Integrand size = 184, antiderivative size = 28 \[ \int \frac {72+\left (72-6 x-384 x^3+192 x^4-24 x^5\right ) \log (x)+\left (-6 x+384 x^3-384 x^4+72 x^5\right ) \log ^2(x)+\left (-64 x^4+48 x^5-4104 x^6+5120 x^7-2304 x^8+448 x^9-32 x^{10}\right ) \log ^3(x)}{-27+\left (432 x^3-216 x^4+27 x^5\right ) \log (x)+\left (-2304 x^6+2304 x^7-864 x^8+144 x^9-9 x^{10}\right ) \log ^2(x)+\left (4096 x^9-6144 x^{10}+3840 x^{11}-1280 x^{12}+240 x^{13}-24 x^{14}+x^{15}\right ) \log ^3(x)} \, dx=\left (4+\frac {x}{x (x+(3-x) x)^2-\frac {3}{\log (x)}}\right )^2 \]
Time = 0.08 (sec) , antiderivative size = 41, normalized size of antiderivative = 1.46 \[ \int \frac {72+\left (72-6 x-384 x^3+192 x^4-24 x^5\right ) \log (x)+\left (-6 x+384 x^3-384 x^4+72 x^5\right ) \log ^2(x)+\left (-64 x^4+48 x^5-4104 x^6+5120 x^7-2304 x^8+448 x^9-32 x^{10}\right ) \log ^3(x)}{-27+\left (432 x^3-216 x^4+27 x^5\right ) \log (x)+\left (-2304 x^6+2304 x^7-864 x^8+144 x^9-9 x^{10}\right ) \log ^2(x)+\left (4096 x^9-6144 x^{10}+3840 x^{11}-1280 x^{12}+240 x^{13}-24 x^{14}+x^{15}\right ) \log ^3(x)} \, dx=\frac {x \log (x) \left (-24+\left (x+128 x^3-64 x^4+8 x^5\right ) \log (x)\right )}{\left (-3+(-4+x)^2 x^3 \log (x)\right )^2} \]
Integrate[(72 + (72 - 6*x - 384*x^3 + 192*x^4 - 24*x^5)*Log[x] + (-6*x + 3 84*x^3 - 384*x^4 + 72*x^5)*Log[x]^2 + (-64*x^4 + 48*x^5 - 4104*x^6 + 5120* x^7 - 2304*x^8 + 448*x^9 - 32*x^10)*Log[x]^3)/(-27 + (432*x^3 - 216*x^4 + 27*x^5)*Log[x] + (-2304*x^6 + 2304*x^7 - 864*x^8 + 144*x^9 - 9*x^10)*Log[x ]^2 + (4096*x^9 - 6144*x^10 + 3840*x^11 - 1280*x^12 + 240*x^13 - 24*x^14 + x^15)*Log[x]^3),x]
Below are the steps used by Rubi to obtain the solution. The rule number used for the transformation is given above next to the arrow. The rules definitions used are listed below.
| \(\displaystyle \int \frac {\left (72 x^5-384 x^4+384 x^3-6 x\right ) \log ^2(x)+\left (-24 x^5+192 x^4-384 x^3-6 x+72\right ) \log (x)+\left (-32 x^{10}+448 x^9-2304 x^8+5120 x^7-4104 x^6+48 x^5-64 x^4\right ) \log ^3(x)+72}{\left (27 x^5-216 x^4+432 x^3\right ) \log (x)+\left (-9 x^{10}+144 x^9-864 x^8+2304 x^7-2304 x^6\right ) \log ^2(x)+\left (x^{15}-24 x^{14}+240 x^{13}-1280 x^{12}+3840 x^{11}-6144 x^{10}+4096 x^9\right ) \log ^3(x)-27} \, dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {6 \left (4 x^5-32 x^4+64 x^3+x-12\right ) \log (x)-6 \left (12 x^4-64 x^3+64 x^2-1\right ) x \log ^2(x)+8 \left (4 x^6-56 x^5+288 x^4-640 x^3+513 x^2-6 x+8\right ) x^4 \log ^3(x)-72}{\left (3-(x-4)^2 x^3 \log (x)\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-\frac {18 \left (x^6-12 x^5+48 x^4-64 x^3+15 x-36\right )}{(x-4)^5 x^5 \left (x^5 \log (x)-8 x^4 \log (x)+16 x^3 \log (x)-3\right )^3}-\frac {8 \left (4 x^5-40 x^4+128 x^3-128 x^2+x-2\right )}{(x-4)^5 x^5}-\frac {6 \left (36 x^5-368 x^4+1216 x^3-1280 x^2+13 x-28\right )}{(x-4)^5 x^5 \left (x^5 \log (x)-8 x^4 \log (x)+16 x^3 \log (x)-3\right )}-\frac {6 \left (4 x^{10}-80 x^9+640 x^8-2560 x^7+5121 x^6-4048 x^5-576 x^4+2048 x^3-2304 x^2+42 x-96\right )}{(x-4)^5 x^5 \left (x^5 \log (x)-8 x^4 \log (x)+16 x^3 \log (x)-3\right )^2}\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle -\frac {27}{64} \int \frac {1}{(x-4)^5 \left (\log (x) x^5-8 \log (x) x^4+16 \log (x) x^3-3\right )^3}dx+\frac {135}{512} \int \frac {1}{(x-4)^4 \left (\log (x) x^5-8 \log (x) x^4+16 \log (x) x^3-3\right )^3}dx-\frac {135 \int \frac {1}{(x-4)^3 \left (\log (x) x^5-8 \log (x) x^4+16 \log (x) x^3-3\right )^3}dx}{2048}-\frac {9351 \int \frac {1}{(x-4)^2 \left (\log (x) x^5-8 \log (x) x^4+16 \log (x) x^3-3\right )^3}dx}{8192}+\frac {19377 \int \frac {1}{(x-4) \left (\log (x) x^5-8 \log (x) x^4+16 \log (x) x^3-3\right )^3}dx}{32768}-\frac {81}{128} \int \frac {1}{x^5 \left (\log (x) x^5-8 \log (x) x^4+16 \log (x) x^3-3\right )^3}dx-\frac {135}{256} \int \frac {1}{x^4 \left (\log (x) x^5-8 \log (x) x^4+16 \log (x) x^3-3\right )^3}dx-\frac {135}{512} \int \frac {1}{x^3 \left (\log (x) x^5-8 \log (x) x^4+16 \log (x) x^3-3\right )^3}dx-\frac {5013 \int \frac {1}{x^2 \left (\log (x) x^5-8 \log (x) x^4+16 \log (x) x^3-3\right )^3}dx}{4096}-\frac {19377 \int \frac {1}{x \left (\log (x) x^5-8 \log (x) x^4+16 \log (x) x^3-3\right )^3}dx}{32768}-24 \int \frac {1}{\left (\log (x) x^5-8 \log (x) x^4+16 \log (x) x^3-3\right )^2}dx-\frac {27}{64} \int \frac {1}{(x-4)^5 \left (\log (x) x^5-8 \log (x) x^4+16 \log (x) x^3-3\right )^2}dx+\frac {9}{32} \int \frac {1}{(x-4)^4 \left (\log (x) x^5-8 \log (x) x^4+16 \log (x) x^3-3\right )^2}dx-\frac {4653}{512} \int \frac {1}{(x-4)^3 \left (\log (x) x^5-8 \log (x) x^4+16 \log (x) x^3-3\right )^2}dx+\frac {3}{4} \int \frac {1}{(x-4)^2 \left (\log (x) x^5-8 \log (x) x^4+16 \log (x) x^3-3\right )^2}dx+\frac {17211 \int \frac {1}{(x-4) \left (\log (x) x^5-8 \log (x) x^4+16 \log (x) x^3-3\right )^2}dx}{16384}-\frac {9}{16} \int \frac {1}{x^5 \left (\log (x) x^5-8 \log (x) x^4+16 \log (x) x^3-3\right )^2}dx-\frac {117}{256} \int \frac {1}{x^4 \left (\log (x) x^5-8 \log (x) x^4+16 \log (x) x^3-3\right )^2}dx-\frac {14049 \int \frac {1}{x^3 \left (\log (x) x^5-8 \log (x) x^4+16 \log (x) x^3-3\right )^2}dx}{1024}-\frac {20283 \int \frac {1}{x^2 \left (\log (x) x^5-8 \log (x) x^4+16 \log (x) x^3-3\right )^2}dx}{4096}-\frac {17211 \int \frac {1}{x \left (\log (x) x^5-8 \log (x) x^4+16 \log (x) x^3-3\right )^2}dx}{16384}-\frac {9}{64} \int \frac {1}{(x-4)^5 \left (\log (x) x^5-8 \log (x) x^4+16 \log (x) x^3-3\right )}dx+\frac {51}{512} \int \frac {1}{(x-4)^4 \left (\log (x) x^5-8 \log (x) x^4+16 \log (x) x^3-3\right )}dx-\frac {12363 \int \frac {1}{(x-4)^3 \left (\log (x) x^5-8 \log (x) x^4+16 \log (x) x^3-3\right )}dx}{2048}+\frac {9261 \int \frac {1}{(x-4)^2 \left (\log (x) x^5-8 \log (x) x^4+16 \log (x) x^3-3\right )}dx}{8192}+\frac {9321 \int \frac {1}{(x-4) \left (\log (x) x^5-8 \log (x) x^4+16 \log (x) x^3-3\right )}dx}{32768}-\frac {21}{128} \int \frac {1}{x^5 \left (\log (x) x^5-8 \log (x) x^4+16 \log (x) x^3-3\right )}dx-\frac {33}{256} \int \frac {1}{x^4 \left (\log (x) x^5-8 \log (x) x^4+16 \log (x) x^3-3\right )}dx-\frac {1935}{256} \int \frac {1}{x^3 \left (\log (x) x^5-8 \log (x) x^4+16 \log (x) x^3-3\right )}dx-\frac {9291 \int \frac {1}{x^2 \left (\log (x) x^5-8 \log (x) x^4+16 \log (x) x^3-3\right )}dx}{4096}-\frac {9321 \int \frac {1}{x \left (\log (x) x^5-8 \log (x) x^4+16 \log (x) x^3-3\right )}dx}{32768}+\frac {1029}{4096 (4-x)}+\frac {1029}{4096 x}+\frac {1029}{2048 (4-x)^2}+\frac {1029}{2048 x^2}+\frac {1}{256 (4-x)^3}+\frac {1}{256 x^3}+\frac {1}{256 (4-x)^4}+\frac {1}{256 x^4}\) |
Int[(72 + (72 - 6*x - 384*x^3 + 192*x^4 - 24*x^5)*Log[x] + (-6*x + 384*x^3 - 384*x^4 + 72*x^5)*Log[x]^2 + (-64*x^4 + 48*x^5 - 4104*x^6 + 5120*x^7 - 2304*x^8 + 448*x^9 - 32*x^10)*Log[x]^3)/(-27 + (432*x^3 - 216*x^4 + 27*x^5 )*Log[x] + (-2304*x^6 + 2304*x^7 - 864*x^8 + 144*x^9 - 9*x^10)*Log[x]^2 + (4096*x^9 - 6144*x^10 + 3840*x^11 - 1280*x^12 + 240*x^13 - 24*x^14 + x^15) *Log[x]^3),x]
3.23.99.3.1 Defintions of rubi rules used
Int[u_, x_Symbol] :> With[{v = SimplifyIntegrand[u, x]}, Int[v, x] /; Simpl erIntegrandQ[v, u, x]]
Time = 1.14 (sec) , antiderivative size = 56, normalized size of antiderivative = 2.00
| method | result | size |
| default | \(\frac {\left (8 x^{5} \ln \left (x \right )-64 x^{4} \ln \left (x \right )+128 x^{3} \ln \left (x \right )+x \ln \left (x \right )-24\right ) x \ln \left (x \right )}{\left (x^{5} \ln \left (x \right )-8 x^{4} \ln \left (x \right )+16 x^{3} \ln \left (x \right )-3\right )^{2}}\) | \(56\) |
| parallelrisch | \(\frac {6144 x^{6} \ln \left (x \right )^{2}+98304 x^{4} \ln \left (x \right )^{2}-18432 x \ln \left (x \right )-49152 x^{5} \ln \left (x \right )^{2}+768 x^{2} \ln \left (x \right )^{2}}{768 x^{10} \ln \left (x \right )^{2}-12288 x^{9} \ln \left (x \right )^{2}+73728 x^{8} \ln \left (x \right )^{2}-196608 x^{7} \ln \left (x \right )^{2}+196608 x^{6} \ln \left (x \right )^{2}-4608 x^{5} \ln \left (x \right )+36864 x^{4} \ln \left (x \right )-73728 x^{3} \ln \left (x \right )+6912}\) | \(114\) |
| risch | \(\frac {8 x^{4}-64 x^{3}+128 x^{2}+1}{\left (x^{4}-16 x^{3}+96 x^{2}-256 x +256\right ) x^{4}}+\frac {24 x^{9} \ln \left (x \right )-384 x^{8} \ln \left (x \right )+2304 x^{7} \ln \left (x \right )-6144 x^{6} \ln \left (x \right )+6150 x^{5} \ln \left (x \right )-48 x^{4} \ln \left (x \right )-72 x^{4}+96 x^{3} \ln \left (x \right )+576 x^{3}-1152 x^{2}-9}{\left (x -4\right ) \left (x^{3}-12 x^{2}+48 x -64\right ) \left (x^{5} \ln \left (x \right )-8 x^{4} \ln \left (x \right )+16 x^{3} \ln \left (x \right )-3\right )^{2} x^{4}}\) | \(158\) |
int(((-32*x^10+448*x^9-2304*x^8+5120*x^7-4104*x^6+48*x^5-64*x^4)*ln(x)^3+( 72*x^5-384*x^4+384*x^3-6*x)*ln(x)^2+(-24*x^5+192*x^4-384*x^3-6*x+72)*ln(x) +72)/((x^15-24*x^14+240*x^13-1280*x^12+3840*x^11-6144*x^10+4096*x^9)*ln(x) ^3+(-9*x^10+144*x^9-864*x^8+2304*x^7-2304*x^6)*ln(x)^2+(27*x^5-216*x^4+432 *x^3)*ln(x)-27),x,method=_RETURNVERBOSE)
(8*x^5*ln(x)-64*x^4*ln(x)+128*x^3*ln(x)+x*ln(x)-24)*x*ln(x)/(x^5*ln(x)-8*x ^4*ln(x)+16*x^3*ln(x)-3)^2
Leaf count of result is larger than twice the leaf count of optimal. 82 vs. \(2 (28) = 56\).
Time = 0.26 (sec) , antiderivative size = 82, normalized size of antiderivative = 2.93 \[ \int \frac {72+\left (72-6 x-384 x^3+192 x^4-24 x^5\right ) \log (x)+\left (-6 x+384 x^3-384 x^4+72 x^5\right ) \log ^2(x)+\left (-64 x^4+48 x^5-4104 x^6+5120 x^7-2304 x^8+448 x^9-32 x^{10}\right ) \log ^3(x)}{-27+\left (432 x^3-216 x^4+27 x^5\right ) \log (x)+\left (-2304 x^6+2304 x^7-864 x^8+144 x^9-9 x^{10}\right ) \log ^2(x)+\left (4096 x^9-6144 x^{10}+3840 x^{11}-1280 x^{12}+240 x^{13}-24 x^{14}+x^{15}\right ) \log ^3(x)} \, dx=\frac {{\left (8 \, x^{6} - 64 \, x^{5} + 128 \, x^{4} + x^{2}\right )} \log \left (x\right )^{2} - 24 \, x \log \left (x\right )}{{\left (x^{10} - 16 \, x^{9} + 96 \, x^{8} - 256 \, x^{7} + 256 \, x^{6}\right )} \log \left (x\right )^{2} - 6 \, {\left (x^{5} - 8 \, x^{4} + 16 \, x^{3}\right )} \log \left (x\right ) + 9} \]
integrate(((-32*x^10+448*x^9-2304*x^8+5120*x^7-4104*x^6+48*x^5-64*x^4)*log (x)^3+(72*x^5-384*x^4+384*x^3-6*x)*log(x)^2+(-24*x^5+192*x^4-384*x^3-6*x+7 2)*log(x)+72)/((x^15-24*x^14+240*x^13-1280*x^12+3840*x^11-6144*x^10+4096*x ^9)*log(x)^3+(-9*x^10+144*x^9-864*x^8+2304*x^7-2304*x^6)*log(x)^2+(27*x^5- 216*x^4+432*x^3)*log(x)-27),x, algorithm=\
((8*x^6 - 64*x^5 + 128*x^4 + x^2)*log(x)^2 - 24*x*log(x))/((x^10 - 16*x^9 + 96*x^8 - 256*x^7 + 256*x^6)*log(x)^2 - 6*(x^5 - 8*x^4 + 16*x^3)*log(x) + 9)
Leaf count of result is larger than twice the leaf count of optimal. 209 vs. \(2 (19) = 38\).
Time = 0.33 (sec) , antiderivative size = 209, normalized size of antiderivative = 7.46 \[ \int \frac {72+\left (72-6 x-384 x^3+192 x^4-24 x^5\right ) \log (x)+\left (-6 x+384 x^3-384 x^4+72 x^5\right ) \log ^2(x)+\left (-64 x^4+48 x^5-4104 x^6+5120 x^7-2304 x^8+448 x^9-32 x^{10}\right ) \log ^3(x)}{-27+\left (432 x^3-216 x^4+27 x^5\right ) \log (x)+\left (-2304 x^6+2304 x^7-864 x^8+144 x^9-9 x^{10}\right ) \log ^2(x)+\left (4096 x^9-6144 x^{10}+3840 x^{11}-1280 x^{12}+240 x^{13}-24 x^{14}+x^{15}\right ) \log ^3(x)} \, dx=- \frac {- 8 x^{4} + 64 x^{3} - 128 x^{2} - 1}{x^{8} - 16 x^{7} + 96 x^{6} - 256 x^{5} + 256 x^{4}} + \frac {- 72 x^{4} + 576 x^{3} - 1152 x^{2} + \left (24 x^{9} - 384 x^{8} + 2304 x^{7} - 6144 x^{6} + 6150 x^{5} - 48 x^{4} + 96 x^{3}\right ) \log {\left (x \right )} - 9}{9 x^{8} - 144 x^{7} + 864 x^{6} - 2304 x^{5} + 2304 x^{4} + \left (- 6 x^{13} + 144 x^{12} - 1440 x^{11} + 7680 x^{10} - 23040 x^{9} + 36864 x^{8} - 24576 x^{7}\right ) \log {\left (x \right )} + \left (x^{18} - 32 x^{17} + 448 x^{16} - 3584 x^{15} + 17920 x^{14} - 57344 x^{13} + 114688 x^{12} - 131072 x^{11} + 65536 x^{10}\right ) \log {\left (x \right )}^{2}} \]
integrate(((-32*x**10+448*x**9-2304*x**8+5120*x**7-4104*x**6+48*x**5-64*x* *4)*ln(x)**3+(72*x**5-384*x**4+384*x**3-6*x)*ln(x)**2+(-24*x**5+192*x**4-3 84*x**3-6*x+72)*ln(x)+72)/((x**15-24*x**14+240*x**13-1280*x**12+3840*x**11 -6144*x**10+4096*x**9)*ln(x)**3+(-9*x**10+144*x**9-864*x**8+2304*x**7-2304 *x**6)*ln(x)**2+(27*x**5-216*x**4+432*x**3)*ln(x)-27),x)
-(-8*x**4 + 64*x**3 - 128*x**2 - 1)/(x**8 - 16*x**7 + 96*x**6 - 256*x**5 + 256*x**4) + (-72*x**4 + 576*x**3 - 1152*x**2 + (24*x**9 - 384*x**8 + 2304 *x**7 - 6144*x**6 + 6150*x**5 - 48*x**4 + 96*x**3)*log(x) - 9)/(9*x**8 - 1 44*x**7 + 864*x**6 - 2304*x**5 + 2304*x**4 + (-6*x**13 + 144*x**12 - 1440* x**11 + 7680*x**10 - 23040*x**9 + 36864*x**8 - 24576*x**7)*log(x) + (x**18 - 32*x**17 + 448*x**16 - 3584*x**15 + 17920*x**14 - 57344*x**13 + 114688* x**12 - 131072*x**11 + 65536*x**10)*log(x)**2)
Leaf count of result is larger than twice the leaf count of optimal. 82 vs. \(2 (28) = 56\).
Time = 0.25 (sec) , antiderivative size = 82, normalized size of antiderivative = 2.93 \[ \int \frac {72+\left (72-6 x-384 x^3+192 x^4-24 x^5\right ) \log (x)+\left (-6 x+384 x^3-384 x^4+72 x^5\right ) \log ^2(x)+\left (-64 x^4+48 x^5-4104 x^6+5120 x^7-2304 x^8+448 x^9-32 x^{10}\right ) \log ^3(x)}{-27+\left (432 x^3-216 x^4+27 x^5\right ) \log (x)+\left (-2304 x^6+2304 x^7-864 x^8+144 x^9-9 x^{10}\right ) \log ^2(x)+\left (4096 x^9-6144 x^{10}+3840 x^{11}-1280 x^{12}+240 x^{13}-24 x^{14}+x^{15}\right ) \log ^3(x)} \, dx=\frac {{\left (8 \, x^{6} - 64 \, x^{5} + 128 \, x^{4} + x^{2}\right )} \log \left (x\right )^{2} - 24 \, x \log \left (x\right )}{{\left (x^{10} - 16 \, x^{9} + 96 \, x^{8} - 256 \, x^{7} + 256 \, x^{6}\right )} \log \left (x\right )^{2} - 6 \, {\left (x^{5} - 8 \, x^{4} + 16 \, x^{3}\right )} \log \left (x\right ) + 9} \]
integrate(((-32*x^10+448*x^9-2304*x^8+5120*x^7-4104*x^6+48*x^5-64*x^4)*log (x)^3+(72*x^5-384*x^4+384*x^3-6*x)*log(x)^2+(-24*x^5+192*x^4-384*x^3-6*x+7 2)*log(x)+72)/((x^15-24*x^14+240*x^13-1280*x^12+3840*x^11-6144*x^10+4096*x ^9)*log(x)^3+(-9*x^10+144*x^9-864*x^8+2304*x^7-2304*x^6)*log(x)^2+(27*x^5- 216*x^4+432*x^3)*log(x)-27),x, algorithm=\
((8*x^6 - 64*x^5 + 128*x^4 + x^2)*log(x)^2 - 24*x*log(x))/((x^10 - 16*x^9 + 96*x^8 - 256*x^7 + 256*x^6)*log(x)^2 - 6*(x^5 - 8*x^4 + 16*x^3)*log(x) + 9)
Leaf count of result is larger than twice the leaf count of optimal. 283 vs. \(2 (28) = 56\).
Time = 0.34 (sec) , antiderivative size = 283, normalized size of antiderivative = 10.11 \[ \int \frac {72+\left (72-6 x-384 x^3+192 x^4-24 x^5\right ) \log (x)+\left (-6 x+384 x^3-384 x^4+72 x^5\right ) \log ^2(x)+\left (-64 x^4+48 x^5-4104 x^6+5120 x^7-2304 x^8+448 x^9-32 x^{10}\right ) \log ^3(x)}{-27+\left (432 x^3-216 x^4+27 x^5\right ) \log (x)+\left (-2304 x^6+2304 x^7-864 x^8+144 x^9-9 x^{10}\right ) \log ^2(x)+\left (4096 x^9-6144 x^{10}+3840 x^{11}-1280 x^{12}+240 x^{13}-24 x^{14}+x^{15}\right ) \log ^3(x)} \, dx=\frac {3 \, {\left (8 \, x^{9} \log \left (x\right ) - 128 \, x^{8} \log \left (x\right ) + 768 \, x^{7} \log \left (x\right ) - 2048 \, x^{6} \log \left (x\right ) + 2050 \, x^{5} \log \left (x\right ) - 16 \, x^{4} \log \left (x\right ) - 24 \, x^{4} + 32 \, x^{3} \log \left (x\right ) + 192 \, x^{3} - 384 \, x^{2} - 3\right )}}{x^{18} \log \left (x\right )^{2} - 32 \, x^{17} \log \left (x\right )^{2} + 448 \, x^{16} \log \left (x\right )^{2} - 3584 \, x^{15} \log \left (x\right )^{2} + 17920 \, x^{14} \log \left (x\right )^{2} - 57344 \, x^{13} \log \left (x\right )^{2} - 6 \, x^{13} \log \left (x\right ) + 114688 \, x^{12} \log \left (x\right )^{2} + 144 \, x^{12} \log \left (x\right ) - 131072 \, x^{11} \log \left (x\right )^{2} - 1440 \, x^{11} \log \left (x\right ) + 65536 \, x^{10} \log \left (x\right )^{2} + 7680 \, x^{10} \log \left (x\right ) - 23040 \, x^{9} \log \left (x\right ) + 36864 \, x^{8} \log \left (x\right ) + 9 \, x^{8} - 24576 \, x^{7} \log \left (x\right ) - 144 \, x^{7} + 864 \, x^{6} - 2304 \, x^{5} + 2304 \, x^{4}} - \frac {1029 \, x^{3} - 14406 \, x^{2} + 65872 \, x - 98864}{4096 \, {\left (x^{4} - 16 \, x^{3} + 96 \, x^{2} - 256 \, x + 256\right )}} + \frac {1029 \, x^{3} + 2058 \, x^{2} + 16 \, x + 16}{4096 \, x^{4}} \]
integrate(((-32*x^10+448*x^9-2304*x^8+5120*x^7-4104*x^6+48*x^5-64*x^4)*log (x)^3+(72*x^5-384*x^4+384*x^3-6*x)*log(x)^2+(-24*x^5+192*x^4-384*x^3-6*x+7 2)*log(x)+72)/((x^15-24*x^14+240*x^13-1280*x^12+3840*x^11-6144*x^10+4096*x ^9)*log(x)^3+(-9*x^10+144*x^9-864*x^8+2304*x^7-2304*x^6)*log(x)^2+(27*x^5- 216*x^4+432*x^3)*log(x)-27),x, algorithm=\
3*(8*x^9*log(x) - 128*x^8*log(x) + 768*x^7*log(x) - 2048*x^6*log(x) + 2050 *x^5*log(x) - 16*x^4*log(x) - 24*x^4 + 32*x^3*log(x) + 192*x^3 - 384*x^2 - 3)/(x^18*log(x)^2 - 32*x^17*log(x)^2 + 448*x^16*log(x)^2 - 3584*x^15*log( x)^2 + 17920*x^14*log(x)^2 - 57344*x^13*log(x)^2 - 6*x^13*log(x) + 114688* x^12*log(x)^2 + 144*x^12*log(x) - 131072*x^11*log(x)^2 - 1440*x^11*log(x) + 65536*x^10*log(x)^2 + 7680*x^10*log(x) - 23040*x^9*log(x) + 36864*x^8*lo g(x) + 9*x^8 - 24576*x^7*log(x) - 144*x^7 + 864*x^6 - 2304*x^5 + 2304*x^4) - 1/4096*(1029*x^3 - 14406*x^2 + 65872*x - 98864)/(x^4 - 16*x^3 + 96*x^2 - 256*x + 256) + 1/4096*(1029*x^3 + 2058*x^2 + 16*x + 16)/x^4
Timed out. \[ \int \frac {72+\left (72-6 x-384 x^3+192 x^4-24 x^5\right ) \log (x)+\left (-6 x+384 x^3-384 x^4+72 x^5\right ) \log ^2(x)+\left (-64 x^4+48 x^5-4104 x^6+5120 x^7-2304 x^8+448 x^9-32 x^{10}\right ) \log ^3(x)}{-27+\left (432 x^3-216 x^4+27 x^5\right ) \log (x)+\left (-2304 x^6+2304 x^7-864 x^8+144 x^9-9 x^{10}\right ) \log ^2(x)+\left (4096 x^9-6144 x^{10}+3840 x^{11}-1280 x^{12}+240 x^{13}-24 x^{14}+x^{15}\right ) \log ^3(x)} \, dx=-\int -\frac {\left (32\,x^{10}-448\,x^9+2304\,x^8-5120\,x^7+4104\,x^6-48\,x^5+64\,x^4\right )\,{\ln \left (x\right )}^3+\left (-72\,x^5+384\,x^4-384\,x^3+6\,x\right )\,{\ln \left (x\right )}^2+\left (24\,x^5-192\,x^4+384\,x^3+6\,x-72\right )\,\ln \left (x\right )-72}{\left (-x^{15}+24\,x^{14}-240\,x^{13}+1280\,x^{12}-3840\,x^{11}+6144\,x^{10}-4096\,x^9\right )\,{\ln \left (x\right )}^3+\left (9\,x^{10}-144\,x^9+864\,x^8-2304\,x^7+2304\,x^6\right )\,{\ln \left (x\right )}^2+\left (-27\,x^5+216\,x^4-432\,x^3\right )\,\ln \left (x\right )+27} \,d x \]
int((log(x)*(6*x + 384*x^3 - 192*x^4 + 24*x^5 - 72) + log(x)^2*(6*x - 384* x^3 + 384*x^4 - 72*x^5) + log(x)^3*(64*x^4 - 48*x^5 + 4104*x^6 - 5120*x^7 + 2304*x^8 - 448*x^9 + 32*x^10) - 72)/(log(x)^2*(2304*x^6 - 2304*x^7 + 864 *x^8 - 144*x^9 + 9*x^10) - log(x)^3*(4096*x^9 - 6144*x^10 + 3840*x^11 - 12 80*x^12 + 240*x^13 - 24*x^14 + x^15) - log(x)*(432*x^3 - 216*x^4 + 27*x^5) + 27),x)
-int(-(log(x)*(6*x + 384*x^3 - 192*x^4 + 24*x^5 - 72) + log(x)^2*(6*x - 38 4*x^3 + 384*x^4 - 72*x^5) + log(x)^3*(64*x^4 - 48*x^5 + 4104*x^6 - 5120*x^ 7 + 2304*x^8 - 448*x^9 + 32*x^10) - 72)/(log(x)^2*(2304*x^6 - 2304*x^7 + 8 64*x^8 - 144*x^9 + 9*x^10) - log(x)^3*(4096*x^9 - 6144*x^10 + 3840*x^11 - 1280*x^12 + 240*x^13 - 24*x^14 + x^15) - log(x)*(432*x^3 - 216*x^4 + 27*x^ 5) + 27), x)