Integrand size = 107, antiderivative size = 18 \[ \int \frac {-24 x^2+16 x^5-8 x^6+\left (-144 x^2+96 x^3+96 x^5-112 x^6+32 x^7\right ) \log (x) \log (\log (x))+\left (8 x^5+\left (-72 x^2+96 x^5-56 x^6\right ) \log (x) \log (\log (x))\right ) \log (\log (\log (x)))+24 x^5 \log (x) \log (\log (x)) \log ^2(\log (\log (x)))}{\log (x) \log (\log (x))} \, dx=\left (6-2 x^3 (2-x+\log (\log (\log (x))))\right )^2 \]
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Time = 0.18 (sec) , antiderivative size = 23, normalized size of antiderivative = 1.28, number of steps used = 3, number of rules used = 3, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.028, Rules used = {6820, 12, 6818} \[ \int \frac {-24 x^2+16 x^5-8 x^6+\left (-144 x^2+96 x^3+96 x^5-112 x^6+32 x^7\right ) \log (x) \log (\log (x))+\left (8 x^5+\left (-72 x^2+96 x^5-56 x^6\right ) \log (x) \log (\log (x))\right ) \log (\log (\log (x)))+24 x^5 \log (x) \log (\log (x)) \log ^2(\log (\log (x)))}{\log (x) \log (\log (x))} \, dx=4 \left (x^4-2 x^3-x^3 \log (\log (\log (x)))+3\right )^2 \]
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Rule 12
Rule 6818
Rule 6820
Rubi steps \begin{align*} \text {integral}& = \int \frac {8 x^2 (1-\log (x) \log (\log (x)) (-6+4 x-3 \log (\log (\log (x))))) \left (-3+2 x^3-x^4+x^3 \log (\log (\log (x)))\right )}{\log (x) \log (\log (x))} \, dx \\ & = 8 \int \frac {x^2 (1-\log (x) \log (\log (x)) (-6+4 x-3 \log (\log (\log (x))))) \left (-3+2 x^3-x^4+x^3 \log (\log (\log (x)))\right )}{\log (x) \log (\log (x))} \, dx \\ & = 4 \left (3-2 x^3+x^4-x^3 \log (\log (\log (x)))\right )^2 \\ \end{align*}
Time = 0.03 (sec) , antiderivative size = 23, normalized size of antiderivative = 1.28 \[ \int \frac {-24 x^2+16 x^5-8 x^6+\left (-144 x^2+96 x^3+96 x^5-112 x^6+32 x^7\right ) \log (x) \log (\log (x))+\left (8 x^5+\left (-72 x^2+96 x^5-56 x^6\right ) \log (x) \log (\log (x))\right ) \log (\log (\log (x)))+24 x^5 \log (x) \log (\log (x)) \log ^2(\log (\log (x)))}{\log (x) \log (\log (x))} \, dx=4 \left (3-2 x^3+x^4-x^3 \log (\log (\log (x)))\right )^2 \]
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Leaf count of result is larger than twice the leaf count of optimal. \(58\) vs. \(2(18)=36\).
Time = 1.78 (sec) , antiderivative size = 59, normalized size of antiderivative = 3.28
method | result | size |
risch | \(4 x^{6} \ln \left (\ln \left (\ln \left (x \right )\right )\right )^{2}+\left (-8 x^{7}+16 x^{6}-24 x^{3}\right ) \ln \left (\ln \left (\ln \left (x \right )\right )\right )+4 x^{8}-16 x^{7}+16 x^{6}+24 x^{4}-48 x^{3}\) | \(59\) |
parallelrisch | \(4 x^{8}-8 \ln \left (\ln \left (\ln \left (x \right )\right )\right ) x^{7}+4 x^{6} \ln \left (\ln \left (\ln \left (x \right )\right )\right )^{2}-16 x^{7}+16 x^{6} \ln \left (\ln \left (\ln \left (x \right )\right )\right )+16 x^{6}+24 x^{4}-24 \ln \left (\ln \left (\ln \left (x \right )\right )\right ) x^{3}-48 x^{3}\) | \(65\) |
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Leaf count of result is larger than twice the leaf count of optimal. 57 vs. \(2 (19) = 38\).
Time = 0.26 (sec) , antiderivative size = 57, normalized size of antiderivative = 3.17 \[ \int \frac {-24 x^2+16 x^5-8 x^6+\left (-144 x^2+96 x^3+96 x^5-112 x^6+32 x^7\right ) \log (x) \log (\log (x))+\left (8 x^5+\left (-72 x^2+96 x^5-56 x^6\right ) \log (x) \log (\log (x))\right ) \log (\log (\log (x)))+24 x^5 \log (x) \log (\log (x)) \log ^2(\log (\log (x)))}{\log (x) \log (\log (x))} \, dx=4 \, x^{8} + 4 \, x^{6} \log \left (\log \left (\log \left (x\right )\right )\right )^{2} - 16 \, x^{7} + 16 \, x^{6} + 24 \, x^{4} - 48 \, x^{3} - 8 \, {\left (x^{7} - 2 \, x^{6} + 3 \, x^{3}\right )} \log \left (\log \left (\log \left (x\right )\right )\right ) \]
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Leaf count of result is larger than twice the leaf count of optimal. 60 vs. \(2 (19) = 38\).
Time = 0.62 (sec) , antiderivative size = 60, normalized size of antiderivative = 3.33 \[ \int \frac {-24 x^2+16 x^5-8 x^6+\left (-144 x^2+96 x^3+96 x^5-112 x^6+32 x^7\right ) \log (x) \log (\log (x))+\left (8 x^5+\left (-72 x^2+96 x^5-56 x^6\right ) \log (x) \log (\log (x))\right ) \log (\log (\log (x)))+24 x^5 \log (x) \log (\log (x)) \log ^2(\log (\log (x)))}{\log (x) \log (\log (x))} \, dx=4 x^{8} - 16 x^{7} + 4 x^{6} \log {\left (\log {\left (\log {\left (x \right )} \right )} \right )}^{2} + 16 x^{6} + 24 x^{4} - 48 x^{3} + \left (- 8 x^{7} + 16 x^{6} - 24 x^{3}\right ) \log {\left (\log {\left (\log {\left (x \right )} \right )} \right )} \]
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Leaf count of result is larger than twice the leaf count of optimal. 57 vs. \(2 (19) = 38\).
Time = 0.25 (sec) , antiderivative size = 57, normalized size of antiderivative = 3.17 \[ \int \frac {-24 x^2+16 x^5-8 x^6+\left (-144 x^2+96 x^3+96 x^5-112 x^6+32 x^7\right ) \log (x) \log (\log (x))+\left (8 x^5+\left (-72 x^2+96 x^5-56 x^6\right ) \log (x) \log (\log (x))\right ) \log (\log (\log (x)))+24 x^5 \log (x) \log (\log (x)) \log ^2(\log (\log (x)))}{\log (x) \log (\log (x))} \, dx=4 \, x^{8} + 4 \, x^{6} \log \left (\log \left (\log \left (x\right )\right )\right )^{2} - 16 \, x^{7} + 16 \, x^{6} + 24 \, x^{4} - 48 \, x^{3} - 8 \, {\left (x^{7} - 2 \, x^{6} + 3 \, x^{3}\right )} \log \left (\log \left (\log \left (x\right )\right )\right ) \]
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Leaf count of result is larger than twice the leaf count of optimal. 122 vs. \(2 (19) = 38\).
Time = 0.35 (sec) , antiderivative size = 122, normalized size of antiderivative = 6.78 \[ \int \frac {-24 x^2+16 x^5-8 x^6+\left (-144 x^2+96 x^3+96 x^5-112 x^6+32 x^7\right ) \log (x) \log (\log (x))+\left (8 x^5+\left (-72 x^2+96 x^5-56 x^6\right ) \log (x) \log (\log (x))\right ) \log (\log (\log (x)))+24 x^5 \log (x) \log (\log (x)) \log ^2(\log (\log (x)))}{\log (x) \log (\log (x))} \, dx=2 \, x^{6} \log \left (x\right )^{2} \log \left (\log \left (x\right )\right )^{2} - 8 \, x^{7} \log \left (x\right ) \log \left (\log \left (x\right )\right ) + 4 \, x^{6} \log \left (x\right ) \log \left (\log \left (x\right )\right ) \log \left (\log \left (\log \left (x\right )\right )\right ) + 4 \, x^{8} + 8 \, x^{6} \log \left (x\right ) \log \left (\log \left (x\right )\right ) - 8 \, x^{7} \log \left (\log \left (\log \left (x\right )\right )\right ) + 4 \, x^{6} \log \left (\log \left (\log \left (x\right )\right )\right )^{2} - 16 \, x^{7} + 16 \, x^{6} \log \left (\log \left (\log \left (x\right )\right )\right ) + \frac {46}{3} \, x^{6} - 24 \, x^{3} \log \left (x\right ) \log \left (\log \left (x\right )\right ) + 24 \, x^{4} - 24 \, x^{3} \log \left (\log \left (\log \left (x\right )\right )\right ) - 48 \, x^{3} \]
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Time = 11.66 (sec) , antiderivative size = 62, normalized size of antiderivative = 3.44 \[ \int \frac {-24 x^2+16 x^5-8 x^6+\left (-144 x^2+96 x^3+96 x^5-112 x^6+32 x^7\right ) \log (x) \log (\log (x))+\left (8 x^5+\left (-72 x^2+96 x^5-56 x^6\right ) \log (x) \log (\log (x))\right ) \log (\log (\log (x)))+24 x^5 \log (x) \log (\log (x)) \log ^2(\log (\log (x)))}{\log (x) \log (\log (x))} \, dx=4\,x^6\,{\ln \left (\ln \left (\ln \left (x\right )\right )\right )}^2-48\,x^3+24\,x^4+16\,x^6-16\,x^7+4\,x^8-\frac {\ln \left (\ln \left (\ln \left (x\right )\right )\right )\,\left (8\,x^8-16\,x^7+24\,x^4\right )}{x} \]
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