {20 \log ^3(x) \log ^6(12 x)}{x}-\frac {14 \log ^4(x) \log ^6(12 x)}{x^2}-\frac {12 \log ^2(x) \log ^7(12 x)}{x^2}-\frac {8 \log ^3(x) \log ^7(12 x)}{x^2}-\frac {4 \log ^4(x) \log ^7(12 x)}{x^2}-\frac {2 \log ^3(x) \log ^8(12 x)}{x^2}+\frac {\log ^4(x) \log ^8(12 x)}{x^2}+4 \int x \log (x) \log ^4(12 x) \, dx-4 \int \frac {\log ^3(x) \log ^8(12 x)}{x^3} \, dx+4 \int \frac {1}{4} x \left (3-6 \log (12 x)+6 \log ^2(12 x)-4 \log ^3(12 x)+2 \log ^4(12 x)\right ) \, dx+6 \int \frac {\log ^2(x) \log ^8(12 x)}{x^3} \, dx+8 \int x \log (x) \log ^3(12 x) \, dx+8 \int x \log ^2(x) \log ^3(12 x) \, dx-8 \int \frac {\log ^4(x) \log ^7(12 x)}{x^3} \, dx+12 \int x \log ^2(x) \log ^2(12 x) \, dx-2 \left (\frac {40}{3} \int \left (-75+\frac {x^2}{3}\right ) \, dx\right )+\frac {40}{3} \int x^2 \log (12 x) \, dx+16 \int \frac {\log ^3(x) \log ^7(12 x)}{x^3} \, dx+24 \int \frac {\log (x) \log ^7(12 x)}{x^3} \, dx-60 \int \frac {\log ^2(x) \log ^6(12 x)}{x^2} \, dx+60 \int \frac {1}{27} x^2 \left (2-6 \log (12 x)+9 \log ^2(12 x)\right ) \, dx+84 \int \frac {\log ^2(x) \log ^6(12 x)}{x^3} \, dx-120 \int \frac {\log ^3(x) \log ^5(12 x)}{x^2} \, dx+120 \int \frac {\log (x) \log ^6(12 x)}{x^2} \, dx+168 \int \frac {\log ^3(x) \log ^5(12 x)}{x^3} \, dx+2 \left (-\frac {28 \log ^3(x) \log ^6(12 x)}{x^2}+84 \int \frac {\log ^2(x) \log ^6(12 x)}{x^3} \, dx+168 \int \frac {\log ^3(x) \log ^5(12 x)}{x^3} \, dx\right )+210 \int \frac {\log ^4(x) \log ^4(12 x)}{x^3} \, dx-300 \int \frac {\log ^5(12 x)}{5 x} \, dx+360 \int \frac {\log ^2(x) \log ^5(12 x)}{x^2} \, dx-500 \int \left (2-2 \log (12 x)+\log ^2(12 x)\right ) \, dx+600 \int \frac {\log ^2(x) \log ^3(12 x)}{x} \, dx-720 \int \frac {-120-120 \log (12 x)-60 \log ^2(12 x)-20 \log ^3(12 x)-5 \log ^4(12 x)-\log ^5(12 x)}{x^2} \, dx-1000 \int \log (12 x) \, dx+7200 \int \frac {\log ^3(x) \log ^2(12 x)}{x^2} \, dx+7200 \int \frac {\log ^2(x) \log ^3(12 x)}{x^2} \, dx+2 \left (-\frac {1800 \log ^2(x) \log ^4(12 x)}{x}+3600 \int \frac {\log (x) \log ^4(12 x)}{x^2} \, dx+7200 \int \frac {\log ^2(x) \log ^3(12 x)}{x^2} \, dx\right ) \\ & = \text {Too large to display} \\ \end{align*}
Time = 0.78 (sec) , antiderivative size = 39, normalized size of antiderivative = 1.39 \[ \int \frac {1250 x^4-200 x^6+6 x^8+\left (1000 x^3-40 x^5\right ) \log (x) \log (12 x)+\left (500 x^3-20 x^5+\left (500 x^3-60 x^5\right ) \log (x)\right ) \log ^2(12 x)+\left (600 x^2-8 x^4\right ) \log ^2(x) \log ^3(12 x)+\left (\left (300 x^2-4 x^4\right ) \log (x)-4 x^4 \log ^2(x)\right ) \log ^4(12 x)+120 x \log ^3(x) \log ^5(12 x)+\left (60 x \log ^2(x)-20 x \log ^3(x)\right ) \log ^6(12 x)+8 \log ^4(x) \log ^7(12 x)+\left (4 \log ^3(x)-2 \log ^4(x)\right ) \log ^8(12 x)}{x^3} \, dx=\frac {\left (25 x^2-x^4+10 x \log (x) \log ^2(12 x)+\log ^2(x) \log ^4(12 x)\right )^2}{x^2} \]
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Leaf count of result is larger than twice the leaf count of optimal. \(102\) vs. \(2(28)=56\).
Time = 3.39 (sec) , antiderivative size = 103, normalized size of antiderivative = 3.68
method | result | size |
parallelrisch | \(-\frac {-1260 x^{8}+63000 x^{6}-787500 x^{4}-25200 \ln \left (x \right )^{3} \ln \left (12 x \right )^{6} x +2520 \ln \left (x \right )^{2} \ln \left (12 x \right )^{4} x^{4}+25200 \ln \left (x \right ) \ln \left (12 x \right )^{2} x^{5}-630000 \ln \left (x \right ) \ln \left (12 x \right )^{2} x^{3}-1260 \ln \left (x \right )^{4} \ln \left (12 x \right )^{8}-189000 \ln \left (12 x \right )^{4} \ln \left (x \right )^{2} x^{2}}{1260 x^{2}}\) | \(103\) |
risch | \(\text {Expression too large to display}\) | \(996\) |
default | \(\text {Expression too large to display}\) | \(2336\) |
parts | \(\text {Expression too large to display}\) | \(2682\) |
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Leaf count of result is larger than twice the leaf count of optimal. 279 vs. \(2 (28) = 56\).
Time = 0.25 (sec) , antiderivative size = 279, normalized size of antiderivative = 9.96 \[ \int \frac {1250 x^4-200 x^6+6 x^8+\left (1000 x^3-40 x^5\right ) \log (x) \log (12 x)+\left (500 x^3-20 x^5+\left (500 x^3-60 x^5\right ) \log (x)\right ) \log ^2(12 x)+\left (600 x^2-8 x^4\right ) \log ^2(x) \log ^3(12 x)+\left (\left (300 x^2-4 x^4\right ) \log (x)-4 x^4 \log ^2(x)\right ) \log ^4(12 x)+120 x \log ^3(x) \log ^5(12 x)+\left (60 x \log ^2(x)-20 x \log ^3(x)\right ) \log ^6(12 x)+8 \log ^4(x) \log ^7(12 x)+\left (4 \log ^3(x)-2 \log ^4(x)\right ) \log ^8(12 x)}{x^3} \, dx=\frac {28 \, \log \left (12\right )^{2} \log \left (x\right )^{10} + 8 \, \log \left (12\right ) \log \left (x\right )^{11} + \log \left (x\right )^{12} + 4 \, {\left (14 \, \log \left (12\right )^{3} + 5 \, x\right )} \log \left (x\right )^{9} + 10 \, {\left (7 \, \log \left (12\right )^{4} + 12 \, x \log \left (12\right )\right )} \log \left (x\right )^{8} + x^{8} + 4 \, {\left (14 \, \log \left (12\right )^{5} + 75 \, x \log \left (12\right )^{2}\right )} \log \left (x\right )^{7} + 2 \, {\left (14 \, \log \left (12\right )^{6} - x^{4} + 200 \, x \log \left (12\right )^{3} + 75 \, x^{2}\right )} \log \left (x\right )^{6} - 50 \, x^{6} + 4 \, {\left (2 \, \log \left (12\right )^{7} + 75 \, x \log \left (12\right )^{4} - 2 \, {\left (x^{4} - 75 \, x^{2}\right )} \log \left (12\right )\right )} \log \left (x\right )^{5} + {\left (\log \left (12\right )^{8} + 120 \, x \log \left (12\right )^{5} - 12 \, {\left (x^{4} - 75 \, x^{2}\right )} \log \left (12\right )^{2}\right )} \log \left (x\right )^{4} + 625 \, x^{4} - 20 \, {\left (x^{5} - 25 \, x^{3}\right )} \log \left (12\right )^{2} \log \left (x\right ) + 4 \, {\left (5 \, x \log \left (12\right )^{6} - 5 \, x^{5} - 2 \, {\left (x^{4} - 75 \, x^{2}\right )} \log \left (12\right )^{3} + 125 \, x^{3}\right )} \log \left (x\right )^{3} - 2 \, {\left ({\left (x^{4} - 75 \, x^{2}\right )} \log \left (12\right )^{4} + 20 \, {\left (x^{5} - 25 \, x^{3}\right )} \log \left (12\right )\right )} \log \left (x\right )^{2}}{x^{2}} \]
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Leaf count of result is larger than twice the leaf count of optimal. 333 vs. \(2 (22) = 44\).
Time = 0.61 (sec) , antiderivative size = 333, normalized size of antiderivative = 11.89 \[ \int \frac {1250 x^4-200 x^6+6 x^8+\left (1000 x^3-40 x^5\right ) \log (x) \log (12 x)+\left (500 x^3-20 x^5+\left (500 x^3-60 x^5\right ) \log (x)\right ) \log ^2(12 x)+\left (600 x^2-8 x^4\right ) \log ^2(x) \log ^3(12 x)+\left (\left (300 x^2-4 x^4\right ) \log (x)-4 x^4 \log ^2(x)\right ) \log ^4(12 x)+120 x \log ^3(x) \log ^5(12 x)+\left (60 x \log ^2(x)-20 x \log ^3(x)\right ) \log ^6(12 x)+8 \log ^4(x) \log ^7(12 x)+\left (4 \log ^3(x)-2 \log ^4(x)\right ) \log ^8(12 x)}{x^3} \, dx=x^{6} - 50 x^{4} + 625 x^{2} + \left (- 20 x^{3} \log {\left (12 \right )}^{2} + 500 x \log {\left (12 \right )}^{2}\right ) \log {\left (x \right )} + \left (- 40 x^{3} \log {\left (12 \right )} - 2 x^{2} \log {\left (12 \right )}^{4} + 1000 x \log {\left (12 \right )} + 150 \log {\left (12 \right )}^{4}\right ) \log {\left (x \right )}^{2} + \frac {\left (- 20 x^{4} - 8 x^{3} \log {\left (12 \right )}^{3} + 500 x^{2} + 600 x \log {\left (12 \right )}^{3} + 20 \log {\left (12 \right )}^{6}\right ) \log {\left (x \right )}^{3}}{x} + \frac {\left (20 x + 56 \log {\left (12 \right )}^{3}\right ) \log {\left (x \right )}^{9}}{x^{2}} + \frac {\left (120 x \log {\left (12 \right )} + 70 \log {\left (12 \right )}^{4}\right ) \log {\left (x \right )}^{8}}{x^{2}} + \frac {\left (300 x \log {\left (12 \right )}^{2} + 56 \log {\left (12 \right )}^{5}\right ) \log {\left (x \right )}^{7}}{x^{2}} + \frac {\left (- 2 x^{4} + 150 x^{2} + 400 x \log {\left (12 \right )}^{3} + 28 \log {\left (12 \right )}^{6}\right ) \log {\left (x \right )}^{6}}{x^{2}} + \frac {\left (- 8 x^{4} \log {\left (12 \right )} + 600 x^{2} \log {\left (12 \right )} + 300 x \log {\left (12 \right )}^{4} + 8 \log {\left (12 \right )}^{7}\right ) \log {\left (x \right )}^{5}}{x^{2}} + \frac {\left (- 12 x^{4} \log {\left (12 \right )}^{2} + 900 x^{2} \log {\left (12 \right )}^{2} + 120 x \log {\left (12 \right )}^{5} + \log {\left (12 \right )}^{8}\right ) \log {\left (x \right )}^{4}}{x^{2}} + \frac {\log {\left (x \right )}^{12}}{x^{2}} + \frac {8 \log {\left (12 \right )} \log {\left (x \right )}^{11}}{x^{2}} + \frac {28 \log {\left (12 \right )}^{2} \log {\left (x \right )}^{10}}{x^{2}} \]
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Leaf count of result is larger than twice the leaf count of optimal. 1994 vs. \(2 (28) = 56\).
Time = 0.35 (sec) , antiderivative size = 1994, normalized size of antiderivative = 71.21 \[ \int \frac {1250 x^4-200 x^6+6 x^8+\left (1000 x^3-40 x^5\right ) \log (x) \log (12 x)+\left (500 x^3-20 x^5+\left (500 x^3-60 x^5\right ) \log (x)\right ) \log ^2(12 x)+\left (600 x^2-8 x^4\right ) \log ^2(x) \log ^3(12 x)+\left (\left (300 x^2-4 x^4\right ) \log (x)-4 x^4 \log ^2(x)\right ) \log ^4(12 x)+120 x \log ^3(x) \log ^5(12 x)+\left (60 x \log ^2(x)-20 x \log ^3(x)\right ) \log ^6(12 x)+8 \log ^4(x) \log ^7(12 x)+\left (4 \log ^3(x)-2 \log ^4(x)\right ) \log ^8(12 x)}{x^3} \, dx=\text {Too large to display} \]
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Leaf count of result is larger than twice the leaf count of optimal. 2318 vs. \(2 (28) = 56\).
Time = 0.91 (sec) , antiderivative size = 2318, normalized size of antiderivative = 82.79 \[ \int \frac {1250 x^4-200 x^6+6 x^8+\left (1000 x^3-40 x^5\right ) \log (x) \log (12 x)+\left (500 x^3-20 x^5+\left (500 x^3-60 x^5\right ) \log (x)\right ) \log ^2(12 x)+\left (600 x^2-8 x^4\right ) \log ^2(x) \log ^3(12 x)+\left (\left (300 x^2-4 x^4\right ) \log (x)-4 x^4 \log ^2(x)\right ) \log ^4(12 x)+120 x \log ^3(x) \log ^5(12 x)+\left (60 x \log ^2(x)-20 x \log ^3(x)\right ) \log ^6(12 x)+8 \log ^4(x) \log ^7(12 x)+\left (4 \log ^3(x)-2 \log ^4(x)\right ) \log ^8(12 x)}{x^3} \, dx=\text {Too large to display} \]
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Time = 16.08 (sec) , antiderivative size = 367, normalized size of antiderivative = 13.11 \[ \int \frac {1250 x^4-200 x^6+6 x^8+\left (1000 x^3-40 x^5\right ) \log (x) \log (12 x)+\left (500 x^3-20 x^5+\left (500 x^3-60 x^5\right ) \log (x)\right ) \log ^2(12 x)+\left (600 x^2-8 x^4\right ) \log ^2(x) \log ^3(12 x)+\left (\left (300 x^2-4 x^4\right ) \log (x)-4 x^4 \log ^2(x)\right ) \log ^4(12 x)+120 x \log ^3(x) \log ^5(12 x)+\left (60 x \log ^2(x)-20 x \log ^3(x)\right ) \log ^6(12 x)+8 \log ^4(x) \log ^7(12 x)+\left (4 \log ^3(x)-2 \log ^4(x)\right ) \log ^8(12 x)}{x^3} \, dx=600\,\ln \left (12\right )\,{\ln \left (x\right )}^5+500\,x\,{\ln \left (x\right )}^3+150\,{\ln \left (x\right )}^6+900\,{\ln \left (12\right )}^2\,{\ln \left (x\right )}^4+600\,{\ln \left (12\right )}^3\,{\ln \left (x\right )}^3+150\,{\ln \left (12\right )}^4\,{\ln \left (x\right )}^2-20\,x^3\,{\ln \left (x\right )}^3-2\,x^2\,{\ln \left (x\right )}^6+\frac {20\,{\ln \left (x\right )}^9}{x}+\frac {{\ln \left (x\right )}^{12}}{x^2}+625\,x^2-50\,x^4+x^6-12\,x^2\,{\ln \left (12\right )}^2\,{\ln \left (x\right )}^4-8\,x^2\,{\ln \left (12\right )}^3\,{\ln \left (x\right )}^3-2\,x^2\,{\ln \left (12\right )}^4\,{\ln \left (x\right )}^2+\frac {300\,{\ln \left (12\right )}^2\,{\ln \left (x\right )}^7}{x}+\frac {400\,{\ln \left (12\right )}^3\,{\ln \left (x\right )}^6}{x}+\frac {300\,{\ln \left (12\right )}^4\,{\ln \left (x\right )}^5}{x}+\frac {120\,{\ln \left (12\right )}^5\,{\ln \left (x\right )}^4}{x}+\frac {20\,{\ln \left (12\right )}^6\,{\ln \left (x\right )}^3}{x}+\frac {28\,{\ln \left (12\right )}^2\,{\ln \left (x\right )}^{10}}{x^2}+\frac {56\,{\ln \left (12\right )}^3\,{\ln \left (x\right )}^9}{x^2}+\frac {70\,{\ln \left (12\right )}^4\,{\ln \left (x\right )}^8}{x^2}+\frac {56\,{\ln \left (12\right )}^5\,{\ln \left (x\right )}^7}{x^2}+\frac {28\,{\ln \left (12\right )}^6\,{\ln \left (x\right )}^6}{x^2}+\frac {8\,{\ln \left (12\right )}^7\,{\ln \left (x\right )}^5}{x^2}+\frac {{\ln \left (12\right )}^8\,{\ln \left (x\right )}^4}{x^2}+1000\,x\,\ln \left (12\right )\,{\ln \left (x\right )}^2+500\,x\,{\ln \left (12\right )}^2\,\ln \left (x\right )-40\,x^3\,\ln \left (12\right )\,{\ln \left (x\right )}^2-20\,x^3\,{\ln \left (12\right )}^2\,\ln \left (x\right )-8\,x^2\,\ln \left (12\right )\,{\ln \left (x\right )}^5+\frac {120\,\ln \left (12\right )\,{\ln \left (x\right )}^8}{x}+\frac {8\,\ln \left (12\right )\,{\ln \left (x\right )}^{11}}{x^2} \]
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