Integrand size = 307, antiderivative size = 35 \[ \int \frac {10368-55296 x+110592 x^2-183624 x^3+473408 x^4-852480 x^5+748360 x^6-321920 x^7+172800 x^8-153600 x^9+51200 x^{10}+\left (-53280 x^3+193920 x^4-232960 x^5+113760 x^6-86400 x^7+115200 x^8-51200 x^9\right ) \log (x)+\left (-8280 x^3+17280 x^4-8320 x^5+10800 x^6-28800 x^7+19200 x^8\right ) \log ^2(x)+\left (2400 x^6-3200 x^7\right ) \log ^3(x)+200 x^6 \log ^4(x)}{1296 x-6912 x^2+13824 x^3-15528 x^4+21376 x^5-34560 x^6+32745 x^7-21040 x^8+21600 x^9-19200 x^{10}+6400 x^{11}+\left (-2160 x^4+8640 x^5-11520 x^6+7820 x^7-10800 x^8+14400 x^9-6400 x^{10}\right ) \log (x)+\left (-360 x^4+960 x^5-640 x^6+1350 x^7-3600 x^8+2400 x^9\right ) \log ^2(x)+\left (300 x^7-400 x^8\right ) \log ^3(x)+25 x^7 \log ^4(x)} \, dx=4 \left (\frac {2}{-\frac {4}{5}+x \left (-x+\frac {\log (x)}{4-\frac {3}{x}}\right )^2}+\log \left (x^2\right )\right ) \]
Time = 0.14 (sec) , antiderivative size = 53, normalized size of antiderivative = 1.51 \[ \int \frac {10368-55296 x+110592 x^2-183624 x^3+473408 x^4-852480 x^5+748360 x^6-321920 x^7+172800 x^8-153600 x^9+51200 x^{10}+\left (-53280 x^3+193920 x^4-232960 x^5+113760 x^6-86400 x^7+115200 x^8-51200 x^9\right ) \log (x)+\left (-8280 x^3+17280 x^4-8320 x^5+10800 x^6-28800 x^7+19200 x^8\right ) \log ^2(x)+\left (2400 x^6-3200 x^7\right ) \log ^3(x)+200 x^6 \log ^4(x)}{1296 x-6912 x^2+13824 x^3-15528 x^4+21376 x^5-34560 x^6+32745 x^7-21040 x^8+21600 x^9-19200 x^{10}+6400 x^{11}+\left (-2160 x^4+8640 x^5-11520 x^6+7820 x^7-10800 x^8+14400 x^9-6400 x^{10}\right ) \log (x)+\left (-360 x^4+960 x^5-640 x^6+1350 x^7-3600 x^8+2400 x^9\right ) \log ^2(x)+\left (300 x^7-400 x^8\right ) \log ^3(x)+25 x^7 \log ^4(x)} \, dx=8 \left (\log (x)+\frac {5 (3-4 x)^2}{(3-4 x)^2 \left (-4+5 x^3\right )+10 (3-4 x) x^3 \log (x)+5 x^3 \log ^2(x)}\right ) \]
Integrate[(10368 - 55296*x + 110592*x^2 - 183624*x^3 + 473408*x^4 - 852480 *x^5 + 748360*x^6 - 321920*x^7 + 172800*x^8 - 153600*x^9 + 51200*x^10 + (- 53280*x^3 + 193920*x^4 - 232960*x^5 + 113760*x^6 - 86400*x^7 + 115200*x^8 - 51200*x^9)*Log[x] + (-8280*x^3 + 17280*x^4 - 8320*x^5 + 10800*x^6 - 2880 0*x^7 + 19200*x^8)*Log[x]^2 + (2400*x^6 - 3200*x^7)*Log[x]^3 + 200*x^6*Log [x]^4)/(1296*x - 6912*x^2 + 13824*x^3 - 15528*x^4 + 21376*x^5 - 34560*x^6 + 32745*x^7 - 21040*x^8 + 21600*x^9 - 19200*x^10 + 6400*x^11 + (-2160*x^4 + 8640*x^5 - 11520*x^6 + 7820*x^7 - 10800*x^8 + 14400*x^9 - 6400*x^10)*Log [x] + (-360*x^4 + 960*x^5 - 640*x^6 + 1350*x^7 - 3600*x^8 + 2400*x^9)*Log[ x]^2 + (300*x^7 - 400*x^8)*Log[x]^3 + 25*x^7*Log[x]^4),x]
8*(Log[x] + (5*(3 - 4*x)^2)/((3 - 4*x)^2*(-4 + 5*x^3) + 10*(3 - 4*x)*x^3*L og[x] + 5*x^3*Log[x]^2))
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.
| \(\displaystyle \int \frac {51200 x^{10}-153600 x^9+172800 x^8-321920 x^7+748360 x^6+200 x^6 \log ^4(x)-852480 x^5+473408 x^4-183624 x^3+110592 x^2+\left (2400 x^6-3200 x^7\right ) \log ^3(x)+\left (19200 x^8-28800 x^7+10800 x^6-8320 x^5+17280 x^4-8280 x^3\right ) \log ^2(x)+\left (-51200 x^9+115200 x^8-86400 x^7+113760 x^6-232960 x^5+193920 x^4-53280 x^3\right ) \log (x)-55296 x+10368}{6400 x^{11}-19200 x^{10}+21600 x^9-21040 x^8+32745 x^7+25 x^7 \log ^4(x)-34560 x^6+21376 x^5-15528 x^4+13824 x^3-6912 x^2+\left (300 x^7-400 x^8\right ) \log ^3(x)+\left (2400 x^9-3600 x^8+1350 x^7-640 x^6+960 x^5-360 x^4\right ) \log ^2(x)+\left (-6400 x^{10}+14400 x^9-10800 x^8+7820 x^7-11520 x^6+8640 x^5-2160 x^4\right ) \log (x)+1296 x} \, dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {8 \left (25 x^6 \log ^4(x)-100 (4 x-3) x^6 \log ^3(x)-20 (3-4 x)^2 \left (20 x^4-15 x^3-36 x+37\right ) x^3 \log (x)+(4 x-3)^3 \left (100 x^7-75 x^6-460 x^4+395 x^3+64 x-48\right )+5 \left (480 x^5-720 x^4+270 x^3-208 x^2+432 x-207\right ) x^3 \log ^2(x)\right )}{x \left ((3-4 x)^2 \left (5 x^3-4\right )+5 x^3 \log ^2(x)+10 (3-4 x) x^3 \log (x)\right )^2}dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle 8 \int \frac {25 \log ^4(x) x^6+100 (3-4 x) \log ^3(x) x^6-5 \left (-480 x^5+720 x^4-270 x^3+208 x^2-432 x+207\right ) \log ^2(x) x^3-20 (3-4 x)^2 \left (20 x^4-15 x^3-36 x+37\right ) \log (x) x^3+(3-4 x)^3 \left (-100 x^7+75 x^6+460 x^4-395 x^3-64 x+48\right )}{x \left (-5 \log ^2(x) x^3-10 (3-4 x) \log (x) x^3+(3-4 x)^2 \left (4-5 x^3\right )\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 8 \int \left (-\frac {10 \left (80 x^5-20 \log (x) x^4-80 x^4+5 \log (x) x^3+15 x^3+32 x^2-96 x+54\right ) (4 x-3)^2}{x \left (80 x^5-40 \log (x) x^4-120 x^4+5 \log ^2(x) x^3+30 \log (x) x^3+45 x^3-64 x^2+96 x-36\right )^2}+\frac {1}{x}-\frac {5 \left (16 x^2-48 x+27\right )}{x \left (80 x^5-40 \log (x) x^4-120 x^4+5 \log ^2(x) x^3+30 \log (x) x^3+45 x^3-64 x^2+96 x-36\right )}\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle 8 \left (\log (x)+21600 \int \frac {1}{\left (80 x^5-40 \log (x) x^4-120 x^4+5 \log ^2(x) x^3+30 \log (x) x^3+45 x^3-64 x^2+96 x-36\right )^2}dx-4860 \int \frac {1}{x \left (80 x^5-40 \log (x) x^4-120 x^4+5 \log ^2(x) x^3+30 \log (x) x^3+45 x^3-64 x^2+96 x-36\right )^2}dx-34560 \int \frac {x}{\left (80 x^5-40 \log (x) x^4-120 x^4+5 \log ^2(x) x^3+30 \log (x) x^3+45 x^3-64 x^2+96 x-36\right )^2}dx+21690 \int \frac {x^2}{\left (80 x^5-40 \log (x) x^4-120 x^4+5 \log ^2(x) x^3+30 \log (x) x^3+45 x^3-64 x^2+96 x-36\right )^2}dx+5680 \int \frac {x^3}{\left (80 x^5-40 \log (x) x^4-120 x^4+5 \log ^2(x) x^3+30 \log (x) x^3+45 x^3-64 x^2+96 x-36\right )^2}dx-28800 \int \frac {x^4}{\left (80 x^5-40 \log (x) x^4-120 x^4+5 \log ^2(x) x^3+30 \log (x) x^3+45 x^3-64 x^2+96 x-36\right )^2}dx+32000 \int \frac {x^5}{\left (80 x^5-40 \log (x) x^4-120 x^4+5 \log ^2(x) x^3+30 \log (x) x^3+45 x^3-64 x^2+96 x-36\right )^2}dx-12800 \int \frac {x^6}{\left (80 x^5-40 \log (x) x^4-120 x^4+5 \log ^2(x) x^3+30 \log (x) x^3+45 x^3-64 x^2+96 x-36\right )^2}dx-450 \int \frac {x^2 \log (x)}{\left (80 x^5-40 \log (x) x^4-120 x^4+5 \log ^2(x) x^3+30 \log (x) x^3+45 x^3-64 x^2+96 x-36\right )^2}dx+3000 \int \frac {x^3 \log (x)}{\left (80 x^5-40 \log (x) x^4-120 x^4+5 \log ^2(x) x^3+30 \log (x) x^3+45 x^3-64 x^2+96 x-36\right )^2}dx-5600 \int \frac {x^4 \log (x)}{\left (80 x^5-40 \log (x) x^4-120 x^4+5 \log ^2(x) x^3+30 \log (x) x^3+45 x^3-64 x^2+96 x-36\right )^2}dx+3200 \int \frac {x^5 \log (x)}{\left (80 x^5-40 \log (x) x^4-120 x^4+5 \log ^2(x) x^3+30 \log (x) x^3+45 x^3-64 x^2+96 x-36\right )^2}dx+240 \int \frac {1}{80 x^5-40 \log (x) x^4-120 x^4+5 \log ^2(x) x^3+30 \log (x) x^3+45 x^3-64 x^2+96 x-36}dx-135 \int \frac {1}{x \left (80 x^5-40 \log (x) x^4-120 x^4+5 \log ^2(x) x^3+30 \log (x) x^3+45 x^3-64 x^2+96 x-36\right )}dx-80 \int \frac {x}{80 x^5-40 \log (x) x^4-120 x^4+5 \log ^2(x) x^3+30 \log (x) x^3+45 x^3-64 x^2+96 x-36}dx\right )\) |
Int[(10368 - 55296*x + 110592*x^2 - 183624*x^3 + 473408*x^4 - 852480*x^5 + 748360*x^6 - 321920*x^7 + 172800*x^8 - 153600*x^9 + 51200*x^10 + (-53280* x^3 + 193920*x^4 - 232960*x^5 + 113760*x^6 - 86400*x^7 + 115200*x^8 - 5120 0*x^9)*Log[x] + (-8280*x^3 + 17280*x^4 - 8320*x^5 + 10800*x^6 - 28800*x^7 + 19200*x^8)*Log[x]^2 + (2400*x^6 - 3200*x^7)*Log[x]^3 + 200*x^6*Log[x]^4) /(1296*x - 6912*x^2 + 13824*x^3 - 15528*x^4 + 21376*x^5 - 34560*x^6 + 3274 5*x^7 - 21040*x^8 + 21600*x^9 - 19200*x^10 + 6400*x^11 + (-2160*x^4 + 8640 *x^5 - 11520*x^6 + 7820*x^7 - 10800*x^8 + 14400*x^9 - 6400*x^10)*Log[x] + (-360*x^4 + 960*x^5 - 640*x^6 + 1350*x^7 - 3600*x^8 + 2400*x^9)*Log[x]^2 + (300*x^7 - 400*x^8)*Log[x]^3 + 25*x^7*Log[x]^4),x]
3.3.73.3.1 Defintions of rubi rules used
Int[(a_)*(Fx_), x_Symbol] :> Simp[a Int[Fx, x], x] /; FreeQ[a, x] && !Ma tchQ[Fx, (b_)*(Gx_) /; FreeQ[b, x]]
Int[u_, x_Symbol] :> With[{v = SimplifyIntegrand[u, x]}, Int[v, x] /; Simpl erIntegrandQ[v, u, x]]
Leaf count of result is larger than twice the leaf count of optimal. \(67\) vs. \(2(33)=66\).
Time = 0.82 (sec) , antiderivative size = 68, normalized size of antiderivative = 1.94
| method | result | size |
| default | \(8 \ln \left (x \right )+\frac {640 x^{2}-960 x +360}{5 x^{3} \ln \left (x \right )^{2}-40 x^{4} \ln \left (x \right )+80 x^{5}+30 x^{3} \ln \left (x \right )-120 x^{4}+45 x^{3}-64 x^{2}+96 x -36}\) | \(68\) |
| risch | \(8 \ln \left (x \right )+\frac {640 x^{2}-960 x +360}{5 x^{3} \ln \left (x \right )^{2}-40 x^{4} \ln \left (x \right )+80 x^{5}+30 x^{3} \ln \left (x \right )-120 x^{4}+45 x^{3}-64 x^{2}+96 x -36}\) | \(68\) |
| parallelrisch | \(\frac {10440-27840 x +200 x^{3} \ln \left (x \right )^{3}+3200 x^{5} \ln \left (x \right )-1600 x^{4} \ln \left (x \right )^{2}+4800 x^{4} \ln \left (x \right )+3840 x \ln \left (x \right )-19200 x^{5}-1440 \ln \left (x \right )+28800 x^{4}-10800 x^{3}+18560 x^{2}-5400 x^{3} \ln \left (x \right )-2560 x^{2} \ln \left (x \right )}{25 x^{3} \ln \left (x \right )^{2}-200 x^{4} \ln \left (x \right )+400 x^{5}+150 x^{3} \ln \left (x \right )-600 x^{4}+225 x^{3}-320 x^{2}+480 x -180}\) | \(133\) |
int((200*x^6*ln(x)^4+(-3200*x^7+2400*x^6)*ln(x)^3+(19200*x^8-28800*x^7+108 00*x^6-8320*x^5+17280*x^4-8280*x^3)*ln(x)^2+(-51200*x^9+115200*x^8-86400*x ^7+113760*x^6-232960*x^5+193920*x^4-53280*x^3)*ln(x)+51200*x^10-153600*x^9 +172800*x^8-321920*x^7+748360*x^6-852480*x^5+473408*x^4-183624*x^3+110592* x^2-55296*x+10368)/(25*x^7*ln(x)^4+(-400*x^8+300*x^7)*ln(x)^3+(2400*x^9-36 00*x^8+1350*x^7-640*x^6+960*x^5-360*x^4)*ln(x)^2+(-6400*x^10+14400*x^9-108 00*x^8+7820*x^7-11520*x^6+8640*x^5-2160*x^4)*ln(x)+6400*x^11-19200*x^10+21 600*x^9-21040*x^8+32745*x^7-34560*x^6+21376*x^5-15528*x^4+13824*x^3-6912*x ^2+1296*x),x,method=_RETURNVERBOSE)
8*ln(x)+40*(16*x^2-24*x+9)/(5*x^3*ln(x)^2-40*x^4*ln(x)+80*x^5+30*x^3*ln(x) -120*x^4+45*x^3-64*x^2+96*x-36)
Leaf count of result is larger than twice the leaf count of optimal. 117 vs. \(2 (32) = 64\).
Time = 0.27 (sec) , antiderivative size = 117, normalized size of antiderivative = 3.34 \[ \int \frac {10368-55296 x+110592 x^2-183624 x^3+473408 x^4-852480 x^5+748360 x^6-321920 x^7+172800 x^8-153600 x^9+51200 x^{10}+\left (-53280 x^3+193920 x^4-232960 x^5+113760 x^6-86400 x^7+115200 x^8-51200 x^9\right ) \log (x)+\left (-8280 x^3+17280 x^4-8320 x^5+10800 x^6-28800 x^7+19200 x^8\right ) \log ^2(x)+\left (2400 x^6-3200 x^7\right ) \log ^3(x)+200 x^6 \log ^4(x)}{1296 x-6912 x^2+13824 x^3-15528 x^4+21376 x^5-34560 x^6+32745 x^7-21040 x^8+21600 x^9-19200 x^{10}+6400 x^{11}+\left (-2160 x^4+8640 x^5-11520 x^6+7820 x^7-10800 x^8+14400 x^9-6400 x^{10}\right ) \log (x)+\left (-360 x^4+960 x^5-640 x^6+1350 x^7-3600 x^8+2400 x^9\right ) \log ^2(x)+\left (300 x^7-400 x^8\right ) \log ^3(x)+25 x^7 \log ^4(x)} \, dx=\frac {8 \, {\left (5 \, x^{3} \log \left (x\right )^{3} - 10 \, {\left (4 \, x^{4} - 3 \, x^{3}\right )} \log \left (x\right )^{2} + 80 \, x^{2} + {\left (80 \, x^{5} - 120 \, x^{4} + 45 \, x^{3} - 64 \, x^{2} + 96 \, x - 36\right )} \log \left (x\right ) - 120 \, x + 45\right )}}{80 \, x^{5} + 5 \, x^{3} \log \left (x\right )^{2} - 120 \, x^{4} + 45 \, x^{3} - 64 \, x^{2} - 10 \, {\left (4 \, x^{4} - 3 \, x^{3}\right )} \log \left (x\right ) + 96 \, x - 36} \]
integrate((200*x^6*log(x)^4+(-3200*x^7+2400*x^6)*log(x)^3+(19200*x^8-28800 *x^7+10800*x^6-8320*x^5+17280*x^4-8280*x^3)*log(x)^2+(-51200*x^9+115200*x^ 8-86400*x^7+113760*x^6-232960*x^5+193920*x^4-53280*x^3)*log(x)+51200*x^10- 153600*x^9+172800*x^8-321920*x^7+748360*x^6-852480*x^5+473408*x^4-183624*x ^3+110592*x^2-55296*x+10368)/(25*x^7*log(x)^4+(-400*x^8+300*x^7)*log(x)^3+ (2400*x^9-3600*x^8+1350*x^7-640*x^6+960*x^5-360*x^4)*log(x)^2+(-6400*x^10+ 14400*x^9-10800*x^8+7820*x^7-11520*x^6+8640*x^5-2160*x^4)*log(x)+6400*x^11 -19200*x^10+21600*x^9-21040*x^8+32745*x^7-34560*x^6+21376*x^5-15528*x^4+13 824*x^3-6912*x^2+1296*x),x, algorithm=\
8*(5*x^3*log(x)^3 - 10*(4*x^4 - 3*x^3)*log(x)^2 + 80*x^2 + (80*x^5 - 120*x ^4 + 45*x^3 - 64*x^2 + 96*x - 36)*log(x) - 120*x + 45)/(80*x^5 + 5*x^3*log (x)^2 - 120*x^4 + 45*x^3 - 64*x^2 - 10*(4*x^4 - 3*x^3)*log(x) + 96*x - 36)
Leaf count of result is larger than twice the leaf count of optimal. 63 vs. \(2 (24) = 48\).
Time = 0.26 (sec) , antiderivative size = 63, normalized size of antiderivative = 1.80 \[ \int \frac {10368-55296 x+110592 x^2-183624 x^3+473408 x^4-852480 x^5+748360 x^6-321920 x^7+172800 x^8-153600 x^9+51200 x^{10}+\left (-53280 x^3+193920 x^4-232960 x^5+113760 x^6-86400 x^7+115200 x^8-51200 x^9\right ) \log (x)+\left (-8280 x^3+17280 x^4-8320 x^5+10800 x^6-28800 x^7+19200 x^8\right ) \log ^2(x)+\left (2400 x^6-3200 x^7\right ) \log ^3(x)+200 x^6 \log ^4(x)}{1296 x-6912 x^2+13824 x^3-15528 x^4+21376 x^5-34560 x^6+32745 x^7-21040 x^8+21600 x^9-19200 x^{10}+6400 x^{11}+\left (-2160 x^4+8640 x^5-11520 x^6+7820 x^7-10800 x^8+14400 x^9-6400 x^{10}\right ) \log (x)+\left (-360 x^4+960 x^5-640 x^6+1350 x^7-3600 x^8+2400 x^9\right ) \log ^2(x)+\left (300 x^7-400 x^8\right ) \log ^3(x)+25 x^7 \log ^4(x)} \, dx=\frac {640 x^{2} - 960 x + 360}{80 x^{5} - 120 x^{4} + 5 x^{3} \log {\left (x \right )}^{2} + 45 x^{3} - 64 x^{2} + 96 x + \left (- 40 x^{4} + 30 x^{3}\right ) \log {\left (x \right )} - 36} + 8 \log {\left (x \right )} \]
integrate((200*x**6*ln(x)**4+(-3200*x**7+2400*x**6)*ln(x)**3+(19200*x**8-2 8800*x**7+10800*x**6-8320*x**5+17280*x**4-8280*x**3)*ln(x)**2+(-51200*x**9 +115200*x**8-86400*x**7+113760*x**6-232960*x**5+193920*x**4-53280*x**3)*ln (x)+51200*x**10-153600*x**9+172800*x**8-321920*x**7+748360*x**6-852480*x** 5+473408*x**4-183624*x**3+110592*x**2-55296*x+10368)/(25*x**7*ln(x)**4+(-4 00*x**8+300*x**7)*ln(x)**3+(2400*x**9-3600*x**8+1350*x**7-640*x**6+960*x** 5-360*x**4)*ln(x)**2+(-6400*x**10+14400*x**9-10800*x**8+7820*x**7-11520*x* *6+8640*x**5-2160*x**4)*ln(x)+6400*x**11-19200*x**10+21600*x**9-21040*x**8 +32745*x**7-34560*x**6+21376*x**5-15528*x**4+13824*x**3-6912*x**2+1296*x), x)
(640*x**2 - 960*x + 360)/(80*x**5 - 120*x**4 + 5*x**3*log(x)**2 + 45*x**3 - 64*x**2 + 96*x + (-40*x**4 + 30*x**3)*log(x) - 36) + 8*log(x)
Leaf count of result is larger than twice the leaf count of optimal. 68 vs. \(2 (32) = 64\).
Time = 0.26 (sec) , antiderivative size = 68, normalized size of antiderivative = 1.94 \[ \int \frac {10368-55296 x+110592 x^2-183624 x^3+473408 x^4-852480 x^5+748360 x^6-321920 x^7+172800 x^8-153600 x^9+51200 x^{10}+\left (-53280 x^3+193920 x^4-232960 x^5+113760 x^6-86400 x^7+115200 x^8-51200 x^9\right ) \log (x)+\left (-8280 x^3+17280 x^4-8320 x^5+10800 x^6-28800 x^7+19200 x^8\right ) \log ^2(x)+\left (2400 x^6-3200 x^7\right ) \log ^3(x)+200 x^6 \log ^4(x)}{1296 x-6912 x^2+13824 x^3-15528 x^4+21376 x^5-34560 x^6+32745 x^7-21040 x^8+21600 x^9-19200 x^{10}+6400 x^{11}+\left (-2160 x^4+8640 x^5-11520 x^6+7820 x^7-10800 x^8+14400 x^9-6400 x^{10}\right ) \log (x)+\left (-360 x^4+960 x^5-640 x^6+1350 x^7-3600 x^8+2400 x^9\right ) \log ^2(x)+\left (300 x^7-400 x^8\right ) \log ^3(x)+25 x^7 \log ^4(x)} \, dx=\frac {40 \, {\left (16 \, x^{2} - 24 \, x + 9\right )}}{80 \, x^{5} + 5 \, x^{3} \log \left (x\right )^{2} - 120 \, x^{4} + 45 \, x^{3} - 64 \, x^{2} - 10 \, {\left (4 \, x^{4} - 3 \, x^{3}\right )} \log \left (x\right ) + 96 \, x - 36} + 8 \, \log \left (x\right ) \]
integrate((200*x^6*log(x)^4+(-3200*x^7+2400*x^6)*log(x)^3+(19200*x^8-28800 *x^7+10800*x^6-8320*x^5+17280*x^4-8280*x^3)*log(x)^2+(-51200*x^9+115200*x^ 8-86400*x^7+113760*x^6-232960*x^5+193920*x^4-53280*x^3)*log(x)+51200*x^10- 153600*x^9+172800*x^8-321920*x^7+748360*x^6-852480*x^5+473408*x^4-183624*x ^3+110592*x^2-55296*x+10368)/(25*x^7*log(x)^4+(-400*x^8+300*x^7)*log(x)^3+ (2400*x^9-3600*x^8+1350*x^7-640*x^6+960*x^5-360*x^4)*log(x)^2+(-6400*x^10+ 14400*x^9-10800*x^8+7820*x^7-11520*x^6+8640*x^5-2160*x^4)*log(x)+6400*x^11 -19200*x^10+21600*x^9-21040*x^8+32745*x^7-34560*x^6+21376*x^5-15528*x^4+13 824*x^3-6912*x^2+1296*x),x, algorithm=\
40*(16*x^2 - 24*x + 9)/(80*x^5 + 5*x^3*log(x)^2 - 120*x^4 + 45*x^3 - 64*x^ 2 - 10*(4*x^4 - 3*x^3)*log(x) + 96*x - 36) + 8*log(x)
Leaf count of result is larger than twice the leaf count of optimal. 67 vs. \(2 (32) = 64\).
Time = 0.44 (sec) , antiderivative size = 67, normalized size of antiderivative = 1.91 \[ \int \frac {10368-55296 x+110592 x^2-183624 x^3+473408 x^4-852480 x^5+748360 x^6-321920 x^7+172800 x^8-153600 x^9+51200 x^{10}+\left (-53280 x^3+193920 x^4-232960 x^5+113760 x^6-86400 x^7+115200 x^8-51200 x^9\right ) \log (x)+\left (-8280 x^3+17280 x^4-8320 x^5+10800 x^6-28800 x^7+19200 x^8\right ) \log ^2(x)+\left (2400 x^6-3200 x^7\right ) \log ^3(x)+200 x^6 \log ^4(x)}{1296 x-6912 x^2+13824 x^3-15528 x^4+21376 x^5-34560 x^6+32745 x^7-21040 x^8+21600 x^9-19200 x^{10}+6400 x^{11}+\left (-2160 x^4+8640 x^5-11520 x^6+7820 x^7-10800 x^8+14400 x^9-6400 x^{10}\right ) \log (x)+\left (-360 x^4+960 x^5-640 x^6+1350 x^7-3600 x^8+2400 x^9\right ) \log ^2(x)+\left (300 x^7-400 x^8\right ) \log ^3(x)+25 x^7 \log ^4(x)} \, dx=\frac {40 \, {\left (16 \, x^{2} - 24 \, x + 9\right )}}{80 \, x^{5} - 40 \, x^{4} \log \left (x\right ) + 5 \, x^{3} \log \left (x\right )^{2} - 120 \, x^{4} + 30 \, x^{3} \log \left (x\right ) + 45 \, x^{3} - 64 \, x^{2} + 96 \, x - 36} + 8 \, \log \left (x\right ) \]
integrate((200*x^6*log(x)^4+(-3200*x^7+2400*x^6)*log(x)^3+(19200*x^8-28800 *x^7+10800*x^6-8320*x^5+17280*x^4-8280*x^3)*log(x)^2+(-51200*x^9+115200*x^ 8-86400*x^7+113760*x^6-232960*x^5+193920*x^4-53280*x^3)*log(x)+51200*x^10- 153600*x^9+172800*x^8-321920*x^7+748360*x^6-852480*x^5+473408*x^4-183624*x ^3+110592*x^2-55296*x+10368)/(25*x^7*log(x)^4+(-400*x^8+300*x^7)*log(x)^3+ (2400*x^9-3600*x^8+1350*x^7-640*x^6+960*x^5-360*x^4)*log(x)^2+(-6400*x^10+ 14400*x^9-10800*x^8+7820*x^7-11520*x^6+8640*x^5-2160*x^4)*log(x)+6400*x^11 -19200*x^10+21600*x^9-21040*x^8+32745*x^7-34560*x^6+21376*x^5-15528*x^4+13 824*x^3-6912*x^2+1296*x),x, algorithm=\
40*(16*x^2 - 24*x + 9)/(80*x^5 - 40*x^4*log(x) + 5*x^3*log(x)^2 - 120*x^4 + 30*x^3*log(x) + 45*x^3 - 64*x^2 + 96*x - 36) + 8*log(x)
Timed out. \[ \int \frac {10368-55296 x+110592 x^2-183624 x^3+473408 x^4-852480 x^5+748360 x^6-321920 x^7+172800 x^8-153600 x^9+51200 x^{10}+\left (-53280 x^3+193920 x^4-232960 x^5+113760 x^6-86400 x^7+115200 x^8-51200 x^9\right ) \log (x)+\left (-8280 x^3+17280 x^4-8320 x^5+10800 x^6-28800 x^7+19200 x^8\right ) \log ^2(x)+\left (2400 x^6-3200 x^7\right ) \log ^3(x)+200 x^6 \log ^4(x)}{1296 x-6912 x^2+13824 x^3-15528 x^4+21376 x^5-34560 x^6+32745 x^7-21040 x^8+21600 x^9-19200 x^{10}+6400 x^{11}+\left (-2160 x^4+8640 x^5-11520 x^6+7820 x^7-10800 x^8+14400 x^9-6400 x^{10}\right ) \log (x)+\left (-360 x^4+960 x^5-640 x^6+1350 x^7-3600 x^8+2400 x^9\right ) \log ^2(x)+\left (300 x^7-400 x^8\right ) \log ^3(x)+25 x^7 \log ^4(x)} \, dx=\int \frac {{\ln \left (x\right )}^3\,\left (2400\,x^6-3200\,x^7\right )-\ln \left (x\right )\,\left (51200\,x^9-115200\,x^8+86400\,x^7-113760\,x^6+232960\,x^5-193920\,x^4+53280\,x^3\right )-{\ln \left (x\right )}^2\,\left (-19200\,x^8+28800\,x^7-10800\,x^6+8320\,x^5-17280\,x^4+8280\,x^3\right )-55296\,x+200\,x^6\,{\ln \left (x\right )}^4+110592\,x^2-183624\,x^3+473408\,x^4-852480\,x^5+748360\,x^6-321920\,x^7+172800\,x^8-153600\,x^9+51200\,x^{10}+10368}{1296\,x-\ln \left (x\right )\,\left (6400\,x^{10}-14400\,x^9+10800\,x^8-7820\,x^7+11520\,x^6-8640\,x^5+2160\,x^4\right )-{\ln \left (x\right )}^2\,\left (-2400\,x^9+3600\,x^8-1350\,x^7+640\,x^6-960\,x^5+360\,x^4\right )+{\ln \left (x\right )}^3\,\left (300\,x^7-400\,x^8\right )+25\,x^7\,{\ln \left (x\right )}^4-6912\,x^2+13824\,x^3-15528\,x^4+21376\,x^5-34560\,x^6+32745\,x^7-21040\,x^8+21600\,x^9-19200\,x^{10}+6400\,x^{11}} \,d x \]
int((log(x)^3*(2400*x^6 - 3200*x^7) - log(x)*(53280*x^3 - 193920*x^4 + 232 960*x^5 - 113760*x^6 + 86400*x^7 - 115200*x^8 + 51200*x^9) - log(x)^2*(828 0*x^3 - 17280*x^4 + 8320*x^5 - 10800*x^6 + 28800*x^7 - 19200*x^8) - 55296* x + 200*x^6*log(x)^4 + 110592*x^2 - 183624*x^3 + 473408*x^4 - 852480*x^5 + 748360*x^6 - 321920*x^7 + 172800*x^8 - 153600*x^9 + 51200*x^10 + 10368)/( 1296*x - log(x)*(2160*x^4 - 8640*x^5 + 11520*x^6 - 7820*x^7 + 10800*x^8 - 14400*x^9 + 6400*x^10) - log(x)^2*(360*x^4 - 960*x^5 + 640*x^6 - 1350*x^7 + 3600*x^8 - 2400*x^9) + log(x)^3*(300*x^7 - 400*x^8) + 25*x^7*log(x)^4 - 6912*x^2 + 13824*x^3 - 15528*x^4 + 21376*x^5 - 34560*x^6 + 32745*x^7 - 210 40*x^8 + 21600*x^9 - 19200*x^10 + 6400*x^11),x)
int((log(x)^3*(2400*x^6 - 3200*x^7) - log(x)*(53280*x^3 - 193920*x^4 + 232 960*x^5 - 113760*x^6 + 86400*x^7 - 115200*x^8 + 51200*x^9) - log(x)^2*(828 0*x^3 - 17280*x^4 + 8320*x^5 - 10800*x^6 + 28800*x^7 - 19200*x^8) - 55296* x + 200*x^6*log(x)^4 + 110592*x^2 - 183624*x^3 + 473408*x^4 - 852480*x^5 + 748360*x^6 - 321920*x^7 + 172800*x^8 - 153600*x^9 + 51200*x^10 + 10368)/( 1296*x - log(x)*(2160*x^4 - 8640*x^5 + 11520*x^6 - 7820*x^7 + 10800*x^8 - 14400*x^9 + 6400*x^10) - log(x)^2*(360*x^4 - 960*x^5 + 640*x^6 - 1350*x^7 + 3600*x^8 - 2400*x^9) + log(x)^3*(300*x^7 - 400*x^8) + 25*x^7*log(x)^4 - 6912*x^2 + 13824*x^3 - 15528*x^4 + 21376*x^5 - 34560*x^6 + 32745*x^7 - 210 40*x^8 + 21600*x^9 - 19200*x^10 + 6400*x^11), x)