Integrand size = 385, antiderivative size = 29 \[ \int \frac {-32768+73728 x-61440 x^2+23040 x^3-3840 x^4+288 x^5-8 x^6+\left (-24576 x+59392 x^2-55296 x^3+24960 x^4-5760 x^5+696 x^6-42 x^7+x^8+\left (-24576+59392 x-55296 x^2+24960 x^3-5760 x^4+696 x^5-42 x^6+x^7\right ) \log (3)\right ) \log \left (x^2+2 x \log (3)+\log ^2(3)\right )+\left (49152-73728 x+33792 x^2-4608 x^3+192 x^4+\left (36864 x-61440 x^2+34560 x^3-7680 x^4+720 x^5-24 x^6+\left (36864-61440 x+34560 x^2-7680 x^3+720 x^4-24 x^5\right ) \log (3)\right ) \log \left (x^2+2 x \log (3)+\log ^2(3)\right )\right ) \log \left (\log \left (x^2+2 x \log (3)+\log ^2(3)\right )\right )+\left (-24576+18432 x-1536 x^2+\left (-18432 x+16896 x^2-3456 x^3+192 x^4+\left (-18432+16896 x-3456 x^2+192 x^3\right ) \log (3)\right ) \log \left (x^2+2 x \log (3)+\log ^2(3)\right )\right ) \log ^2\left (\log \left (x^2+2 x \log (3)+\log ^2(3)\right )\right )+\left (4096+\left (3072 x-512 x^2+(3072-512 x) \log (3)\right ) \log \left (x^2+2 x \log (3)+\log ^2(3)\right )\right ) \log ^3\left (\log \left (x^2+2 x \log (3)+\log ^2(3)\right )\right )}{(800 x+800 \log (3)) \log \left (x^2+2 x \log (3)+\log ^2(3)\right )} \, dx=-5+\frac {1}{25} \left (-\frac {1}{4} (-4+x)^2+x+2 \log \left (\log \left ((x+\log (3))^2\right )\right )\right )^4 \]
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Time = 0.41 (sec) , antiderivative size = 24, normalized size of antiderivative = 0.83, number of steps used = 3, number of rules used = 3, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.008, Rules used = {6820, 12, 6818} \[ \int \frac {-32768+73728 x-61440 x^2+23040 x^3-3840 x^4+288 x^5-8 x^6+\left (-24576 x+59392 x^2-55296 x^3+24960 x^4-5760 x^5+696 x^6-42 x^7+x^8+\left (-24576+59392 x-55296 x^2+24960 x^3-5760 x^4+696 x^5-42 x^6+x^7\right ) \log (3)\right ) \log \left (x^2+2 x \log (3)+\log ^2(3)\right )+\left (49152-73728 x+33792 x^2-4608 x^3+192 x^4+\left (36864 x-61440 x^2+34560 x^3-7680 x^4+720 x^5-24 x^6+\left (36864-61440 x+34560 x^2-7680 x^3+720 x^4-24 x^5\right ) \log (3)\right ) \log \left (x^2+2 x \log (3)+\log ^2(3)\right )\right ) \log \left (\log \left (x^2+2 x \log (3)+\log ^2(3)\right )\right )+\left (-24576+18432 x-1536 x^2+\left (-18432 x+16896 x^2-3456 x^3+192 x^4+\left (-18432+16896 x-3456 x^2+192 x^3\right ) \log (3)\right ) \log \left (x^2+2 x \log (3)+\log ^2(3)\right )\right ) \log ^2\left (\log \left (x^2+2 x \log (3)+\log ^2(3)\right )\right )+\left (4096+\left (3072 x-512 x^2+(3072-512 x) \log (3)\right ) \log \left (x^2+2 x \log (3)+\log ^2(3)\right )\right ) \log ^3\left (\log \left (x^2+2 x \log (3)+\log ^2(3)\right )\right )}{(800 x+800 \log (3)) \log \left (x^2+2 x \log (3)+\log ^2(3)\right )} \, dx=\frac {\left (x^2-12 x-8 \log \left (\log \left ((x+\log (3))^2\right )\right )+16\right )^4}{6400} \]
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Rule 12
Rule 6818
Rule 6820
Rubi steps \begin{align*} \text {integral}& = \int \frac {\left (-8+(-6+x) (x+\log (3)) \log \left ((x+\log (3))^2\right )\right ) \left (16-12 x+x^2-8 \log \left (\log \left ((x+\log (3))^2\right )\right )\right )^3}{800 (x+\log (3)) \log \left ((x+\log (3))^2\right )} \, dx \\ & = \frac {1}{800} \int \frac {\left (-8+(-6+x) (x+\log (3)) \log \left ((x+\log (3))^2\right )\right ) \left (16-12 x+x^2-8 \log \left (\log \left ((x+\log (3))^2\right )\right )\right )^3}{(x+\log (3)) \log \left ((x+\log (3))^2\right )} \, dx \\ & = \frac {\left (16-12 x+x^2-8 \log \left (\log \left ((x+\log (3))^2\right )\right )\right )^4}{6400} \\ \end{align*}
Time = 0.08 (sec) , antiderivative size = 24, normalized size of antiderivative = 0.83 \[ \int \frac {-32768+73728 x-61440 x^2+23040 x^3-3840 x^4+288 x^5-8 x^6+\left (-24576 x+59392 x^2-55296 x^3+24960 x^4-5760 x^5+696 x^6-42 x^7+x^8+\left (-24576+59392 x-55296 x^2+24960 x^3-5760 x^4+696 x^5-42 x^6+x^7\right ) \log (3)\right ) \log \left (x^2+2 x \log (3)+\log ^2(3)\right )+\left (49152-73728 x+33792 x^2-4608 x^3+192 x^4+\left (36864 x-61440 x^2+34560 x^3-7680 x^4+720 x^5-24 x^6+\left (36864-61440 x+34560 x^2-7680 x^3+720 x^4-24 x^5\right ) \log (3)\right ) \log \left (x^2+2 x \log (3)+\log ^2(3)\right )\right ) \log \left (\log \left (x^2+2 x \log (3)+\log ^2(3)\right )\right )+\left (-24576+18432 x-1536 x^2+\left (-18432 x+16896 x^2-3456 x^3+192 x^4+\left (-18432+16896 x-3456 x^2+192 x^3\right ) \log (3)\right ) \log \left (x^2+2 x \log (3)+\log ^2(3)\right )\right ) \log ^2\left (\log \left (x^2+2 x \log (3)+\log ^2(3)\right )\right )+\left (4096+\left (3072 x-512 x^2+(3072-512 x) \log (3)\right ) \log \left (x^2+2 x \log (3)+\log ^2(3)\right )\right ) \log ^3\left (\log \left (x^2+2 x \log (3)+\log ^2(3)\right )\right )}{(800 x+800 \log (3)) \log \left (x^2+2 x \log (3)+\log ^2(3)\right )} \, dx=\frac {\left (16-12 x+x^2-8 \log \left (\log \left ((x+\log (3))^2\right )\right )\right )^4}{6400} \]
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Leaf count of result is larger than twice the leaf count of optimal. \(369\) vs. \(2(25)=50\).
Time = 2.31 (sec) , antiderivative size = 370, normalized size of antiderivative = 12.76
method | result | size |
parallelrisch | \(\frac {9 \ln \left (\ln \left (\ln \left (3\right )^{2}+2 x \ln \left (3\right )+x^{2}\right )\right ) x^{5}}{50}-\frac {36 {\ln \left (\ln \left (\ln \left (3\right )^{2}+2 x \ln \left (3\right )+x^{2}\right )\right )}^{2} x^{3}}{25}+\frac {3 {\ln \left (\ln \left (\ln \left (3\right )^{2}+2 x \ln \left (3\right )+x^{2}\right )\right )}^{2} x^{4}}{50}+\frac {96 {\ln \left (\ln \left (\ln \left (3\right )^{2}+2 x \ln \left (3\right )+x^{2}\right )\right )}^{3} x}{25}-\frac {\ln \left (\ln \left (\ln \left (3\right )^{2}+2 x \ln \left (3\right )+x^{2}\right )\right ) x^{6}}{200}-\frac {8 {\ln \left (\ln \left (\ln \left (3\right )^{2}+2 x \ln \left (3\right )+x^{2}\right )\right )}^{3} x^{2}}{25}-\frac {768 x}{25}-\frac {12 \ln \left (\ln \left (\ln \left (3\right )^{2}+2 x \ln \left (3\right )+x^{2}\right )\right ) x^{4}}{5}+\frac {264 {\ln \left (\ln \left (\ln \left (3\right )^{2}+2 x \ln \left (3\right )+x^{2}\right )\right )}^{2} x^{2}}{25}+\frac {72 \ln \left (\ln \left (\ln \left (3\right )^{2}+2 x \ln \left (3\right )+x^{2}\right )\right ) x^{3}}{5}-\frac {576 {\ln \left (\ln \left (\ln \left (3\right )^{2}+2 x \ln \left (3\right )+x^{2}\right )\right )}^{2} x}{25}-\frac {192 \ln \left (\ln \left (\ln \left (3\right )^{2}+2 x \ln \left (3\right )+x^{2}\right )\right ) x^{2}}{5}+\frac {1152 \ln \left (\ln \left (\ln \left (3\right )^{2}+2 x \ln \left (3\right )+x^{2}\right )\right ) x}{25}-\frac {512 \ln \left (\ln \left (\ln \left (3\right )^{2}+2 x \ln \left (3\right )+x^{2}\right )\right )}{25}-\frac {928 \ln \left (3\right )^{2}}{25}-\frac {3 x^{7}}{400}+\frac {x^{8}}{6400}+\frac {29 x^{6}}{200}-\frac {36 x^{5}}{25}+\frac {1536 \ln \left (3\right )}{25}+\frac {39 x^{4}}{5}-\frac {576 x^{3}}{25}+\frac {928 x^{2}}{25}-\frac {128 {\ln \left (\ln \left (\ln \left (3\right )^{2}+2 x \ln \left (3\right )+x^{2}\right )\right )}^{3}}{25}+\frac {384 {\ln \left (\ln \left (\ln \left (3\right )^{2}+2 x \ln \left (3\right )+x^{2}\right )\right )}^{2}}{25}+\frac {16 {\ln \left (\ln \left (\ln \left (3\right )^{2}+2 x \ln \left (3\right )+x^{2}\right )\right )}^{4}}{25}\) | \(370\) |
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Leaf count of result is larger than twice the leaf count of optimal. 167 vs. \(2 (25) = 50\).
Time = 0.25 (sec) , antiderivative size = 167, normalized size of antiderivative = 5.76 \[ \int \frac {-32768+73728 x-61440 x^2+23040 x^3-3840 x^4+288 x^5-8 x^6+\left (-24576 x+59392 x^2-55296 x^3+24960 x^4-5760 x^5+696 x^6-42 x^7+x^8+\left (-24576+59392 x-55296 x^2+24960 x^3-5760 x^4+696 x^5-42 x^6+x^7\right ) \log (3)\right ) \log \left (x^2+2 x \log (3)+\log ^2(3)\right )+\left (49152-73728 x+33792 x^2-4608 x^3+192 x^4+\left (36864 x-61440 x^2+34560 x^3-7680 x^4+720 x^5-24 x^6+\left (36864-61440 x+34560 x^2-7680 x^3+720 x^4-24 x^5\right ) \log (3)\right ) \log \left (x^2+2 x \log (3)+\log ^2(3)\right )\right ) \log \left (\log \left (x^2+2 x \log (3)+\log ^2(3)\right )\right )+\left (-24576+18432 x-1536 x^2+\left (-18432 x+16896 x^2-3456 x^3+192 x^4+\left (-18432+16896 x-3456 x^2+192 x^3\right ) \log (3)\right ) \log \left (x^2+2 x \log (3)+\log ^2(3)\right )\right ) \log ^2\left (\log \left (x^2+2 x \log (3)+\log ^2(3)\right )\right )+\left (4096+\left (3072 x-512 x^2+(3072-512 x) \log (3)\right ) \log \left (x^2+2 x \log (3)+\log ^2(3)\right )\right ) \log ^3\left (\log \left (x^2+2 x \log (3)+\log ^2(3)\right )\right )}{(800 x+800 \log (3)) \log \left (x^2+2 x \log (3)+\log ^2(3)\right )} \, dx=\frac {1}{6400} \, x^{8} - \frac {3}{400} \, x^{7} + \frac {29}{200} \, x^{6} - \frac {36}{25} \, x^{5} + \frac {39}{5} \, x^{4} - \frac {8}{25} \, {\left (x^{2} - 12 \, x + 16\right )} \log \left (\log \left (x^{2} + 2 \, x \log \left (3\right ) + \log \left (3\right )^{2}\right )\right )^{3} + \frac {16}{25} \, \log \left (\log \left (x^{2} + 2 \, x \log \left (3\right ) + \log \left (3\right )^{2}\right )\right )^{4} - \frac {576}{25} \, x^{3} + \frac {3}{50} \, {\left (x^{4} - 24 \, x^{3} + 176 \, x^{2} - 384 \, x + 256\right )} \log \left (\log \left (x^{2} + 2 \, x \log \left (3\right ) + \log \left (3\right )^{2}\right )\right )^{2} + \frac {928}{25} \, x^{2} - \frac {1}{200} \, {\left (x^{6} - 36 \, x^{5} + 480 \, x^{4} - 2880 \, x^{3} + 7680 \, x^{2} - 9216 \, x + 4096\right )} \log \left (\log \left (x^{2} + 2 \, x \log \left (3\right ) + \log \left (3\right )^{2}\right )\right ) - \frac {768}{25} \, x \]
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Leaf count of result is larger than twice the leaf count of optimal. 236 vs. \(2 (24) = 48\).
Time = 0.49 (sec) , antiderivative size = 236, normalized size of antiderivative = 8.14 \[ \int \frac {-32768+73728 x-61440 x^2+23040 x^3-3840 x^4+288 x^5-8 x^6+\left (-24576 x+59392 x^2-55296 x^3+24960 x^4-5760 x^5+696 x^6-42 x^7+x^8+\left (-24576+59392 x-55296 x^2+24960 x^3-5760 x^4+696 x^5-42 x^6+x^7\right ) \log (3)\right ) \log \left (x^2+2 x \log (3)+\log ^2(3)\right )+\left (49152-73728 x+33792 x^2-4608 x^3+192 x^4+\left (36864 x-61440 x^2+34560 x^3-7680 x^4+720 x^5-24 x^6+\left (36864-61440 x+34560 x^2-7680 x^3+720 x^4-24 x^5\right ) \log (3)\right ) \log \left (x^2+2 x \log (3)+\log ^2(3)\right )\right ) \log \left (\log \left (x^2+2 x \log (3)+\log ^2(3)\right )\right )+\left (-24576+18432 x-1536 x^2+\left (-18432 x+16896 x^2-3456 x^3+192 x^4+\left (-18432+16896 x-3456 x^2+192 x^3\right ) \log (3)\right ) \log \left (x^2+2 x \log (3)+\log ^2(3)\right )\right ) \log ^2\left (\log \left (x^2+2 x \log (3)+\log ^2(3)\right )\right )+\left (4096+\left (3072 x-512 x^2+(3072-512 x) \log (3)\right ) \log \left (x^2+2 x \log (3)+\log ^2(3)\right )\right ) \log ^3\left (\log \left (x^2+2 x \log (3)+\log ^2(3)\right )\right )}{(800 x+800 \log (3)) \log \left (x^2+2 x \log (3)+\log ^2(3)\right )} \, dx=\frac {x^{8}}{6400} - \frac {3 x^{7}}{400} + \frac {29 x^{6}}{200} - \frac {36 x^{5}}{25} + \frac {39 x^{4}}{5} - \frac {576 x^{3}}{25} + \frac {928 x^{2}}{25} - \frac {768 x}{25} + \left (- \frac {8 x^{2}}{25} + \frac {96 x}{25} - \frac {128}{25}\right ) \log {\left (\log {\left (x^{2} + 2 x \log {\left (3 \right )} + \log {\left (3 \right )}^{2} \right )} \right )}^{3} + \left (\frac {3 x^{4}}{50} - \frac {36 x^{3}}{25} + \frac {264 x^{2}}{25} - \frac {576 x}{25} + \frac {384}{25}\right ) \log {\left (\log {\left (x^{2} + 2 x \log {\left (3 \right )} + \log {\left (3 \right )}^{2} \right )} \right )}^{2} + \left (- \frac {x^{6}}{200} + \frac {9 x^{5}}{50} - \frac {12 x^{4}}{5} + \frac {72 x^{3}}{5} - \frac {192 x^{2}}{5} + \frac {1152 x}{25}\right ) \log {\left (\log {\left (x^{2} + 2 x \log {\left (3 \right )} + \log {\left (3 \right )}^{2} \right )} \right )} + \frac {16 \log {\left (\log {\left (x^{2} + 2 x \log {\left (3 \right )} + \log {\left (3 \right )}^{2} \right )} \right )}^{4}}{25} - \frac {512 \log {\left (\log {\left (x^{2} + 2 x \log {\left (3 \right )} + \log {\left (3 \right )}^{2} \right )} \right )}}{25} \]
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Leaf count of result is larger than twice the leaf count of optimal. 264 vs. \(2 (25) = 50\).
Time = 0.32 (sec) , antiderivative size = 264, normalized size of antiderivative = 9.10 \[ \int \frac {-32768+73728 x-61440 x^2+23040 x^3-3840 x^4+288 x^5-8 x^6+\left (-24576 x+59392 x^2-55296 x^3+24960 x^4-5760 x^5+696 x^6-42 x^7+x^8+\left (-24576+59392 x-55296 x^2+24960 x^3-5760 x^4+696 x^5-42 x^6+x^7\right ) \log (3)\right ) \log \left (x^2+2 x \log (3)+\log ^2(3)\right )+\left (49152-73728 x+33792 x^2-4608 x^3+192 x^4+\left (36864 x-61440 x^2+34560 x^3-7680 x^4+720 x^5-24 x^6+\left (36864-61440 x+34560 x^2-7680 x^3+720 x^4-24 x^5\right ) \log (3)\right ) \log \left (x^2+2 x \log (3)+\log ^2(3)\right )\right ) \log \left (\log \left (x^2+2 x \log (3)+\log ^2(3)\right )\right )+\left (-24576+18432 x-1536 x^2+\left (-18432 x+16896 x^2-3456 x^3+192 x^4+\left (-18432+16896 x-3456 x^2+192 x^3\right ) \log (3)\right ) \log \left (x^2+2 x \log (3)+\log ^2(3)\right )\right ) \log ^2\left (\log \left (x^2+2 x \log (3)+\log ^2(3)\right )\right )+\left (4096+\left (3072 x-512 x^2+(3072-512 x) \log (3)\right ) \log \left (x^2+2 x \log (3)+\log ^2(3)\right )\right ) \log ^3\left (\log \left (x^2+2 x \log (3)+\log ^2(3)\right )\right )}{(800 x+800 \log (3)) \log \left (x^2+2 x \log (3)+\log ^2(3)\right )} \, dx=\frac {1}{6400} \, x^{8} - \frac {3}{400} \, x^{7} - \frac {1}{200} \, x^{6} {\left (\log \left (2\right ) - 29\right )} + \frac {9}{50} \, x^{5} {\left (\log \left (2\right ) - 8\right )} + \frac {3}{50} \, {\left (\log \left (2\right )^{2} - 40 \, \log \left (2\right ) + 130\right )} x^{4} - \frac {36}{25} \, {\left (\log \left (2\right )^{2} - 10 \, \log \left (2\right ) + 16\right )} x^{3} - \frac {8}{25} \, {\left (x^{2} - 12 \, x - 8 \, \log \left (2\right ) + 16\right )} \log \left (\log \left (x + \log \left (3\right )\right )\right )^{3} + \frac {16}{25} \, \log \left (\log \left (x + \log \left (3\right )\right )\right )^{4} - \frac {8}{25} \, {\left (\log \left (2\right )^{3} - 33 \, \log \left (2\right )^{2} + 120 \, \log \left (2\right ) - 116\right )} x^{2} + \frac {3}{50} \, {\left (x^{4} - 24 \, x^{3} - 16 \, x^{2} {\left (\log \left (2\right ) - 11\right )} + 192 \, x {\left (\log \left (2\right ) - 2\right )} + 64 \, \log \left (2\right )^{2} - 256 \, \log \left (2\right ) + 256\right )} \log \left (\log \left (x + \log \left (3\right )\right )\right )^{2} + \frac {96}{25} \, {\left (\log \left (2\right )^{3} - 6 \, \log \left (2\right )^{2} + 12 \, \log \left (2\right ) - 8\right )} x - \frac {1}{200} \, {\left (x^{6} - 36 \, x^{5} - 24 \, x^{4} {\left (\log \left (2\right ) - 20\right )} + 576 \, x^{3} {\left (\log \left (2\right ) - 5\right )} + 192 \, {\left (\log \left (2\right )^{2} - 22 \, \log \left (2\right ) + 40\right )} x^{2} - 512 \, \log \left (2\right )^{3} - 2304 \, {\left (\log \left (2\right )^{2} - 4 \, \log \left (2\right ) + 4\right )} x + 3072 \, \log \left (2\right )^{2} - 6144 \, \log \left (2\right )\right )} \log \left (\log \left (x + \log \left (3\right )\right )\right ) - \frac {512}{25} \, \log \left (\log \left (x + \log \left (3\right )\right )\right ) \]
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Leaf count of result is larger than twice the leaf count of optimal. 183 vs. \(2 (25) = 50\).
Time = 1.76 (sec) , antiderivative size = 183, normalized size of antiderivative = 6.31 \[ \int \frac {-32768+73728 x-61440 x^2+23040 x^3-3840 x^4+288 x^5-8 x^6+\left (-24576 x+59392 x^2-55296 x^3+24960 x^4-5760 x^5+696 x^6-42 x^7+x^8+\left (-24576+59392 x-55296 x^2+24960 x^3-5760 x^4+696 x^5-42 x^6+x^7\right ) \log (3)\right ) \log \left (x^2+2 x \log (3)+\log ^2(3)\right )+\left (49152-73728 x+33792 x^2-4608 x^3+192 x^4+\left (36864 x-61440 x^2+34560 x^3-7680 x^4+720 x^5-24 x^6+\left (36864-61440 x+34560 x^2-7680 x^3+720 x^4-24 x^5\right ) \log (3)\right ) \log \left (x^2+2 x \log (3)+\log ^2(3)\right )\right ) \log \left (\log \left (x^2+2 x \log (3)+\log ^2(3)\right )\right )+\left (-24576+18432 x-1536 x^2+\left (-18432 x+16896 x^2-3456 x^3+192 x^4+\left (-18432+16896 x-3456 x^2+192 x^3\right ) \log (3)\right ) \log \left (x^2+2 x \log (3)+\log ^2(3)\right )\right ) \log ^2\left (\log \left (x^2+2 x \log (3)+\log ^2(3)\right )\right )+\left (4096+\left (3072 x-512 x^2+(3072-512 x) \log (3)\right ) \log \left (x^2+2 x \log (3)+\log ^2(3)\right )\right ) \log ^3\left (\log \left (x^2+2 x \log (3)+\log ^2(3)\right )\right )}{(800 x+800 \log (3)) \log \left (x^2+2 x \log (3)+\log ^2(3)\right )} \, dx=\frac {1}{6400} \, x^{8} - \frac {3}{400} \, x^{7} + \frac {29}{200} \, x^{6} - \frac {36}{25} \, x^{5} + \frac {39}{5} \, x^{4} - \frac {8}{25} \, {\left (x^{2} - 12 \, x + 16\right )} \log \left (\log \left (x^{2} + 2 \, x \log \left (3\right ) + \log \left (3\right )^{2}\right )\right )^{3} + \frac {16}{25} \, \log \left (\log \left (x^{2} + 2 \, x \log \left (3\right ) + \log \left (3\right )^{2}\right )\right )^{4} - \frac {576}{25} \, x^{3} + \frac {3}{50} \, {\left (x^{4} - 24 \, x^{3} + 176 \, x^{2} - 384 \, x + 256\right )} \log \left (\log \left (x^{2} + 2 \, x \log \left (3\right ) + \log \left (3\right )^{2}\right )\right )^{2} + \frac {928}{25} \, x^{2} - \frac {1}{200} \, {\left (x^{6} - 36 \, x^{5} + 480 \, x^{4} - 2880 \, x^{3} + 7680 \, x^{2} - 9216 \, x\right )} \log \left (\log \left (x^{2} + 2 \, x \log \left (3\right ) + \log \left (3\right )^{2}\right )\right ) - \frac {768}{25} \, x - \frac {512}{25} \, \log \left (\log \left (x^{2} + 2 \, x \log \left (3\right ) + \log \left (3\right )^{2}\right )\right ) \]
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Time = 13.48 (sec) , antiderivative size = 187, normalized size of antiderivative = 6.45 \[ \int \frac {-32768+73728 x-61440 x^2+23040 x^3-3840 x^4+288 x^5-8 x^6+\left (-24576 x+59392 x^2-55296 x^3+24960 x^4-5760 x^5+696 x^6-42 x^7+x^8+\left (-24576+59392 x-55296 x^2+24960 x^3-5760 x^4+696 x^5-42 x^6+x^7\right ) \log (3)\right ) \log \left (x^2+2 x \log (3)+\log ^2(3)\right )+\left (49152-73728 x+33792 x^2-4608 x^3+192 x^4+\left (36864 x-61440 x^2+34560 x^3-7680 x^4+720 x^5-24 x^6+\left (36864-61440 x+34560 x^2-7680 x^3+720 x^4-24 x^5\right ) \log (3)\right ) \log \left (x^2+2 x \log (3)+\log ^2(3)\right )\right ) \log \left (\log \left (x^2+2 x \log (3)+\log ^2(3)\right )\right )+\left (-24576+18432 x-1536 x^2+\left (-18432 x+16896 x^2-3456 x^3+192 x^4+\left (-18432+16896 x-3456 x^2+192 x^3\right ) \log (3)\right ) \log \left (x^2+2 x \log (3)+\log ^2(3)\right )\right ) \log ^2\left (\log \left (x^2+2 x \log (3)+\log ^2(3)\right )\right )+\left (4096+\left (3072 x-512 x^2+(3072-512 x) \log (3)\right ) \log \left (x^2+2 x \log (3)+\log ^2(3)\right )\right ) \log ^3\left (\log \left (x^2+2 x \log (3)+\log ^2(3)\right )\right )}{(800 x+800 \log (3)) \log \left (x^2+2 x \log (3)+\log ^2(3)\right )} \, dx=\frac {16\,{\ln \left (\ln \left (x^2+2\,\ln \left (3\right )\,x+{\ln \left (3\right )}^2\right )\right )}^4}{25}-\frac {512\,\ln \left (\ln \left (x^2+2\,\ln \left (3\right )\,x+{\ln \left (3\right )}^2\right )\right )}{25}-{\ln \left (\ln \left (x^2+2\,\ln \left (3\right )\,x+{\ln \left (3\right )}^2\right )\right )}^3\,\left (\frac {8\,x^2}{25}-\frac {96\,x}{25}+\frac {128}{25}\right )-\frac {768\,x}{25}+{\ln \left (\ln \left (x^2+2\,\ln \left (3\right )\,x+{\ln \left (3\right )}^2\right )\right )}^2\,\left (\frac {3\,x^4}{50}-\frac {36\,x^3}{25}+\frac {264\,x^2}{25}-\frac {576\,x}{25}+\frac {384}{25}\right )+\ln \left (\ln \left (x^2+2\,\ln \left (3\right )\,x+{\ln \left (3\right )}^2\right )\right )\,\left (-\frac {x^6}{200}+\frac {9\,x^5}{50}-\frac {12\,x^4}{5}+\frac {72\,x^3}{5}-\frac {192\,x^2}{5}+\frac {1152\,x}{25}\right )+\frac {928\,x^2}{25}-\frac {576\,x^3}{25}+\frac {39\,x^4}{5}-\frac {36\,x^5}{25}+\frac {29\,x^6}{200}-\frac {3\,x^7}{400}+\frac {x^8}{6400} \]
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