\(\int \frac {10368-55296 x+110592 x^2-183624 x^3+473408 x^4-852480 x^5+748360 x^6-321920 x^7+172800 x^8-153600 x^9+51200 x^{10}+(-53280 x^3+193920 x^4-232960 x^5+113760 x^6-86400 x^7+115200 x^8-51200 x^9) \log (x)+(-8280 x^3+17280 x^4-8320 x^5+10800 x^6-28800 x^7+19200 x^8) \log ^2(x)+(2400 x^6-3200 x^7) \log ^3(x)+200 x^6 \log ^4(x)}{1296 x-6912 x^2+13824 x^3-15528 x^4+21376 x^5-34560 x^6+32745 x^7-21040 x^8+21600 x^9-19200 x^{10}+6400 x^{11}+(-2160 x^4+8640 x^5-11520 x^6+7820 x^7-10800 x^8+14400 x^9-6400 x^{10}) \log (x)+(-360 x^4+960 x^5-640 x^6+1350 x^7-3600 x^8+2400 x^9) \log ^2(x)+(300 x^7-400 x^8) \log ^3(x)+25 x^7 \log ^4(x)} \, dx\) [6273]

Optimal result

Integrand size = 307, antiderivative size = 35 \[ \int \frac {10368-55296 x+110592 x^2-183624 x^3+473408 x^4-852480 x^5+748360 x^6-321920 x^7+172800 x^8-153600 x^9+51200 x^{10}+\left (-53280 x^3+193920 x^4-232960 x^5+113760 x^6-86400 x^7+115200 x^8-51200 x^9\right ) \log (x)+\left (-8280 x^3+17280 x^4-8320 x^5+10800 x^6-28800 x^7+19200 x^8\right ) \log ^2(x)+\left (2400 x^6-3200 x^7\right ) \log ^3(x)+200 x^6 \log ^4(x)}{1296 x-6912 x^2+13824 x^3-15528 x^4+21376 x^5-34560 x^6+32745 x^7-21040 x^8+21600 x^9-19200 x^{10}+6400 x^{11}+\left (-2160 x^4+8640 x^5-11520 x^6+7820 x^7-10800 x^8+14400 x^9-6400 x^{10}\right ) \log (x)+\left (-360 x^4+960 x^5-640 x^6+1350 x^7-3600 x^8+2400 x^9\right ) \log ^2(x)+\left (300 x^7-400 x^8\right ) \log ^3(x)+25 x^7 \log ^4(x)} \, dx=4 \left (\frac {2}{-\frac {4}{5}+x \left (-x+\frac {\log (x)}{4-\frac {3}{x}}\right )^2}+\log \left (x^2\right )\right ) \]

[Out]

4*ln(x^2)+8/(x*(ln(x)/(4-3/x)-x)^2-4/5)

Rubi [F]

\[ \int \frac {10368-55296 x+110592 x^2-183624 x^3+473408 x^4-852480 x^5+748360 x^6-321920 x^7+172800 x^8-153600 x^9+51200 x^{10}+\left (-53280 x^3+193920 x^4-232960 x^5+113760 x^6-86400 x^7+115200 x^8-51200 x^9\right ) \log (x)+\left (-8280 x^3+17280 x^4-8320 x^5+10800 x^6-28800 x^7+19200 x^8\right ) \log ^2(x)+\left (2400 x^6-3200 x^7\right ) \log ^3(x)+200 x^6 \log ^4(x)}{1296 x-6912 x^2+13824 x^3-15528 x^4+21376 x^5-34560 x^6+32745 x^7-21040 x^8+21600 x^9-19200 x^{10}+6400 x^{11}+\left (-2160 x^4+8640 x^5-11520 x^6+7820 x^7-10800 x^8+14400 x^9-6400 x^{10}\right ) \log (x)+\left (-360 x^4+960 x^5-640 x^6+1350 x^7-3600 x^8+2400 x^9\right ) \log ^2(x)+\left (300 x^7-400 x^8\right ) \log ^3(x)+25 x^7 \log ^4(x)} \, dx=\int \frac {10368-55296 x+110592 x^2-183624 x^3+473408 x^4-852480 x^5+748360 x^6-321920 x^7+172800 x^8-153600 x^9+51200 x^{10}+\left (-53280 x^3+193920 x^4-232960 x^5+113760 x^6-86400 x^7+115200 x^8-51200 x^9\right ) \log (x)+\left (-8280 x^3+17280 x^4-8320 x^5+10800 x^6-28800 x^7+19200 x^8\right ) \log ^2(x)+\left (2400 x^6-3200 x^7\right ) \log ^3(x)+200 x^6 \log ^4(x)}{1296 x-6912 x^2+13824 x^3-15528 x^4+21376 x^5-34560 x^6+32745 x^7-21040 x^8+21600 x^9-19200 x^{10}+6400 x^{11}+\left (-2160 x^4+8640 x^5-11520 x^6+7820 x^7-10800 x^8+14400 x^9-6400 x^{10}\right ) \log (x)+\left (-360 x^4+960 x^5-640 x^6+1350 x^7-3600 x^8+2400 x^9\right ) \log ^2(x)+\left (300 x^7-400 x^8\right ) \log ^3(x)+25 x^7 \log ^4(x)} \, dx \]

[In]

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 - 51
200*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 +
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 - 10
800*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]

[Out]

8*Log[x] + 172800*Defer[Int][(-36 + 96*x - 64*x^2 + 45*x^3 - 120*x^4 + 80*x^5 + 30*x^3*Log[x] - 40*x^4*Log[x]
+ 5*x^3*Log[x]^2)^(-2), x] - 38880*Defer[Int][1/(x*(-36 + 96*x - 64*x^2 + 45*x^3 - 120*x^4 + 80*x^5 + 30*x^3*L
og[x] - 40*x^4*Log[x] + 5*x^3*Log[x]^2)^2), x] - 276480*Defer[Int][x/(-36 + 96*x - 64*x^2 + 45*x^3 - 120*x^4 +
80*x^5 + 30*x^3*Log[x] - 40*x^4*Log[x] + 5*x^3*Log[x]^2)^2, x] + 173520*Defer[Int][x^2/(-36 + 96*x - 64*x^2 +
45*x^3 - 120*x^4 + 80*x^5 + 30*x^3*Log[x] - 40*x^4*Log[x] + 5*x^3*Log[x]^2)^2, x] + 45440*Defer[Int][x^3/(-36
+ 96*x - 64*x^2 + 45*x^3 - 120*x^4 + 80*x^5 + 30*x^3*Log[x] - 40*x^4*Log[x] + 5*x^3*Log[x]^2)^2, x] - 230400*
Defer[Int][x^4/(-36 + 96*x - 64*x^2 + 45*x^3 - 120*x^4 + 80*x^5 + 30*x^3*Log[x] - 40*x^4*Log[x] + 5*x^3*Log[x]
^2)^2, x] + 256000*Defer[Int][x^5/(-36 + 96*x - 64*x^2 + 45*x^3 - 120*x^4 + 80*x^5 + 30*x^3*Log[x] - 40*x^4*Lo
g[x] + 5*x^3*Log[x]^2)^2, x] - 102400*Defer[Int][x^6/(-36 + 96*x - 64*x^2 + 45*x^3 - 120*x^4 + 80*x^5 + 30*x^3
*Log[x] - 40*x^4*Log[x] + 5*x^3*Log[x]^2)^2, x] - 3600*Defer[Int][(x^2*Log[x])/(-36 + 96*x - 64*x^2 + 45*x^3 -
120*x^4 + 80*x^5 + 30*x^3*Log[x] - 40*x^4*Log[x] + 5*x^3*Log[x]^2)^2, x] + 24000*Defer[Int][(x^3*Log[x])/(-36
+ 96*x - 64*x^2 + 45*x^3 - 120*x^4 + 80*x^5 + 30*x^3*Log[x] - 40*x^4*Log[x] + 5*x^3*Log[x]^2)^2, x] - 44800*D
efer[Int][(x^4*Log[x])/(-36 + 96*x - 64*x^2 + 45*x^3 - 120*x^4 + 80*x^5 + 30*x^3*Log[x] - 40*x^4*Log[x] + 5*x^
3*Log[x]^2)^2, x] + 25600*Defer[Int][(x^5*Log[x])/(-36 + 96*x - 64*x^2 + 45*x^3 - 120*x^4 + 80*x^5 + 30*x^3*Lo
g[x] - 40*x^4*Log[x] + 5*x^3*Log[x]^2)^2, x] + 1920*Defer[Int][(-36 + 96*x - 64*x^2 + 45*x^3 - 120*x^4 + 80*x^
5 + 30*x^3*Log[x] - 40*x^4*Log[x] + 5*x^3*Log[x]^2)^(-1), x] - 640*Defer[Int][x/(-36 + 96*x - 64*x^2 + 45*x^3
- 120*x^4 + 80*x^5 + 30*x^3*Log[x] - 40*x^4*Log[x] + 5*x^3*Log[x]^2), x] - 1080*Defer[Int][((3 - 4*x)^2*x*(-4
+ 5*x^3) + 10*(3 - 4*x)*x^4*Log[x] + 5*x^4*Log[x]^2)^(-1), x]

Rubi steps \begin{align*} \text {integral}& = \int \frac {8 \left ((-3+4 x)^3 \left (-48+64 x+395 x^3-460 x^4-75 x^6+100 x^7\right )-20 (3-4 x)^2 x^3 \left (37-36 x-15 x^3+20 x^4\right ) \log (x)+5 x^3 \left (-207+432 x-208 x^2+270 x^3-720 x^4+480 x^5\right ) \log ^2(x)-100 x^6 (-3+4 x) \log ^3(x)+25 x^6 \log ^4(x)\right )}{x \left ((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 )^2} \, dx \\ & = 8 \int \frac {(-3+4 x)^3 \left (-48+64 x+395 x^3-460 x^4-75 x^6+100 x^7\right )-20 (3-4 x)^2 x^3 \left (37-36 x-15 x^3+20 x^4\right ) \log (x)+5 x^3 \left (-207+432 x-208 x^2+270 x^3-720 x^4+480 x^5\right ) \log ^2(x)-100 x^6 (-3+4 x) \log ^3(x)+25 x^6 \log ^4(x)}{x \left ((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 )^2} \, dx \\ & = 8 \int \left (\frac {1}{x}-\frac {10 (-3+4 x)^2 \left (54-96 x+32 x^2+15 x^3-80 x^4+80 x^5+5 x^3 \log (x)-20 x^4 \log (x)\right )}{x \left (-36+96 x-64 x^2+45 x^3-120 x^4+80 x^5+30 x^3 \log (x)-40 x^4 \log (x)+5 x^3 \log ^2(x)\right )^2}-\frac {5 \left (27-48 x+16 x^2\right )}{x \left (-36+96 x-64 x^2+45 x^3-120 x^4+80 x^5+30 x^3 \log (x)-40 x^4 \log (x)+5 x^3 \log ^2(x)\right )}\right ) \, dx \\ & = 8 \log (x)-40 \int \frac {27-48 x+16 x^2}{x \left (-36+96 x-64 x^2+45 x^3-120 x^4+80 x^5+30 x^3 \log (x)-40 x^4 \log (x)+5 x^3 \log ^2(x)\right )} \, dx-80 \int \frac {(-3+4 x)^2 \left (54-96 x+32 x^2+15 x^3-80 x^4+80 x^5+5 x^3 \log (x)-20 x^4 \log (x)\right )}{x \left (-36+96 x-64 x^2+45 x^3-120 x^4+80 x^5+30 x^3 \log (x)-40 x^4 \log (x)+5 x^3 \log ^2(x)\right )^2} \, dx \\ & = 8 \log (x)-40 \int \frac {27-48 x+16 x^2}{(3-4 x)^2 x \left (-4+5 x^3\right )+10 (3-4 x) x^4 \log (x)+5 x^4 \log ^2(x)} \, dx-80 \int \left (-\frac {24 \left (54-96 x+32 x^2+15 x^3-80 x^4+80 x^5+5 x^3 \log (x)-20 x^4 \log (x)\right )}{\left (-36+96 x-64 x^2+45 x^3-120 x^4+80 x^5+30 x^3 \log (x)-40 x^4 \log (x)+5 x^3 \log ^2(x)\right )^2}+\frac {9 \left (54-96 x+32 x^2+15 x^3-80 x^4+80 x^5+5 x^3 \log (x)-20 x^4 \log (x)\right )}{x \left (-36+96 x-64 x^2+45 x^3-120 x^4+80 x^5+30 x^3 \log (x)-40 x^4 \log (x)+5 x^3 \log ^2(x)\right )^2}+\frac {16 x \left (54-96 x+32 x^2+15 x^3-80 x^4+80 x^5+5 x^3 \log (x)-20 x^4 \log (x)\right )}{\left (-36+96 x-64 x^2+45 x^3-120 x^4+80 x^5+30 x^3 \log (x)-40 x^4 \log (x)+5 x^3 \log ^2(x)\right )^2}\right ) \, dx \\ & = 8 \log (x)-40 \int \left (-\frac {48}{-36+96 x-64 x^2+45 x^3-120 x^4+80 x^5+30 x^3 \log (x)-40 x^4 \log (x)+5 x^3 \log ^2(x)}+\frac {27}{x \left (-36+96 x-64 x^2+45 x^3-120 x^4+80 x^5+30 x^3 \log (x)-40 x^4 \log (x)+5 x^3 \log ^2(x)\right )}+\frac {16 x}{-36+96 x-64 x^2+45 x^3-120 x^4+80 x^5+30 x^3 \log (x)-40 x^4 \log (x)+5 x^3 \log ^2(x)}\right ) \, dx-720 \int \frac {54-96 x+32 x^2+15 x^3-80 x^4+80 x^5+5 x^3 \log (x)-20 x^4 \log (x)}{x \left (-36+96 x-64 x^2+45 x^3-120 x^4+80 x^5+30 x^3 \log (x)-40 x^4 \log (x)+5 x^3 \log ^2(x)\right )^2} \, dx-1280 \int \frac {x \left (54-96 x+32 x^2+15 x^3-80 x^4+80 x^5+5 x^3 \log (x)-20 x^4 \log (x)\right )}{\left (-36+96 x-64 x^2+45 x^3-120 x^4+80 x^5+30 x^3 \log (x)-40 x^4 \log (x)+5 x^3 \log ^2(x)\right )^2} \, dx+1920 \int \frac {54-96 x+32 x^2+15 x^3-80 x^4+80 x^5+5 x^3 \log (x)-20 x^4 \log (x)}{\left (-36+96 x-64 x^2+45 x^3-120 x^4+80 x^5+30 x^3 \log (x)-40 x^4 \log (x)+5 x^3 \log ^2(x)\right )^2} \, dx \\ & = \text {Too large to display} \\ \end{align*}

Mathematica [A] (verified)

Time = 0.14 (sec) , antiderivative size = 53, normalized size of antiderivative = 1.51 \[ \int \frac {10368-55296 x+110592 x^2-183624 x^3+473408 x^4-852480 x^5+748360 x^6-321920 x^7+172800 x^8-153600 x^9+51200 x^{10}+\left (-53280 x^3+193920 x^4-232960 x^5+113760 x^6-86400 x^7+115200 x^8-51200 x^9\right ) \log (x)+\left (-8280 x^3+17280 x^4-8320 x^5+10800 x^6-28800 x^7+19200 x^8\right ) \log ^2(x)+\left (2400 x^6-3200 x^7\right ) \log ^3(x)+200 x^6 \log ^4(x)}{1296 x-6912 x^2+13824 x^3-15528 x^4+21376 x^5-34560 x^6+32745 x^7-21040 x^8+21600 x^9-19200 x^{10}+6400 x^{11}+\left (-2160 x^4+8640 x^5-11520 x^6+7820 x^7-10800 x^8+14400 x^9-6400 x^{10}\right ) \log (x)+\left (-360 x^4+960 x^5-640 x^6+1350 x^7-3600 x^8+2400 x^9\right ) \log ^2(x)+\left (300 x^7-400 x^8\right ) \log ^3(x)+25 x^7 \log ^4(x)} \, dx=8 \left (\log (x)+\frac {5 (3-4 x)^2}{(3-4 x)^2 \left (-4+5 x^3\right )+10 (3-4 x) x^3 \log (x)+5 x^3 \log ^2(x)}\right ) \]

[In]

Integrate[(10368 - 55296*x + 110592*x^2 - 183624*x^3 + 473408*x^4 - 852480*x^5 + 748360*x^6 - 321920*x^7 + 172
800*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 - 28800*x^7 + 19200*x^8)*Log[x]^2 + (240
0*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]

[Out]

8*(Log[x] + (5*(3 - 4*x)^2)/((3 - 4*x)^2*(-4 + 5*x^3) + 10*(3 - 4*x)*x^3*Log[x] + 5*x^3*Log[x]^2))

Maple [B] (verified)

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	\(\frac {10440-27840 x +200 x^{3} \ln \left (x \right )^{3}+3200 x^{5} \ln \left (x \right )-1600 x^{4} \ln \left (x \right )^{2}+4800 x^{4} \ln \left (x \right )+3840 x \ln \left (x \right )-19200 x^{5}-1440 \ln \left (x \right )+28800 x^{4}-10800 x^{3}+18560 x^{2}-5400 x^{3} \ln \left (x \right )-2560 x^{2} \ln \left (x \right )}{25 x^{3} \ln \left (x \right )^{2}-200 x^{4} \ln \left (x \right )+400 x^{5}+150 x^{3} \ln \left (x \right )-600 x^{4}+225 x^{3}-320 x^{2}+480 x -180}\)	\(133\)

[In]

int((200*x^6*ln(x)^4+(-3200*x^7+2400*x^6)*ln(x)^3+(19200*x^8-28800*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
+(-400*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^7-3456
0*x^6+21376*x^5-15528*x^4+13824*x^3-6912*x^2+1296*x),x,method=_RETURNVERBOSE)

[Out]

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)

Fricas [B] (verification not implemented)

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 \[ \int \frac {10368-55296 x+110592 x^2-183624 x^3+473408 x^4-852480 x^5+748360 x^6-321920 x^7+172800 x^8-153600 x^9+51200 x^{10}+\left (-53280 x^3+193920 x^4-232960 x^5+113760 x^6-86400 x^7+115200 x^8-51200 x^9\right ) \log (x)+\left (-8280 x^3+17280 x^4-8320 x^5+10800 x^6-28800 x^7+19200 x^8\right ) \log ^2(x)+\left (2400 x^6-3200 x^7\right ) \log ^3(x)+200 x^6 \log ^4(x)}{1296 x-6912 x^2+13824 x^3-15528 x^4+21376 x^5-34560 x^6+32745 x^7-21040 x^8+21600 x^9-19200 x^{10}+6400 x^{11}+\left (-2160 x^4+8640 x^5-11520 x^6+7820 x^7-10800 x^8+14400 x^9-6400 x^{10}\right ) \log (x)+\left (-360 x^4+960 x^5-640 x^6+1350 x^7-3600 x^8+2400 x^9\right ) \log ^2(x)+\left (300 x^7-400 x^8\right ) \log ^3(x)+25 x^7 \log ^4(x)} \, dx=\frac {8 \, {\left (5 \, x^{3} \log \left (x\right )^{3} - 10 \, {\left (4 \, x^{4} - 3 \, x^{3}\right )} \log \left (x\right )^{2} + 80 \, x^{2} + {\left (80 \, x^{5} - 120 \, x^{4} + 45 \, x^{3} - 64 \, x^{2} + 96 \, x - 36\right )} \log \left (x\right ) - 120 \, x + 45\right )}}{80 \, x^{5} + 5 \, x^{3} \log \left (x\right )^{2} - 120 \, x^{4} + 45 \, x^{3} - 64 \, x^{2} - 10 \, {\left (4 \, x^{4} - 3 \, x^{3}\right )} \log \left (x\right ) + 96 \, x - 36} \]

[In]

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^4-82
80*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^1
0-153600*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+13824*x^3-6912*x^2+1296*x),x, algorithm="fricas")

[Out]

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)*lo
g(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 - 3
6)

Sympy [B] (verification not implemented)

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 \[ \int \frac {10368-55296 x+110592 x^2-183624 x^3+473408 x^4-852480 x^5+748360 x^6-321920 x^7+172800 x^8-153600 x^9+51200 x^{10}+\left (-53280 x^3+193920 x^4-232960 x^5+113760 x^6-86400 x^7+115200 x^8-51200 x^9\right ) \log (x)+\left (-8280 x^3+17280 x^4-8320 x^5+10800 x^6-28800 x^7+19200 x^8\right ) \log ^2(x)+\left (2400 x^6-3200 x^7\right ) \log ^3(x)+200 x^6 \log ^4(x)}{1296 x-6912 x^2+13824 x^3-15528 x^4+21376 x^5-34560 x^6+32745 x^7-21040 x^8+21600 x^9-19200 x^{10}+6400 x^{11}+\left (-2160 x^4+8640 x^5-11520 x^6+7820 x^7-10800 x^8+14400 x^9-6400 x^{10}\right ) \log (x)+\left (-360 x^4+960 x^5-640 x^6+1350 x^7-3600 x^8+2400 x^9\right ) \log ^2(x)+\left (300 x^7-400 x^8\right ) \log ^3(x)+25 x^7 \log ^4(x)} \, dx=\frac {640 x^{2} - 960 x + 360}{80 x^{5} - 120 x^{4} + 5 x^{3} \log {\left (x \right )}^{2} + 45 x^{3} - 64 x^{2} + 96 x + \left (- 40 x^{4} + 30 x^{3}\right ) \log {\left (x \right )} - 36} + 8 \log {\left (x \right )} \]

[In]

integrate((200*x**6*ln(x)**4+(-3200*x**7+2400*x**6)*ln(x)**3+(19200*x**8-28800*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+(-400*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)+64
00*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+12
96*x),x)

[Out]

(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)

Maxima [B] (verification not implemented)

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 \[ \int \frac {10368-55296 x+110592 x^2-183624 x^3+473408 x^4-852480 x^5+748360 x^6-321920 x^7+172800 x^8-153600 x^9+51200 x^{10}+\left (-53280 x^3+193920 x^4-232960 x^5+113760 x^6-86400 x^7+115200 x^8-51200 x^9\right ) \log (x)+\left (-8280 x^3+17280 x^4-8320 x^5+10800 x^6-28800 x^7+19200 x^8\right ) \log ^2(x)+\left (2400 x^6-3200 x^7\right ) \log ^3(x)+200 x^6 \log ^4(x)}{1296 x-6912 x^2+13824 x^3-15528 x^4+21376 x^5-34560 x^6+32745 x^7-21040 x^8+21600 x^9-19200 x^{10}+6400 x^{11}+\left (-2160 x^4+8640 x^5-11520 x^6+7820 x^7-10800 x^8+14400 x^9-6400 x^{10}\right ) \log (x)+\left (-360 x^4+960 x^5-640 x^6+1350 x^7-3600 x^8+2400 x^9\right ) \log ^2(x)+\left (300 x^7-400 x^8\right ) \log ^3(x)+25 x^7 \log ^4(x)} \, dx=\frac {40 \, {\left (16 \, x^{2} - 24 \, x + 9\right )}}{80 \, x^{5} + 5 \, x^{3} \log \left (x\right )^{2} - 120 \, x^{4} + 45 \, x^{3} - 64 \, x^{2} - 10 \, {\left (4 \, x^{4} - 3 \, x^{3}\right )} \log \left (x\right ) + 96 \, x - 36} + 8 \, \log \left (x\right ) \]

[In]

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^4-82
80*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^1
0-153600*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+13824*x^3-6912*x^2+1296*x),x, algorithm="maxima")

[Out]

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)

Giac [B] (verification not implemented)

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 \[ \int \frac {10368-55296 x+110592 x^2-183624 x^3+473408 x^4-852480 x^5+748360 x^6-321920 x^7+172800 x^8-153600 x^9+51200 x^{10}+\left (-53280 x^3+193920 x^4-232960 x^5+113760 x^6-86400 x^7+115200 x^8-51200 x^9\right ) \log (x)+\left (-8280 x^3+17280 x^4-8320 x^5+10800 x^6-28800 x^7+19200 x^8\right ) \log ^2(x)+\left (2400 x^6-3200 x^7\right ) \log ^3(x)+200 x^6 \log ^4(x)}{1296 x-6912 x^2+13824 x^3-15528 x^4+21376 x^5-34560 x^6+32745 x^7-21040 x^8+21600 x^9-19200 x^{10}+6400 x^{11}+\left (-2160 x^4+8640 x^5-11520 x^6+7820 x^7-10800 x^8+14400 x^9-6400 x^{10}\right ) \log (x)+\left (-360 x^4+960 x^5-640 x^6+1350 x^7-3600 x^8+2400 x^9\right ) \log ^2(x)+\left (300 x^7-400 x^8\right ) \log ^3(x)+25 x^7 \log ^4(x)} \, dx=\frac {40 \, {\left (16 \, x^{2} - 24 \, x + 9\right )}}{80 \, x^{5} - 40 \, x^{4} \log \left (x\right ) + 5 \, x^{3} \log \left (x\right )^{2} - 120 \, x^{4} + 30 \, x^{3} \log \left (x\right ) + 45 \, x^{3} - 64 \, x^{2} + 96 \, x - 36} + 8 \, \log \left (x\right ) \]

[In]

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^4-82
80*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^1
0-153600*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+13824*x^3-6912*x^2+1296*x),x, algorithm="giac")

[Out]

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)

Mupad [F(-1)]

Timed out. \[ \int \frac {10368-55296 x+110592 x^2-183624 x^3+473408 x^4-852480 x^5+748360 x^6-321920 x^7+172800 x^8-153600 x^9+51200 x^{10}+\left (-53280 x^3+193920 x^4-232960 x^5+113760 x^6-86400 x^7+115200 x^8-51200 x^9\right ) \log (x)+\left (-8280 x^3+17280 x^4-8320 x^5+10800 x^6-28800 x^7+19200 x^8\right ) \log ^2(x)+\left (2400 x^6-3200 x^7\right ) \log ^3(x)+200 x^6 \log ^4(x)}{1296 x-6912 x^2+13824 x^3-15528 x^4+21376 x^5-34560 x^6+32745 x^7-21040 x^8+21600 x^9-19200 x^{10}+6400 x^{11}+\left (-2160 x^4+8640 x^5-11520 x^6+7820 x^7-10800 x^8+14400 x^9-6400 x^{10}\right ) \log (x)+\left (-360 x^4+960 x^5-640 x^6+1350 x^7-3600 x^8+2400 x^9\right ) \log ^2(x)+\left (300 x^7-400 x^8\right ) \log ^3(x)+25 x^7 \log ^4(x)} \, dx=\int \frac {{\ln \left (x\right )}^3\,\left (2400\,x^6-3200\,x^7\right )-\ln \left (x\right )\,\left (51200\,x^9-115200\,x^8+86400\,x^7-113760\,x^6+232960\,x^5-193920\,x^4+53280\,x^3\right )-{\ln \left (x\right )}^2\,\left (-19200\,x^8+28800\,x^7-10800\,x^6+8320\,x^5-17280\,x^4+8280\,x^3\right )-55296\,x+200\,x^6\,{\ln \left (x\right )}^4+110592\,x^2-183624\,x^3+473408\,x^4-852480\,x^5+748360\,x^6-321920\,x^7+172800\,x^8-153600\,x^9+51200\,x^{10}+10368}{1296\,x-\ln \left (x\right )\,\left (6400\,x^{10}-14400\,x^9+10800\,x^8-7820\,x^7+11520\,x^6-8640\,x^5+2160\,x^4\right )-{\ln \left (x\right )}^2\,\left (-2400\,x^9+3600\,x^8-1350\,x^7+640\,x^6-960\,x^5+360\,x^4\right )+{\ln \left (x\right )}^3\,\left (300\,x^7-400\,x^8\right )+25\,x^7\,{\ln \left (x\right )}^4-6912\,x^2+13824\,x^3-15528\,x^4+21376\,x^5-34560\,x^6+32745\,x^7-21040\,x^8+21600\,x^9-19200\,x^{10}+6400\,x^{11}} \,d x \]

[In]

int((log(x)^3*(2400*x^6 - 3200*x^7) - log(x)*(53280*x^3 - 193920*x^4 + 232960*x^5 - 113760*x^6 + 86400*x^7 - 1
15200*x^8 + 51200*x^9) - log(x)^2*(8280*x^3 - 17280*x^4 + 8320*x^5 - 10800*x^6 + 28800*x^7 - 19200*x^8) - 5529
6*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
- 21040*x^8 + 21600*x^9 - 19200*x^10 + 6400*x^11),x)

[Out]

int((log(x)^3*(2400*x^6 - 3200*x^7) - log(x)*(53280*x^3 - 193920*x^4 + 232960*x^5 - 113760*x^6 + 86400*x^7 - 1
15200*x^8 + 51200*x^9) - log(x)^2*(8280*x^3 - 17280*x^4 + 8320*x^5 - 10800*x^6 + 28800*x^7 - 19200*x^8) - 5529
6*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
- 21040*x^8 + 21600*x^9 - 19200*x^10 + 6400*x^11), x)