Integrand size = 177, antiderivative size = 20 \[ \int \frac {32 x+160 \log (3)-32 \log ^2(3)}{-x^4-9 x^3 \log (3)-27 x^2 \log ^2(3)-27 x \log ^3(3)+\left (-15 x^3 \log (3)+\left (-90 x^2+3 x^3\right ) \log ^2(3)+\left (-135 x+18 x^2\right ) \log ^3(3)+27 x \log ^4(3)\right ) \log (x)+\left (-75 x^2 \log ^2(3)+\left (-225 x+30 x^2\right ) \log ^3(3)+\left (90 x-3 x^2\right ) \log ^4(3)-9 x \log ^5(3)\right ) \log ^2(x)+\left (-125 x \log ^3(3)+75 x \log ^4(3)-15 x \log ^5(3)+x \log ^6(3)\right ) \log ^3(x)} \, dx=\frac {16}{(x+\log (3) (3+(5-\log (3)) \log (x)))^2} \]
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Time = 0.19 (sec) , antiderivative size = 19, normalized size of antiderivative = 0.95, number of steps used = 3, number of rules used = 3, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.017, Rules used = {6820, 12, 6818} \[ \int \frac {32 x+160 \log (3)-32 \log ^2(3)}{-x^4-9 x^3 \log (3)-27 x^2 \log ^2(3)-27 x \log ^3(3)+\left (-15 x^3 \log (3)+\left (-90 x^2+3 x^3\right ) \log ^2(3)+\left (-135 x+18 x^2\right ) \log ^3(3)+27 x \log ^4(3)\right ) \log (x)+\left (-75 x^2 \log ^2(3)+\left (-225 x+30 x^2\right ) \log ^3(3)+\left (90 x-3 x^2\right ) \log ^4(3)-9 x \log ^5(3)\right ) \log ^2(x)+\left (-125 x \log ^3(3)+75 x \log ^4(3)-15 x \log ^5(3)+x \log ^6(3)\right ) \log ^3(x)} \, dx=\frac {16}{(x+(5-\log (3)) \log (3) \log (x)+\log (27))^2} \]
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Rule 12
Rule 6818
Rule 6820
Rubi steps \begin{align*} \text {integral}& = \int \frac {32 (-x+(-5+\log (3)) \log (3))}{x (x+\log (27)-(-5+\log (3)) \log (3) \log (x))^3} \, dx \\ & = 32 \int \frac {-x+(-5+\log (3)) \log (3)}{x (x+\log (27)-(-5+\log (3)) \log (3) \log (x))^3} \, dx \\ & = \frac {16}{(x+\log (27)+(5-\log (3)) \log (3) \log (x))^2} \\ \end{align*}
Time = 0.04 (sec) , antiderivative size = 18, normalized size of antiderivative = 0.90 \[ \int \frac {32 x+160 \log (3)-32 \log ^2(3)}{-x^4-9 x^3 \log (3)-27 x^2 \log ^2(3)-27 x \log ^3(3)+\left (-15 x^3 \log (3)+\left (-90 x^2+3 x^3\right ) \log ^2(3)+\left (-135 x+18 x^2\right ) \log ^3(3)+27 x \log ^4(3)\right ) \log (x)+\left (-75 x^2 \log ^2(3)+\left (-225 x+30 x^2\right ) \log ^3(3)+\left (90 x-3 x^2\right ) \log ^4(3)-9 x \log ^5(3)\right ) \log ^2(x)+\left (-125 x \log ^3(3)+75 x \log ^4(3)-15 x \log ^5(3)+x \log ^6(3)\right ) \log ^3(x)} \, dx=\frac {16}{(x+\log (27)-(-5+\log (3)) \log (3) \log (x))^2} \]
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Time = 3.30 (sec) , antiderivative size = 26, normalized size of antiderivative = 1.30
method | result | size |
default | \(\frac {16}{\left (\ln \left (3\right )^{2} \ln \left (x \right )-5 \ln \left (3\right ) \ln \left (x \right )-3 \ln \left (3\right )-x \right )^{2}}\) | \(26\) |
norman | \(\frac {16}{\left (\ln \left (3\right )^{2} \ln \left (x \right )-5 \ln \left (3\right ) \ln \left (x \right )-3 \ln \left (3\right )-x \right )^{2}}\) | \(26\) |
risch | \(\frac {16}{\left (\ln \left (3\right )^{2} \ln \left (x \right )-5 \ln \left (3\right ) \ln \left (x \right )-3 \ln \left (3\right )-x \right )^{2}}\) | \(26\) |
parallelrisch | \(\frac {16}{\ln \left (x \right )^{2} \ln \left (3\right )^{4}-10 \ln \left (3\right )^{3} \ln \left (x \right )^{2}-6 \ln \left (x \right ) \ln \left (3\right )^{3}-2 x \ln \left (x \right ) \ln \left (3\right )^{2}+25 \ln \left (3\right )^{2} \ln \left (x \right )^{2}+30 \ln \left (3\right )^{2} \ln \left (x \right )+10 x \ln \left (3\right ) \ln \left (x \right )+9 \ln \left (3\right )^{2}+6 x \ln \left (3\right )+x^{2}}\) | \(81\) |
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Leaf count of result is larger than twice the leaf count of optimal. 65 vs. \(2 (20) = 40\).
Time = 0.27 (sec) , antiderivative size = 65, normalized size of antiderivative = 3.25 \[ \int \frac {32 x+160 \log (3)-32 \log ^2(3)}{-x^4-9 x^3 \log (3)-27 x^2 \log ^2(3)-27 x \log ^3(3)+\left (-15 x^3 \log (3)+\left (-90 x^2+3 x^3\right ) \log ^2(3)+\left (-135 x+18 x^2\right ) \log ^3(3)+27 x \log ^4(3)\right ) \log (x)+\left (-75 x^2 \log ^2(3)+\left (-225 x+30 x^2\right ) \log ^3(3)+\left (90 x-3 x^2\right ) \log ^4(3)-9 x \log ^5(3)\right ) \log ^2(x)+\left (-125 x \log ^3(3)+75 x \log ^4(3)-15 x \log ^5(3)+x \log ^6(3)\right ) \log ^3(x)} \, dx=\frac {16}{{\left (\log \left (3\right )^{4} - 10 \, \log \left (3\right )^{3} + 25 \, \log \left (3\right )^{2}\right )} \log \left (x\right )^{2} + x^{2} + 6 \, x \log \left (3\right ) + 9 \, \log \left (3\right )^{2} - 2 \, {\left ({\left (x - 15\right )} \log \left (3\right )^{2} + 3 \, \log \left (3\right )^{3} - 5 \, x \log \left (3\right )\right )} \log \left (x\right )} \]
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Leaf count of result is larger than twice the leaf count of optimal. 73 vs. \(2 (17) = 34\).
Time = 0.22 (sec) , antiderivative size = 73, normalized size of antiderivative = 3.65 \[ \int \frac {32 x+160 \log (3)-32 \log ^2(3)}{-x^4-9 x^3 \log (3)-27 x^2 \log ^2(3)-27 x \log ^3(3)+\left (-15 x^3 \log (3)+\left (-90 x^2+3 x^3\right ) \log ^2(3)+\left (-135 x+18 x^2\right ) \log ^3(3)+27 x \log ^4(3)\right ) \log (x)+\left (-75 x^2 \log ^2(3)+\left (-225 x+30 x^2\right ) \log ^3(3)+\left (90 x-3 x^2\right ) \log ^4(3)-9 x \log ^5(3)\right ) \log ^2(x)+\left (-125 x \log ^3(3)+75 x \log ^4(3)-15 x \log ^5(3)+x \log ^6(3)\right ) \log ^3(x)} \, dx=\frac {16}{x^{2} + 6 x \log {\left (3 \right )} + \left (- 2 x \log {\left (3 \right )}^{2} + 10 x \log {\left (3 \right )} - 6 \log {\left (3 \right )}^{3} + 30 \log {\left (3 \right )}^{2}\right ) \log {\left (x \right )} + \left (- 10 \log {\left (3 \right )}^{3} + \log {\left (3 \right )}^{4} + 25 \log {\left (3 \right )}^{2}\right ) \log {\left (x \right )}^{2} + 9 \log {\left (3 \right )}^{2}} \]
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Leaf count of result is larger than twice the leaf count of optimal. 69 vs. \(2 (20) = 40\).
Time = 0.34 (sec) , antiderivative size = 69, normalized size of antiderivative = 3.45 \[ \int \frac {32 x+160 \log (3)-32 \log ^2(3)}{-x^4-9 x^3 \log (3)-27 x^2 \log ^2(3)-27 x \log ^3(3)+\left (-15 x^3 \log (3)+\left (-90 x^2+3 x^3\right ) \log ^2(3)+\left (-135 x+18 x^2\right ) \log ^3(3)+27 x \log ^4(3)\right ) \log (x)+\left (-75 x^2 \log ^2(3)+\left (-225 x+30 x^2\right ) \log ^3(3)+\left (90 x-3 x^2\right ) \log ^4(3)-9 x \log ^5(3)\right ) \log ^2(x)+\left (-125 x \log ^3(3)+75 x \log ^4(3)-15 x \log ^5(3)+x \log ^6(3)\right ) \log ^3(x)} \, dx=\frac {16}{{\left (\log \left (3\right )^{4} - 10 \, \log \left (3\right )^{3} + 25 \, \log \left (3\right )^{2}\right )} \log \left (x\right )^{2} + x^{2} + 6 \, x \log \left (3\right ) + 9 \, \log \left (3\right )^{2} - 2 \, {\left (3 \, \log \left (3\right )^{3} + {\left (\log \left (3\right )^{2} - 5 \, \log \left (3\right )\right )} x - 15 \, \log \left (3\right )^{2}\right )} \log \left (x\right )} \]
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Leaf count of result is larger than twice the leaf count of optimal. 206 vs. \(2 (20) = 40\).
Time = 0.29 (sec) , antiderivative size = 206, normalized size of antiderivative = 10.30 \[ \int \frac {32 x+160 \log (3)-32 \log ^2(3)}{-x^4-9 x^3 \log (3)-27 x^2 \log ^2(3)-27 x \log ^3(3)+\left (-15 x^3 \log (3)+\left (-90 x^2+3 x^3\right ) \log ^2(3)+\left (-135 x+18 x^2\right ) \log ^3(3)+27 x \log ^4(3)\right ) \log (x)+\left (-75 x^2 \log ^2(3)+\left (-225 x+30 x^2\right ) \log ^3(3)+\left (90 x-3 x^2\right ) \log ^4(3)-9 x \log ^5(3)\right ) \log ^2(x)+\left (-125 x \log ^3(3)+75 x \log ^4(3)-15 x \log ^5(3)+x \log ^6(3)\right ) \log ^3(x)} \, dx=\frac {16 \, {\left (\log \left (3\right )^{2} - x - 5 \, \log \left (3\right )\right )}}{\log \left (3\right )^{6} \log \left (x\right )^{2} - x \log \left (3\right )^{4} \log \left (x\right )^{2} - 15 \, \log \left (3\right )^{5} \log \left (x\right )^{2} - 2 \, x \log \left (3\right )^{4} \log \left (x\right ) - 6 \, \log \left (3\right )^{5} \log \left (x\right ) + 10 \, x \log \left (3\right )^{3} \log \left (x\right )^{2} + 75 \, \log \left (3\right )^{4} \log \left (x\right )^{2} + 2 \, x^{2} \log \left (3\right )^{2} \log \left (x\right ) + 26 \, x \log \left (3\right )^{3} \log \left (x\right ) + 60 \, \log \left (3\right )^{4} \log \left (x\right ) - 25 \, x \log \left (3\right )^{2} \log \left (x\right )^{2} - 125 \, \log \left (3\right )^{3} \log \left (x\right )^{2} + x^{2} \log \left (3\right )^{2} + 6 \, x \log \left (3\right )^{3} + 9 \, \log \left (3\right )^{4} - 10 \, x^{2} \log \left (3\right ) \log \left (x\right ) - 80 \, x \log \left (3\right )^{2} \log \left (x\right ) - 150 \, \log \left (3\right )^{3} \log \left (x\right ) - x^{3} - 11 \, x^{2} \log \left (3\right ) - 39 \, x \log \left (3\right )^{2} - 45 \, \log \left (3\right )^{3}} \]
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Timed out. \[ \int \frac {32 x+160 \log (3)-32 \log ^2(3)}{-x^4-9 x^3 \log (3)-27 x^2 \log ^2(3)-27 x \log ^3(3)+\left (-15 x^3 \log (3)+\left (-90 x^2+3 x^3\right ) \log ^2(3)+\left (-135 x+18 x^2\right ) \log ^3(3)+27 x \log ^4(3)\right ) \log (x)+\left (-75 x^2 \log ^2(3)+\left (-225 x+30 x^2\right ) \log ^3(3)+\left (90 x-3 x^2\right ) \log ^4(3)-9 x \log ^5(3)\right ) \log ^2(x)+\left (-125 x \log ^3(3)+75 x \log ^4(3)-15 x \log ^5(3)+x \log ^6(3)\right ) \log ^3(x)} \, dx=\int -\frac {32\,x+160\,\ln \left (3\right )-32\,{\ln \left (3\right )}^2}{27\,x^2\,{\ln \left (3\right )}^2+\ln \left (x\right )\,\left ({\ln \left (3\right )}^3\,\left (135\,x-18\,x^2\right )+15\,x^3\,\ln \left (3\right )-27\,x\,{\ln \left (3\right )}^4+{\ln \left (3\right )}^2\,\left (90\,x^2-3\,x^3\right )\right )+{\ln \left (x\right )}^3\,\left (125\,x\,{\ln \left (3\right )}^3-75\,x\,{\ln \left (3\right )}^4+15\,x\,{\ln \left (3\right )}^5-x\,{\ln \left (3\right )}^6\right )+27\,x\,{\ln \left (3\right )}^3+9\,x^3\,\ln \left (3\right )+x^4+{\ln \left (x\right )}^2\,\left (75\,x^2\,{\ln \left (3\right )}^2-{\ln \left (3\right )}^4\,\left (90\,x-3\,x^2\right )+{\ln \left (3\right )}^3\,\left (225\,x-30\,x^2\right )+9\,x\,{\ln \left (3\right )}^5\right )} \,d x \]
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