Integrand size = 1012, antiderivative size = 26 \[ \text {the integral} =\left (1+\frac {e^{10}}{\log \left (1+9 (-4+x)^4\right ) (x+\log (x))}\right )^4 \]
Leaf count is larger than twice the leaf count of optimal. \(132\) vs. \(2(26)=52\).
Time = 0.22 (sec) , antiderivative size = 132, normalized size of antiderivative = 5.08 \[ \text {the integral} =\frac {e^{10} \left (e^{30}+4 e^{20} (x+\log (x)) \log \left (2305-2304 x+864 x^2-144 x^3+9 x^4\right )+6 e^{10} (x+\log (x))^2 \log ^2\left (2305-2304 x+864 x^2-144 x^3+9 x^4\right )+4 (x+\log (x))^3 \log ^3\left (2305-2304 x+864 x^2-144 x^3+9 x^4\right )\right )}{(x+\log (x))^4 \log ^4\left (2305-2304 x+864 x^2-144 x^3+9 x^4\right )} \]
Integrate[(E^40*(9216*x^2 - 6912*x^3 + 1728*x^4 - 144*x^5) + E^40*(9216*x - 6912*x^2 + 1728*x^3 - 144*x^4)*Log[x] + (E^40*(-9220 - 4*x + 5760*x^2 - 2880*x^3 + 540*x^4 - 36*x^5) + E^30*(27648*x^3 - 20736*x^4 + 5184*x^5 - 43 2*x^6) + E^30*(55296*x^2 - 41472*x^3 + 10368*x^4 - 864*x^5)*Log[x] + E^30* (27648*x - 20736*x^2 + 5184*x^3 - 432*x^4)*Log[x]^2)*Log[2305 - 2304*x + 8 64*x^2 - 144*x^3 + 9*x^4] + (E^30*(-27660*x - 12*x^2 + 17280*x^3 - 8640*x^ 4 + 1620*x^5 - 108*x^6) + E^20*(27648*x^4 - 20736*x^5 + 5184*x^6 - 432*x^7 ) + (E^30*(-27660 - 12*x + 17280*x^2 - 8640*x^3 + 1620*x^4 - 108*x^5) + E^ 20*(82944*x^3 - 62208*x^4 + 15552*x^5 - 1296*x^6))*Log[x] + E^20*(82944*x^ 2 - 62208*x^3 + 15552*x^4 - 1296*x^5)*Log[x]^2 + E^20*(27648*x - 20736*x^2 + 5184*x^3 - 432*x^4)*Log[x]^3)*Log[2305 - 2304*x + 864*x^2 - 144*x^3 + 9 *x^4]^2 + (E^20*(-27660*x^2 - 12*x^3 + 17280*x^4 - 8640*x^5 + 1620*x^6 - 1 08*x^7) + E^10*(9216*x^5 - 6912*x^6 + 1728*x^7 - 144*x^8) + (E^20*(-55320* x - 24*x^2 + 34560*x^3 - 17280*x^4 + 3240*x^5 - 216*x^6) + E^10*(36864*x^4 - 27648*x^5 + 6912*x^6 - 576*x^7))*Log[x] + (E^20*(-27660 - 12*x + 17280* x^2 - 8640*x^3 + 1620*x^4 - 108*x^5) + E^10*(55296*x^3 - 41472*x^4 + 10368 *x^5 - 864*x^6))*Log[x]^2 + E^10*(36864*x^2 - 27648*x^3 + 6912*x^4 - 576*x ^5)*Log[x]^3 + E^10*(9216*x - 6912*x^2 + 1728*x^3 - 144*x^4)*Log[x]^4)*Log [2305 - 2304*x + 864*x^2 - 144*x^3 + 9*x^4]^3 + (E^10*(-9220*x^3 - 4*x^4 + 5760*x^5 - 2880*x^6 + 540*x^7 - 36*x^8) + E^10*(-27660*x^2 - 12*x^3 + 172 80*x^4 - 8640*x^5 + 1620*x^6 - 108*x^7)*Log[x] + E^10*(-27660*x - 12*x^2 + 17280*x^3 - 8640*x^4 + 1620*x^5 - 108*x^6)*Log[x]^2 + E^10*(-9220 - 4*x + 5760*x^2 - 2880*x^3 + 540*x^4 - 36*x^5)*Log[x]^3)*Log[2305 - 2304*x + 864 *x^2 - 144*x^3 + 9*x^4]^4)/((2305*x^6 - 2304*x^7 + 864*x^8 - 144*x^9 + 9*x ^10 + (11525*x^5 - 11520*x^6 + 4320*x^7 - 720*x^8 + 45*x^9)*Log[x] + (2305 0*x^4 - 23040*x^5 + 8640*x^6 - 1440*x^7 + 90*x^8)*Log[x]^2 + (23050*x^3 - 23040*x^4 + 8640*x^5 - 1440*x^6 + 90*x^7)*Log[x]^3 + (11525*x^2 - 11520*x^ 3 + 4320*x^4 - 720*x^5 + 45*x^6)*Log[x]^4 + (2305*x - 2304*x^2 + 864*x^3 - 144*x^4 + 9*x^5)*Log[x]^5)*Log[2305 - 2304*x + 864*x^2 - 144*x^3 + 9*x^4] ^5),x]
(E^10*(E^30 + 4*E^20*(x + Log[x])*Log[2305 - 2304*x + 864*x^2 - 144*x^3 + 9*x^4] + 6*E^10*(x + Log[x])^2*Log[2305 - 2304*x + 864*x^2 - 144*x^3 + 9*x ^4]^2 + 4*(x + Log[x])^3*Log[2305 - 2304*x + 864*x^2 - 144*x^3 + 9*x^4]^3) )/((x + Log[x])^4*Log[2305 - 2304*x + 864*x^2 - 144*x^3 + 9*x^4]^4)
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 (e^{10} \left (-36 x^5+540 x^4-2880 x^3+5760 x^2-4 x-9220\right ) \log ^3(x)+e^{10} \left (-108 x^6+1620 x^5-8640 x^4+17280 x^3-12 x^2-27660 x\right ) \log ^2(x)+e^{10} \left (-108 x^7+1620 x^6-8640 x^5+17280 x^4-12 x^3-27660 x^2\right ) \log (x)+e^{10} \left (-36 x^8+540 x^7-2880 x^6+5760 x^5-4 x^4-9220 x^3\right )\right ) \log ^4\left (9 x^4-144 x^3+864 x^2-2304 x+2305\right )+\left (e^{10} \left (-144 x^4+1728 x^3-6912 x^2+9216 x\right ) \log ^4(x)+e^{10} \left (-576 x^5+6912 x^4-27648 x^3+36864 x^2\right ) \log ^3(x)+\left (e^{20} \left (-108 x^5+1620 x^4-8640 x^3+17280 x^2-12 x-27660\right )+e^{10} \left (-864 x^6+10368 x^5-41472 x^4+55296 x^3\right )\right ) \log ^2(x)+\left (e^{20} \left (-216 x^6+3240 x^5-17280 x^4+34560 x^3-24 x^2-55320 x\right )+e^{10} \left (-576 x^7+6912 x^6-27648 x^5+36864 x^4\right )\right ) \log (x)+e^{20} \left (-108 x^7+1620 x^6-8640 x^5+17280 x^4-12 x^3-27660 x^2\right )+e^{10} \left (-144 x^8+1728 x^7-6912 x^6+9216 x^5\right )\right ) \log ^3\left (9 x^4-144 x^3+864 x^2-2304 x+2305\right )+\left (e^{20} \left (-432 x^4+5184 x^3-20736 x^2+27648 x\right ) \log ^3(x)+e^{20} \left (-1296 x^5+15552 x^4-62208 x^3+82944 x^2\right ) \log ^2(x)+\left (e^{30} \left (-108 x^5+1620 x^4-8640 x^3+17280 x^2-12 x-27660\right )+e^{20} \left (-1296 x^6+15552 x^5-62208 x^4+82944 x^3\right )\right ) \log (x)+e^{30} \left (-108 x^6+1620 x^5-8640 x^4+17280 x^3-12 x^2-27660 x\right )+e^{20} \left (-432 x^7+5184 x^6-20736 x^5+27648 x^4\right )\right ) \log ^2\left (9 x^4-144 x^3+864 x^2-2304 x+2305\right )+\left (e^{30} \left (-432 x^4+5184 x^3-20736 x^2+27648 x\right ) \log ^2(x)+e^{30} \left (-864 x^5+10368 x^4-41472 x^3+55296 x^2\right ) \log (x)+e^{40} \left (-36 x^5+540 x^4-2880 x^3+5760 x^2-4 x-9220\right )+e^{30} \left (-432 x^6+5184 x^5-20736 x^4+27648 x^3\right )\right ) \log \left (9 x^4-144 x^3+864 x^2-2304 x+2305\right )+e^{40} \left (-144 x^5+1728 x^4-6912 x^3+9216 x^2\right )+e^{40} \left (-144 x^4+1728 x^3-6912 x^2+9216 x\right ) \log (x)}{\left (9 x^{10}-144 x^9+864 x^8-2304 x^7+2305 x^6+\left (9 x^5-144 x^4+864 x^3-2304 x^2+2305 x\right ) \log ^5(x)+\left (45 x^6-720 x^5+4320 x^4-11520 x^3+11525 x^2\right ) \log ^4(x)+\left (90 x^7-1440 x^6+8640 x^5-23040 x^4+23050 x^3\right ) \log ^3(x)+\left (90 x^8-1440 x^7+8640 x^6-23040 x^5+23050 x^4\right ) \log ^2(x)+\left (45 x^9-720 x^8+4320 x^7-11520 x^6+11525 x^5\right ) \log (x)\right ) \log ^5\left (9 x^4-144 x^3+864 x^2-2304 x+2305\right )} \, dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {4 e^{10} \left (-36 x^2 (x-4)^3-\left (9 x^5-135 x^4+720 x^3-1440 x^2+x+2305\right ) \log \left (9 x^4-144 x^3+864 x^2-2304 x+2305\right )-36 x (x-4)^3 \log (x)\right ) \left ((x+\log (x)) \log \left (9 x^4-144 x^3+864 x^2-2304 x+2305\right )+e^{10}\right )^3}{x \left (9 x^4-144 x^3+864 x^2-2304 x+2305\right ) (x+\log (x))^5 \log ^5\left (9 x^4-144 x^3+864 x^2-2304 x+2305\right )}dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle 4 e^{10} \int \frac {\left (36 x^2 (4-x)^3+36 x \log (x) (4-x)^3-\left (9 x^5-135 x^4+720 x^3-1440 x^2+x+2305\right ) \log \left (9 x^4-144 x^3+864 x^2-2304 x+2305\right )\right ) \left ((x+\log (x)) \log \left (9 x^4-144 x^3+864 x^2-2304 x+2305\right )+e^{10}\right )^3}{x \left (9 x^4-144 x^3+864 x^2-2304 x+2305\right ) (x+\log (x))^5 \log ^5\left (9 x^4-144 x^3+864 x^2-2304 x+2305\right )}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 4 e^{10} \int \left (-\frac {36 e^{30} (x-4)^3}{\left (9 x^4-144 x^3+864 x^2-2304 x+2305\right ) (x+\log (x))^4 \log ^5\left (9 x^4-144 x^3+864 x^2-2304 x+2305\right )}+\frac {-x-1}{x (x+\log (x))^2 \log \left (9 x^4-144 x^3+864 x^2-2304 x+2305\right )}+\frac {3 \left (-12 x^6-24 \log (x) x^5+144 \left (1-\frac {e^{10}}{16}\right ) x^5-12 \log ^2(x) x^4+288 \log (x) x^4-576 \left (1-\frac {15 e^{10}}{64}\right ) x^4+144 \log ^2(x) x^3-1152 \log (x) x^3+768 \left (1-\frac {15 e^{10}}{16}\right ) x^3-576 \log ^2(x) x^2+1536 \log (x) x^2+1440 e^{10} x^2+768 \log ^2(x) x-e^{10} x-2305 e^{10}\right )}{x \left (9 x^4-144 x^3+864 x^2-2304 x+2305\right ) (x+\log (x))^3 \log ^2\left (9 x^4-144 x^3+864 x^2-2304 x+2305\right )}+\frac {3 e^{10} \left (-36 x^6-72 \log (x) x^5+432 \left (1-\frac {e^{10}}{48}\right ) x^5-36 \log ^2(x) x^4+864 \log (x) x^4-1728 \left (1-\frac {5 e^{10}}{64}\right ) x^4+432 \log ^2(x) x^3-3456 \log (x) x^3+2304 \left (1-\frac {5 e^{10}}{16}\right ) x^3-1728 \log ^2(x) x^2+4608 \log (x) x^2+1440 e^{10} x^2+2304 \log ^2(x) x-e^{10} x-2305 e^{10}\right )}{x \left (9 x^4-144 x^3+864 x^2-2304 x+2305\right ) (x+\log (x))^4 \log ^3\left (9 x^4-144 x^3+864 x^2-2304 x+2305\right )}+\frac {e^{20} \left (-108 x^6-216 \log (x) x^5+1296 \left (1-\frac {e^{10}}{144}\right ) x^5-108 \log ^2(x) x^4+2592 \log (x) x^4-5184 \left (1-\frac {5 e^{10}}{192}\right ) x^4+1296 \log ^2(x) x^3-10368 \log (x) x^3+6912 \left (1-\frac {5 e^{10}}{48}\right ) x^3-5184 \log ^2(x) x^2+13824 \log (x) x^2+1440 e^{10} x^2+6912 \log ^2(x) x-e^{10} x-2305 e^{10}\right )}{x \left (9 x^4-144 x^3+864 x^2-2304 x+2305\right ) (x+\log (x))^5 \log ^4\left (9 x^4-144 x^3+864 x^2-2304 x+2305\right )}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 4 e^{10} \int \frac {\left (-36 x^2 (x-4)^3-36 x \log (x) (x-4)^3-\left (9 x^5-135 x^4+720 x^3-1440 x^2+x+2305\right ) \log \left (9 x^4-144 x^3+864 x^2-2304 x+2305\right )\right ) \left ((x+\log (x)) \log \left (9 x^4-144 x^3+864 x^2-2304 x+2305\right )+e^{10}\right )^3}{x \left (9 x^4-144 x^3+864 x^2-2304 x+2305\right ) (x+\log (x))^5 \log ^5\left (9 x^4-144 x^3+864 x^2-2304 x+2305\right )}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 4 e^{10} \int \left (-\frac {36 e^{30} (x-4)^3}{\left (9 x^4-144 x^3+864 x^2-2304 x+2305\right ) (x+\log (x))^4 \log ^5\left (9 x^4-144 x^3+864 x^2-2304 x+2305\right )}+\frac {-x-1}{x (x+\log (x))^2 \log \left (9 x^4-144 x^3+864 x^2-2304 x+2305\right )}+\frac {3 \left (-12 x^6-24 \log (x) x^5+144 \left (1-\frac {e^{10}}{16}\right ) x^5-12 \log ^2(x) x^4+288 \log (x) x^4-576 \left (1-\frac {15 e^{10}}{64}\right ) x^4+144 \log ^2(x) x^3-1152 \log (x) x^3+768 \left (1-\frac {15 e^{10}}{16}\right ) x^3-576 \log ^2(x) x^2+1536 \log (x) x^2+1440 e^{10} x^2+768 \log ^2(x) x-e^{10} x-2305 e^{10}\right )}{x \left (9 x^4-144 x^3+864 x^2-2304 x+2305\right ) (x+\log (x))^3 \log ^2\left (9 x^4-144 x^3+864 x^2-2304 x+2305\right )}+\frac {3 e^{10} \left (-36 x^6-72 \log (x) x^5+432 \left (1-\frac {e^{10}}{48}\right ) x^5-36 \log ^2(x) x^4+864 \log (x) x^4-1728 \left (1-\frac {5 e^{10}}{64}\right ) x^4+432 \log ^2(x) x^3-3456 \log (x) x^3+2304 \left (1-\frac {5 e^{10}}{16}\right ) x^3-1728 \log ^2(x) x^2+4608 \log (x) x^2+1440 e^{10} x^2+2304 \log ^2(x) x-e^{10} x-2305 e^{10}\right )}{x \left (9 x^4-144 x^3+864 x^2-2304 x+2305\right ) (x+\log (x))^4 \log ^3\left (9 x^4-144 x^3+864 x^2-2304 x+2305\right )}+\frac {e^{20} \left (-108 x^6-216 \log (x) x^5+1296 \left (1-\frac {e^{10}}{144}\right ) x^5-108 \log ^2(x) x^4+2592 \log (x) x^4-5184 \left (1-\frac {5 e^{10}}{192}\right ) x^4+1296 \log ^2(x) x^3-10368 \log (x) x^3+6912 \left (1-\frac {5 e^{10}}{48}\right ) x^3-5184 \log ^2(x) x^2+13824 \log (x) x^2+1440 e^{10} x^2+6912 \log ^2(x) x-e^{10} x-2305 e^{10}\right )}{x \left (9 x^4-144 x^3+864 x^2-2304 x+2305\right ) (x+\log (x))^5 \log ^4\left (9 x^4-144 x^3+864 x^2-2304 x+2305\right )}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 4 e^{10} \int \frac {\left (-36 x^2 (x-4)^3-36 x \log (x) (x-4)^3-\left (9 x^5-135 x^4+720 x^3-1440 x^2+x+2305\right ) \log \left (9 x^4-144 x^3+864 x^2-2304 x+2305\right )\right ) \left ((x+\log (x)) \log \left (9 x^4-144 x^3+864 x^2-2304 x+2305\right )+e^{10}\right )^3}{x \left (9 x^4-144 x^3+864 x^2-2304 x+2305\right ) (x+\log (x))^5 \log ^5\left (9 x^4-144 x^3+864 x^2-2304 x+2305\right )}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 4 e^{10} \int \left (-\frac {36 e^{30} (x-4)^3}{\left (9 x^4-144 x^3+864 x^2-2304 x+2305\right ) (x+\log (x))^4 \log ^5\left (9 x^4-144 x^3+864 x^2-2304 x+2305\right )}+\frac {-x-1}{x (x+\log (x))^2 \log \left (9 x^4-144 x^3+864 x^2-2304 x+2305\right )}+\frac {3 \left (-12 x^6-24 \log (x) x^5+144 \left (1-\frac {e^{10}}{16}\right ) x^5-12 \log ^2(x) x^4+288 \log (x) x^4-576 \left (1-\frac {15 e^{10}}{64}\right ) x^4+144 \log ^2(x) x^3-1152 \log (x) x^3+768 \left (1-\frac {15 e^{10}}{16}\right ) x^3-576 \log ^2(x) x^2+1536 \log (x) x^2+1440 e^{10} x^2+768 \log ^2(x) x-e^{10} x-2305 e^{10}\right )}{x \left (9 x^4-144 x^3+864 x^2-2304 x+2305\right ) (x+\log (x))^3 \log ^2\left (9 x^4-144 x^3+864 x^2-2304 x+2305\right )}+\frac {3 e^{10} \left (-36 x^6-72 \log (x) x^5+432 \left (1-\frac {e^{10}}{48}\right ) x^5-36 \log ^2(x) x^4+864 \log (x) x^4-1728 \left (1-\frac {5 e^{10}}{64}\right ) x^4+432 \log ^2(x) x^3-3456 \log (x) x^3+2304 \left (1-\frac {5 e^{10}}{16}\right ) x^3-1728 \log ^2(x) x^2+4608 \log (x) x^2+1440 e^{10} x^2+2304 \log ^2(x) x-e^{10} x-2305 e^{10}\right )}{x \left (9 x^4-144 x^3+864 x^2-2304 x+2305\right ) (x+\log (x))^4 \log ^3\left (9 x^4-144 x^3+864 x^2-2304 x+2305\right )}+\frac {e^{20} \left (-108 x^6-216 \log (x) x^5+1296 \left (1-\frac {e^{10}}{144}\right ) x^5-108 \log ^2(x) x^4+2592 \log (x) x^4-5184 \left (1-\frac {5 e^{10}}{192}\right ) x^4+1296 \log ^2(x) x^3-10368 \log (x) x^3+6912 \left (1-\frac {5 e^{10}}{48}\right ) x^3-5184 \log ^2(x) x^2+13824 \log (x) x^2+1440 e^{10} x^2+6912 \log ^2(x) x-e^{10} x-2305 e^{10}\right )}{x \left (9 x^4-144 x^3+864 x^2-2304 x+2305\right ) (x+\log (x))^5 \log ^4\left (9 x^4-144 x^3+864 x^2-2304 x+2305\right )}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 4 e^{10} \int \frac {\left (-36 x^2 (x-4)^3-36 x \log (x) (x-4)^3-\left (9 x^5-135 x^4+720 x^3-1440 x^2+x+2305\right ) \log \left (9 x^4-144 x^3+864 x^2-2304 x+2305\right )\right ) \left ((x+\log (x)) \log \left (9 x^4-144 x^3+864 x^2-2304 x+2305\right )+e^{10}\right )^3}{x \left (9 x^4-144 x^3+864 x^2-2304 x+2305\right ) (x+\log (x))^5 \log ^5\left (9 x^4-144 x^3+864 x^2-2304 x+2305\right )}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 4 e^{10} \int \left (-\frac {36 e^{30} (x-4)^3}{\left (9 x^4-144 x^3+864 x^2-2304 x+2305\right ) (x+\log (x))^4 \log ^5\left (9 x^4-144 x^3+864 x^2-2304 x+2305\right )}+\frac {-x-1}{x (x+\log (x))^2 \log \left (9 x^4-144 x^3+864 x^2-2304 x+2305\right )}+\frac {3 \left (-12 x^6-24 \log (x) x^5+144 \left (1-\frac {e^{10}}{16}\right ) x^5-12 \log ^2(x) x^4+288 \log (x) x^4-576 \left (1-\frac {15 e^{10}}{64}\right ) x^4+144 \log ^2(x) x^3-1152 \log (x) x^3+768 \left (1-\frac {15 e^{10}}{16}\right ) x^3-576 \log ^2(x) x^2+1536 \log (x) x^2+1440 e^{10} x^2+768 \log ^2(x) x-e^{10} x-2305 e^{10}\right )}{x \left (9 x^4-144 x^3+864 x^2-2304 x+2305\right ) (x+\log (x))^3 \log ^2\left (9 x^4-144 x^3+864 x^2-2304 x+2305\right )}+\frac {3 e^{10} \left (-36 x^6-72 \log (x) x^5+432 \left (1-\frac {e^{10}}{48}\right ) x^5-36 \log ^2(x) x^4+864 \log (x) x^4-1728 \left (1-\frac {5 e^{10}}{64}\right ) x^4+432 \log ^2(x) x^3-3456 \log (x) x^3+2304 \left (1-\frac {5 e^{10}}{16}\right ) x^3-1728 \log ^2(x) x^2+4608 \log (x) x^2+1440 e^{10} x^2+2304 \log ^2(x) x-e^{10} x-2305 e^{10}\right )}{x \left (9 x^4-144 x^3+864 x^2-2304 x+2305\right ) (x+\log (x))^4 \log ^3\left (9 x^4-144 x^3+864 x^2-2304 x+2305\right )}+\frac {e^{20} \left (-108 x^6-216 \log (x) x^5+1296 \left (1-\frac {e^{10}}{144}\right ) x^5-108 \log ^2(x) x^4+2592 \log (x) x^4-5184 \left (1-\frac {5 e^{10}}{192}\right ) x^4+1296 \log ^2(x) x^3-10368 \log (x) x^3+6912 \left (1-\frac {5 e^{10}}{48}\right ) x^3-5184 \log ^2(x) x^2+13824 \log (x) x^2+1440 e^{10} x^2+6912 \log ^2(x) x-e^{10} x-2305 e^{10}\right )}{x \left (9 x^4-144 x^3+864 x^2-2304 x+2305\right ) (x+\log (x))^5 \log ^4\left (9 x^4-144 x^3+864 x^2-2304 x+2305\right )}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 4 e^{10} \int \frac {\left (-36 x^2 (x-4)^3-36 x \log (x) (x-4)^3-\left (9 x^5-135 x^4+720 x^3-1440 x^2+x+2305\right ) \log \left (9 x^4-144 x^3+864 x^2-2304 x+2305\right )\right ) \left ((x+\log (x)) \log \left (9 x^4-144 x^3+864 x^2-2304 x+2305\right )+e^{10}\right )^3}{x \left (9 x^4-144 x^3+864 x^2-2304 x+2305\right ) (x+\log (x))^5 \log ^5\left (9 x^4-144 x^3+864 x^2-2304 x+2305\right )}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 4 e^{10} \int \left (-\frac {36 e^{30} (x-4)^3}{\left (9 x^4-144 x^3+864 x^2-2304 x+2305\right ) (x+\log (x))^4 \log ^5\left (9 x^4-144 x^3+864 x^2-2304 x+2305\right )}+\frac {-x-1}{x (x+\log (x))^2 \log \left (9 x^4-144 x^3+864 x^2-2304 x+2305\right )}+\frac {3 \left (-12 x^6-24 \log (x) x^5+144 \left (1-\frac {e^{10}}{16}\right ) x^5-12 \log ^2(x) x^4+288 \log (x) x^4-576 \left (1-\frac {15 e^{10}}{64}\right ) x^4+144 \log ^2(x) x^3-1152 \log (x) x^3+768 \left (1-\frac {15 e^{10}}{16}\right ) x^3-576 \log ^2(x) x^2+1536 \log (x) x^2+1440 e^{10} x^2+768 \log ^2(x) x-e^{10} x-2305 e^{10}\right )}{x \left (9 x^4-144 x^3+864 x^2-2304 x+2305\right ) (x+\log (x))^3 \log ^2\left (9 x^4-144 x^3+864 x^2-2304 x+2305\right )}+\frac {3 e^{10} \left (-36 x^6-72 \log (x) x^5+432 \left (1-\frac {e^{10}}{48}\right ) x^5-36 \log ^2(x) x^4+864 \log (x) x^4-1728 \left (1-\frac {5 e^{10}}{64}\right ) x^4+432 \log ^2(x) x^3-3456 \log (x) x^3+2304 \left (1-\frac {5 e^{10}}{16}\right ) x^3-1728 \log ^2(x) x^2+4608 \log (x) x^2+1440 e^{10} x^2+2304 \log ^2(x) x-e^{10} x-2305 e^{10}\right )}{x \left (9 x^4-144 x^3+864 x^2-2304 x+2305\right ) (x+\log (x))^4 \log ^3\left (9 x^4-144 x^3+864 x^2-2304 x+2305\right )}+\frac {e^{20} \left (-108 x^6-216 \log (x) x^5+1296 \left (1-\frac {e^{10}}{144}\right ) x^5-108 \log ^2(x) x^4+2592 \log (x) x^4-5184 \left (1-\frac {5 e^{10}}{192}\right ) x^4+1296 \log ^2(x) x^3-10368 \log (x) x^3+6912 \left (1-\frac {5 e^{10}}{48}\right ) x^3-5184 \log ^2(x) x^2+13824 \log (x) x^2+1440 e^{10} x^2+6912 \log ^2(x) x-e^{10} x-2305 e^{10}\right )}{x \left (9 x^4-144 x^3+864 x^2-2304 x+2305\right ) (x+\log (x))^5 \log ^4\left (9 x^4-144 x^3+864 x^2-2304 x+2305\right )}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 4 e^{10} \int \frac {\left (-36 x^2 (x-4)^3-36 x \log (x) (x-4)^3-\left (9 x^5-135 x^4+720 x^3-1440 x^2+x+2305\right ) \log \left (9 x^4-144 x^3+864 x^2-2304 x+2305\right )\right ) \left ((x+\log (x)) \log \left (9 x^4-144 x^3+864 x^2-2304 x+2305\right )+e^{10}\right )^3}{x \left (9 x^4-144 x^3+864 x^2-2304 x+2305\right ) (x+\log (x))^5 \log ^5\left (9 x^4-144 x^3+864 x^2-2304 x+2305\right )}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 4 e^{10} \int \left (-\frac {36 e^{30} (x-4)^3}{\left (9 x^4-144 x^3+864 x^2-2304 x+2305\right ) (x+\log (x))^4 \log ^5\left (9 x^4-144 x^3+864 x^2-2304 x+2305\right )}+\frac {-x-1}{x (x+\log (x))^2 \log \left (9 x^4-144 x^3+864 x^2-2304 x+2305\right )}+\frac {3 \left (-12 x^6-24 \log (x) x^5+144 \left (1-\frac {e^{10}}{16}\right ) x^5-12 \log ^2(x) x^4+288 \log (x) x^4-576 \left (1-\frac {15 e^{10}}{64}\right ) x^4+144 \log ^2(x) x^3-1152 \log (x) x^3+768 \left (1-\frac {15 e^{10}}{16}\right ) x^3-576 \log ^2(x) x^2+1536 \log (x) x^2+1440 e^{10} x^2+768 \log ^2(x) x-e^{10} x-2305 e^{10}\right )}{x \left (9 x^4-144 x^3+864 x^2-2304 x+2305\right ) (x+\log (x))^3 \log ^2\left (9 x^4-144 x^3+864 x^2-2304 x+2305\right )}+\frac {3 e^{10} \left (-36 x^6-72 \log (x) x^5+432 \left (1-\frac {e^{10}}{48}\right ) x^5-36 \log ^2(x) x^4+864 \log (x) x^4-1728 \left (1-\frac {5 e^{10}}{64}\right ) x^4+432 \log ^2(x) x^3-3456 \log (x) x^3+2304 \left (1-\frac {5 e^{10}}{16}\right ) x^3-1728 \log ^2(x) x^2+4608 \log (x) x^2+1440 e^{10} x^2+2304 \log ^2(x) x-e^{10} x-2305 e^{10}\right )}{x \left (9 x^4-144 x^3+864 x^2-2304 x+2305\right ) (x+\log (x))^4 \log ^3\left (9 x^4-144 x^3+864 x^2-2304 x+2305\right )}+\frac {e^{20} \left (-108 x^6-216 \log (x) x^5+1296 \left (1-\frac {e^{10}}{144}\right ) x^5-108 \log ^2(x) x^4+2592 \log (x) x^4-5184 \left (1-\frac {5 e^{10}}{192}\right ) x^4+1296 \log ^2(x) x^3-10368 \log (x) x^3+6912 \left (1-\frac {5 e^{10}}{48}\right ) x^3-5184 \log ^2(x) x^2+13824 \log (x) x^2+1440 e^{10} x^2+6912 \log ^2(x) x-e^{10} x-2305 e^{10}\right )}{x \left (9 x^4-144 x^3+864 x^2-2304 x+2305\right ) (x+\log (x))^5 \log ^4\left (9 x^4-144 x^3+864 x^2-2304 x+2305\right )}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 4 e^{10} \int \frac {\left (-36 x^2 (x-4)^3-36 x \log (x) (x-4)^3-\left (9 x^5-135 x^4+720 x^3-1440 x^2+x+2305\right ) \log \left (9 x^4-144 x^3+864 x^2-2304 x+2305\right )\right ) \left ((x+\log (x)) \log \left (9 x^4-144 x^3+864 x^2-2304 x+2305\right )+e^{10}\right )^3}{x \left (9 x^4-144 x^3+864 x^2-2304 x+2305\right ) (x+\log (x))^5 \log ^5\left (9 x^4-144 x^3+864 x^2-2304 x+2305\right )}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 4 e^{10} \int \left (-\frac {36 e^{30} (x-4)^3}{\left (9 x^4-144 x^3+864 x^2-2304 x+2305\right ) (x+\log (x))^4 \log ^5\left (9 x^4-144 x^3+864 x^2-2304 x+2305\right )}+\frac {-x-1}{x (x+\log (x))^2 \log \left (9 x^4-144 x^3+864 x^2-2304 x+2305\right )}+\frac {3 \left (-12 x^6-24 \log (x) x^5+144 \left (1-\frac {e^{10}}{16}\right ) x^5-12 \log ^2(x) x^4+288 \log (x) x^4-576 \left (1-\frac {15 e^{10}}{64}\right ) x^4+144 \log ^2(x) x^3-1152 \log (x) x^3+768 \left (1-\frac {15 e^{10}}{16}\right ) x^3-576 \log ^2(x) x^2+1536 \log (x) x^2+1440 e^{10} x^2+768 \log ^2(x) x-e^{10} x-2305 e^{10}\right )}{x \left (9 x^4-144 x^3+864 x^2-2304 x+2305\right ) (x+\log (x))^3 \log ^2\left (9 x^4-144 x^3+864 x^2-2304 x+2305\right )}+\frac {3 e^{10} \left (-36 x^6-72 \log (x) x^5+432 \left (1-\frac {e^{10}}{48}\right ) x^5-36 \log ^2(x) x^4+864 \log (x) x^4-1728 \left (1-\frac {5 e^{10}}{64}\right ) x^4+432 \log ^2(x) x^3-3456 \log (x) x^3+2304 \left (1-\frac {5 e^{10}}{16}\right ) x^3-1728 \log ^2(x) x^2+4608 \log (x) x^2+1440 e^{10} x^2+2304 \log ^2(x) x-e^{10} x-2305 e^{10}\right )}{x \left (9 x^4-144 x^3+864 x^2-2304 x+2305\right ) (x+\log (x))^4 \log ^3\left (9 x^4-144 x^3+864 x^2-2304 x+2305\right )}+\frac {e^{20} \left (-108 x^6-216 \log (x) x^5+1296 \left (1-\frac {e^{10}}{144}\right ) x^5-108 \log ^2(x) x^4+2592 \log (x) x^4-5184 \left (1-\frac {5 e^{10}}{192}\right ) x^4+1296 \log ^2(x) x^3-10368 \log (x) x^3+6912 \left (1-\frac {5 e^{10}}{48}\right ) x^3-5184 \log ^2(x) x^2+13824 \log (x) x^2+1440 e^{10} x^2+6912 \log ^2(x) x-e^{10} x-2305 e^{10}\right )}{x \left (9 x^4-144 x^3+864 x^2-2304 x+2305\right ) (x+\log (x))^5 \log ^4\left (9 x^4-144 x^3+864 x^2-2304 x+2305\right )}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 4 e^{10} \int \frac {\left (-36 x^2 (x-4)^3-36 x \log (x) (x-4)^3-\left (9 x^5-135 x^4+720 x^3-1440 x^2+x+2305\right ) \log \left (9 x^4-144 x^3+864 x^2-2304 x+2305\right )\right ) \left ((x+\log (x)) \log \left (9 x^4-144 x^3+864 x^2-2304 x+2305\right )+e^{10}\right )^3}{x \left (9 x^4-144 x^3+864 x^2-2304 x+2305\right ) (x+\log (x))^5 \log ^5\left (9 x^4-144 x^3+864 x^2-2304 x+2305\right )}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 4 e^{10} \int \left (-\frac {36 e^{30} (x-4)^3}{\left (9 x^4-144 x^3+864 x^2-2304 x+2305\right ) (x+\log (x))^4 \log ^5\left (9 x^4-144 x^3+864 x^2-2304 x+2305\right )}+\frac {-x-1}{x (x+\log (x))^2 \log \left (9 x^4-144 x^3+864 x^2-2304 x+2305\right )}+\frac {3 \left (-12 x^6-24 \log (x) x^5+144 \left (1-\frac {e^{10}}{16}\right ) x^5-12 \log ^2(x) x^4+288 \log (x) x^4-576 \left (1-\frac {15 e^{10}}{64}\right ) x^4+144 \log ^2(x) x^3-1152 \log (x) x^3+768 \left (1-\frac {15 e^{10}}{16}\right ) x^3-576 \log ^2(x) x^2+1536 \log (x) x^2+1440 e^{10} x^2+768 \log ^2(x) x-e^{10} x-2305 e^{10}\right )}{x \left (9 x^4-144 x^3+864 x^2-2304 x+2305\right ) (x+\log (x))^3 \log ^2\left (9 x^4-144 x^3+864 x^2-2304 x+2305\right )}+\frac {3 e^{10} \left (-36 x^6-72 \log (x) x^5+432 \left (1-\frac {e^{10}}{48}\right ) x^5-36 \log ^2(x) x^4+864 \log (x) x^4-1728 \left (1-\frac {5 e^{10}}{64}\right ) x^4+432 \log ^2(x) x^3-3456 \log (x) x^3+2304 \left (1-\frac {5 e^{10}}{16}\right ) x^3-1728 \log ^2(x) x^2+4608 \log (x) x^2+1440 e^{10} x^2+2304 \log ^2(x) x-e^{10} x-2305 e^{10}\right )}{x \left (9 x^4-144 x^3+864 x^2-2304 x+2305\right ) (x+\log (x))^4 \log ^3\left (9 x^4-144 x^3+864 x^2-2304 x+2305\right )}+\frac {e^{20} \left (-108 x^6-216 \log (x) x^5+1296 \left (1-\frac {e^{10}}{144}\right ) x^5-108 \log ^2(x) x^4+2592 \log (x) x^4-5184 \left (1-\frac {5 e^{10}}{192}\right ) x^4+1296 \log ^2(x) x^3-10368 \log (x) x^3+6912 \left (1-\frac {5 e^{10}}{48}\right ) x^3-5184 \log ^2(x) x^2+13824 \log (x) x^2+1440 e^{10} x^2+6912 \log ^2(x) x-e^{10} x-2305 e^{10}\right )}{x \left (9 x^4-144 x^3+864 x^2-2304 x+2305\right ) (x+\log (x))^5 \log ^4\left (9 x^4-144 x^3+864 x^2-2304 x+2305\right )}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 4 e^{10} \int \frac {\left (-36 x^2 (x-4)^3-36 x \log (x) (x-4)^3-\left (9 x^5-135 x^4+720 x^3-1440 x^2+x+2305\right ) \log \left (9 x^4-144 x^3+864 x^2-2304 x+2305\right )\right ) \left ((x+\log (x)) \log \left (9 x^4-144 x^3+864 x^2-2304 x+2305\right )+e^{10}\right )^3}{x \left (9 x^4-144 x^3+864 x^2-2304 x+2305\right ) (x+\log (x))^5 \log ^5\left (9 x^4-144 x^3+864 x^2-2304 x+2305\right )}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 4 e^{10} \int \left (-\frac {36 e^{30} (x-4)^3}{\left (9 x^4-144 x^3+864 x^2-2304 x+2305\right ) (x+\log (x))^4 \log ^5\left (9 x^4-144 x^3+864 x^2-2304 x+2305\right )}+\frac {-x-1}{x (x+\log (x))^2 \log \left (9 x^4-144 x^3+864 x^2-2304 x+2305\right )}+\frac {3 \left (-12 x^6-24 \log (x) x^5+144 \left (1-\frac {e^{10}}{16}\right ) x^5-12 \log ^2(x) x^4+288 \log (x) x^4-576 \left (1-\frac {15 e^{10}}{64}\right ) x^4+144 \log ^2(x) x^3-1152 \log (x) x^3+768 \left (1-\frac {15 e^{10}}{16}\right ) x^3-576 \log ^2(x) x^2+1536 \log (x) x^2+1440 e^{10} x^2+768 \log ^2(x) x-e^{10} x-2305 e^{10}\right )}{x \left (9 x^4-144 x^3+864 x^2-2304 x+2305\right ) (x+\log (x))^3 \log ^2\left (9 x^4-144 x^3+864 x^2-2304 x+2305\right )}+\frac {3 e^{10} \left (-36 x^6-72 \log (x) x^5+432 \left (1-\frac {e^{10}}{48}\right ) x^5-36 \log ^2(x) x^4+864 \log (x) x^4-1728 \left (1-\frac {5 e^{10}}{64}\right ) x^4+432 \log ^2(x) x^3-3456 \log (x) x^3+2304 \left (1-\frac {5 e^{10}}{16}\right ) x^3-1728 \log ^2(x) x^2+4608 \log (x) x^2+1440 e^{10} x^2+2304 \log ^2(x) x-e^{10} x-2305 e^{10}\right )}{x \left (9 x^4-144 x^3+864 x^2-2304 x+2305\right ) (x+\log (x))^4 \log ^3\left (9 x^4-144 x^3+864 x^2-2304 x+2305\right )}+\frac {e^{20} \left (-108 x^6-216 \log (x) x^5+1296 \left (1-\frac {e^{10}}{144}\right ) x^5-108 \log ^2(x) x^4+2592 \log (x) x^4-5184 \left (1-\frac {5 e^{10}}{192}\right ) x^4+1296 \log ^2(x) x^3-10368 \log (x) x^3+6912 \left (1-\frac {5 e^{10}}{48}\right ) x^3-5184 \log ^2(x) x^2+13824 \log (x) x^2+1440 e^{10} x^2+6912 \log ^2(x) x-e^{10} x-2305 e^{10}\right )}{x \left (9 x^4-144 x^3+864 x^2-2304 x+2305\right ) (x+\log (x))^5 \log ^4\left (9 x^4-144 x^3+864 x^2-2304 x+2305\right )}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 4 e^{10} \int \frac {\left (-36 x^2 (x-4)^3-36 x \log (x) (x-4)^3-\left (9 x^5-135 x^4+720 x^3-1440 x^2+x+2305\right ) \log \left (9 x^4-144 x^3+864 x^2-2304 x+2305\right )\right ) \left ((x+\log (x)) \log \left (9 x^4-144 x^3+864 x^2-2304 x+2305\right )+e^{10}\right )^3}{x \left (9 x^4-144 x^3+864 x^2-2304 x+2305\right ) (x+\log (x))^5 \log ^5\left (9 x^4-144 x^3+864 x^2-2304 x+2305\right )}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 4 e^{10} \int \left (-\frac {36 e^{30} (x-4)^3}{\left (9 x^4-144 x^3+864 x^2-2304 x+2305\right ) (x+\log (x))^4 \log ^5\left (9 x^4-144 x^3+864 x^2-2304 x+2305\right )}+\frac {-x-1}{x (x+\log (x))^2 \log \left (9 x^4-144 x^3+864 x^2-2304 x+2305\right )}+\frac {3 \left (-12 x^6-24 \log (x) x^5+144 \left (1-\frac {e^{10}}{16}\right ) x^5-12 \log ^2(x) x^4+288 \log (x) x^4-576 \left (1-\frac {15 e^{10}}{64}\right ) x^4+144 \log ^2(x) x^3-1152 \log (x) x^3+768 \left (1-\frac {15 e^{10}}{16}\right ) x^3-576 \log ^2(x) x^2+1536 \log (x) x^2+1440 e^{10} x^2+768 \log ^2(x) x-e^{10} x-2305 e^{10}\right )}{x \left (9 x^4-144 x^3+864 x^2-2304 x+2305\right ) (x+\log (x))^3 \log ^2\left (9 x^4-144 x^3+864 x^2-2304 x+2305\right )}+\frac {3 e^{10} \left (-36 x^6-72 \log (x) x^5+432 \left (1-\frac {e^{10}}{48}\right ) x^5-36 \log ^2(x) x^4+864 \log (x) x^4-1728 \left (1-\frac {5 e^{10}}{64}\right ) x^4+432 \log ^2(x) x^3-3456 \log (x) x^3+2304 \left (1-\frac {5 e^{10}}{16}\right ) x^3-1728 \log ^2(x) x^2+4608 \log (x) x^2+1440 e^{10} x^2+2304 \log ^2(x) x-e^{10} x-2305 e^{10}\right )}{x \left (9 x^4-144 x^3+864 x^2-2304 x+2305\right ) (x+\log (x))^4 \log ^3\left (9 x^4-144 x^3+864 x^2-2304 x+2305\right )}+\frac {e^{20} \left (-108 x^6-216 \log (x) x^5+1296 \left (1-\frac {e^{10}}{144}\right ) x^5-108 \log ^2(x) x^4+2592 \log (x) x^4-5184 \left (1-\frac {5 e^{10}}{192}\right ) x^4+1296 \log ^2(x) x^3-10368 \log (x) x^3+6912 \left (1-\frac {5 e^{10}}{48}\right ) x^3-5184 \log ^2(x) x^2+13824 \log (x) x^2+1440 e^{10} x^2+6912 \log ^2(x) x-e^{10} x-2305 e^{10}\right )}{x \left (9 x^4-144 x^3+864 x^2-2304 x+2305\right ) (x+\log (x))^5 \log ^4\left (9 x^4-144 x^3+864 x^2-2304 x+2305\right )}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 4 e^{10} \int \frac {\left (-36 x^2 (x-4)^3-36 x \log (x) (x-4)^3-\left (9 x^5-135 x^4+720 x^3-1440 x^2+x+2305\right ) \log \left (9 x^4-144 x^3+864 x^2-2304 x+2305\right )\right ) \left ((x+\log (x)) \log \left (9 x^4-144 x^3+864 x^2-2304 x+2305\right )+e^{10}\right )^3}{x \left (9 x^4-144 x^3+864 x^2-2304 x+2305\right ) (x+\log (x))^5 \log ^5\left (9 x^4-144 x^3+864 x^2-2304 x+2305\right )}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 4 e^{10} \int \left (-\frac {36 e^{30} (x-4)^3}{\left (9 x^4-144 x^3+864 x^2-2304 x+2305\right ) (x+\log (x))^4 \log ^5\left (9 x^4-144 x^3+864 x^2-2304 x+2305\right )}+\frac {-x-1}{x (x+\log (x))^2 \log \left (9 x^4-144 x^3+864 x^2-2304 x+2305\right )}+\frac {3 \left (-12 x^6-24 \log (x) x^5+144 \left (1-\frac {e^{10}}{16}\right ) x^5-12 \log ^2(x) x^4+288 \log (x) x^4-576 \left (1-\frac {15 e^{10}}{64}\right ) x^4+144 \log ^2(x) x^3-1152 \log (x) x^3+768 \left (1-\frac {15 e^{10}}{16}\right ) x^3-576 \log ^2(x) x^2+1536 \log (x) x^2+1440 e^{10} x^2+768 \log ^2(x) x-e^{10} x-2305 e^{10}\right )}{x \left (9 x^4-144 x^3+864 x^2-2304 x+2305\right ) (x+\log (x))^3 \log ^2\left (9 x^4-144 x^3+864 x^2-2304 x+2305\right )}+\frac {3 e^{10} \left (-36 x^6-72 \log (x) x^5+432 \left (1-\frac {e^{10}}{48}\right ) x^5-36 \log ^2(x) x^4+864 \log (x) x^4-1728 \left (1-\frac {5 e^{10}}{64}\right ) x^4+432 \log ^2(x) x^3-3456 \log (x) x^3+2304 \left (1-\frac {5 e^{10}}{16}\right ) x^3-1728 \log ^2(x) x^2+4608 \log (x) x^2+1440 e^{10} x^2+2304 \log ^2(x) x-e^{10} x-2305 e^{10}\right )}{x \left (9 x^4-144 x^3+864 x^2-2304 x+2305\right ) (x+\log (x))^4 \log ^3\left (9 x^4-144 x^3+864 x^2-2304 x+2305\right )}+\frac {e^{20} \left (-108 x^6-216 \log (x) x^5+1296 \left (1-\frac {e^{10}}{144}\right ) x^5-108 \log ^2(x) x^4+2592 \log (x) x^4-5184 \left (1-\frac {5 e^{10}}{192}\right ) x^4+1296 \log ^2(x) x^3-10368 \log (x) x^3+6912 \left (1-\frac {5 e^{10}}{48}\right ) x^3-5184 \log ^2(x) x^2+13824 \log (x) x^2+1440 e^{10} x^2+6912 \log ^2(x) x-e^{10} x-2305 e^{10}\right )}{x \left (9 x^4-144 x^3+864 x^2-2304 x+2305\right ) (x+\log (x))^5 \log ^4\left (9 x^4-144 x^3+864 x^2-2304 x+2305\right )}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 4 e^{10} \int \frac {\left (-36 x^2 (x-4)^3-36 x \log (x) (x-4)^3-\left (9 x^5-135 x^4+720 x^3-1440 x^2+x+2305\right ) \log \left (9 x^4-144 x^3+864 x^2-2304 x+2305\right )\right ) \left ((x+\log (x)) \log \left (9 x^4-144 x^3+864 x^2-2304 x+2305\right )+e^{10}\right )^3}{x \left (9 x^4-144 x^3+864 x^2-2304 x+2305\right ) (x+\log (x))^5 \log ^5\left (9 x^4-144 x^3+864 x^2-2304 x+2305\right )}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 4 e^{10} \int \left (-\frac {36 e^{30} (x-4)^3}{\left (9 x^4-144 x^3+864 x^2-2304 x+2305\right ) (x+\log (x))^4 \log ^5\left (9 x^4-144 x^3+864 x^2-2304 x+2305\right )}+\frac {-x-1}{x (x+\log (x))^2 \log \left (9 x^4-144 x^3+864 x^2-2304 x+2305\right )}+\frac {3 \left (-12 x^6-24 \log (x) x^5+144 \left (1-\frac {e^{10}}{16}\right ) x^5-12 \log ^2(x) x^4+288 \log (x) x^4-576 \left (1-\frac {15 e^{10}}{64}\right ) x^4+144 \log ^2(x) x^3-1152 \log (x) x^3+768 \left (1-\frac {15 e^{10}}{16}\right ) x^3-576 \log ^2(x) x^2+1536 \log (x) x^2+1440 e^{10} x^2+768 \log ^2(x) x-e^{10} x-2305 e^{10}\right )}{x \left (9 x^4-144 x^3+864 x^2-2304 x+2305\right ) (x+\log (x))^3 \log ^2\left (9 x^4-144 x^3+864 x^2-2304 x+2305\right )}+\frac {3 e^{10} \left (-36 x^6-72 \log (x) x^5+432 \left (1-\frac {e^{10}}{48}\right ) x^5-36 \log ^2(x) x^4+864 \log (x) x^4-1728 \left (1-\frac {5 e^{10}}{64}\right ) x^4+432 \log ^2(x) x^3-3456 \log (x) x^3+2304 \left (1-\frac {5 e^{10}}{16}\right ) x^3-1728 \log ^2(x) x^2+4608 \log (x) x^2+1440 e^{10} x^2+2304 \log ^2(x) x-e^{10} x-2305 e^{10}\right )}{x \left (9 x^4-144 x^3+864 x^2-2304 x+2305\right ) (x+\log (x))^4 \log ^3\left (9 x^4-144 x^3+864 x^2-2304 x+2305\right )}+\frac {e^{20} \left (-108 x^6-216 \log (x) x^5+1296 \left (1-\frac {e^{10}}{144}\right ) x^5-108 \log ^2(x) x^4+2592 \log (x) x^4-5184 \left (1-\frac {5 e^{10}}{192}\right ) x^4+1296 \log ^2(x) x^3-10368 \log (x) x^3+6912 \left (1-\frac {5 e^{10}}{48}\right ) x^3-5184 \log ^2(x) x^2+13824 \log (x) x^2+1440 e^{10} x^2+6912 \log ^2(x) x-e^{10} x-2305 e^{10}\right )}{x \left (9 x^4-144 x^3+864 x^2-2304 x+2305\right ) (x+\log (x))^5 \log ^4\left (9 x^4-144 x^3+864 x^2-2304 x+2305\right )}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 4 e^{10} \int \frac {\left (-36 x^2 (x-4)^3-36 x \log (x) (x-4)^3-\left (9 x^5-135 x^4+720 x^3-1440 x^2+x+2305\right ) \log \left (9 x^4-144 x^3+864 x^2-2304 x+2305\right )\right ) \left ((x+\log (x)) \log \left (9 x^4-144 x^3+864 x^2-2304 x+2305\right )+e^{10}\right )^3}{x \left (9 x^4-144 x^3+864 x^2-2304 x+2305\right ) (x+\log (x))^5 \log ^5\left (9 x^4-144 x^3+864 x^2-2304 x+2305\right )}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 4 e^{10} \int \left (-\frac {36 e^{30} (x-4)^3}{\left (9 x^4-144 x^3+864 x^2-2304 x+2305\right ) (x+\log (x))^4 \log ^5\left (9 x^4-144 x^3+864 x^2-2304 x+2305\right )}+\frac {-x-1}{x (x+\log (x))^2 \log \left (9 x^4-144 x^3+864 x^2-2304 x+2305\right )}+\frac {3 \left (-12 x^6-24 \log (x) x^5+144 \left (1-\frac {e^{10}}{16}\right ) x^5-12 \log ^2(x) x^4+288 \log (x) x^4-576 \left (1-\frac {15 e^{10}}{64}\right ) x^4+144 \log ^2(x) x^3-1152 \log (x) x^3+768 \left (1-\frac {15 e^{10}}{16}\right ) x^3-576 \log ^2(x) x^2+1536 \log (x) x^2+1440 e^{10} x^2+768 \log ^2(x) x-e^{10} x-2305 e^{10}\right )}{x \left (9 x^4-144 x^3+864 x^2-2304 x+2305\right ) (x+\log (x))^3 \log ^2\left (9 x^4-144 x^3+864 x^2-2304 x+2305\right )}+\frac {3 e^{10} \left (-36 x^6-72 \log (x) x^5+432 \left (1-\frac {e^{10}}{48}\right ) x^5-36 \log ^2(x) x^4+864 \log (x) x^4-1728 \left (1-\frac {5 e^{10}}{64}\right ) x^4+432 \log ^2(x) x^3-3456 \log (x) x^3+2304 \left (1-\frac {5 e^{10}}{16}\right ) x^3-1728 \log ^2(x) x^2+4608 \log (x) x^2+1440 e^{10} x^2+2304 \log ^2(x) x-e^{10} x-2305 e^{10}\right )}{x \left (9 x^4-144 x^3+864 x^2-2304 x+2305\right ) (x+\log (x))^4 \log ^3\left (9 x^4-144 x^3+864 x^2-2304 x+2305\right )}+\frac {e^{20} \left (-108 x^6-216 \log (x) x^5+1296 \left (1-\frac {e^{10}}{144}\right ) x^5-108 \log ^2(x) x^4+2592 \log (x) x^4-5184 \left (1-\frac {5 e^{10}}{192}\right ) x^4+1296 \log ^2(x) x^3-10368 \log (x) x^3+6912 \left (1-\frac {5 e^{10}}{48}\right ) x^3-5184 \log ^2(x) x^2+13824 \log (x) x^2+1440 e^{10} x^2+6912 \log ^2(x) x-e^{10} x-2305 e^{10}\right )}{x \left (9 x^4-144 x^3+864 x^2-2304 x+2305\right ) (x+\log (x))^5 \log ^4\left (9 x^4-144 x^3+864 x^2-2304 x+2305\right )}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 4 e^{10} \int \frac {\left (-36 x^2 (x-4)^3-36 x \log (x) (x-4)^3-\left (9 x^5-135 x^4+720 x^3-1440 x^2+x+2305\right ) \log \left (9 x^4-144 x^3+864 x^2-2304 x+2305\right )\right ) \left ((x+\log (x)) \log \left (9 x^4-144 x^3+864 x^2-2304 x+2305\right )+e^{10}\right )^3}{x \left (9 x^4-144 x^3+864 x^2-2304 x+2305\right ) (x+\log (x))^5 \log ^5\left (9 x^4-144 x^3+864 x^2-2304 x+2305\right )}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 4 e^{10} \int \left (-\frac {36 e^{30} (x-4)^3}{\left (9 x^4-144 x^3+864 x^2-2304 x+2305\right ) (x+\log (x))^4 \log ^5\left (9 x^4-144 x^3+864 x^2-2304 x+2305\right )}+\frac {-x-1}{x (x+\log (x))^2 \log \left (9 x^4-144 x^3+864 x^2-2304 x+2305\right )}+\frac {3 \left (-12 x^6-24 \log (x) x^5+144 \left (1-\frac {e^{10}}{16}\right ) x^5-12 \log ^2(x) x^4+288 \log (x) x^4-576 \left (1-\frac {15 e^{10}}{64}\right ) x^4+144 \log ^2(x) x^3-1152 \log (x) x^3+768 \left (1-\frac {15 e^{10}}{16}\right ) x^3-576 \log ^2(x) x^2+1536 \log (x) x^2+1440 e^{10} x^2+768 \log ^2(x) x-e^{10} x-2305 e^{10}\right )}{x \left (9 x^4-144 x^3+864 x^2-2304 x+2305\right ) (x+\log (x))^3 \log ^2\left (9 x^4-144 x^3+864 x^2-2304 x+2305\right )}+\frac {3 e^{10} \left (-36 x^6-72 \log (x) x^5+432 \left (1-\frac {e^{10}}{48}\right ) x^5-36 \log ^2(x) x^4+864 \log (x) x^4-1728 \left (1-\frac {5 e^{10}}{64}\right ) x^4+432 \log ^2(x) x^3-3456 \log (x) x^3+2304 \left (1-\frac {5 e^{10}}{16}\right ) x^3-1728 \log ^2(x) x^2+4608 \log (x) x^2+1440 e^{10} x^2+2304 \log ^2(x) x-e^{10} x-2305 e^{10}\right )}{x \left (9 x^4-144 x^3+864 x^2-2304 x+2305\right ) (x+\log (x))^4 \log ^3\left (9 x^4-144 x^3+864 x^2-2304 x+2305\right )}+\frac {e^{20} \left (-108 x^6-216 \log (x) x^5+1296 \left (1-\frac {e^{10}}{144}\right ) x^5-108 \log ^2(x) x^4+2592 \log (x) x^4-5184 \left (1-\frac {5 e^{10}}{192}\right ) x^4+1296 \log ^2(x) x^3-10368 \log (x) x^3+6912 \left (1-\frac {5 e^{10}}{48}\right ) x^3-5184 \log ^2(x) x^2+13824 \log (x) x^2+1440 e^{10} x^2+6912 \log ^2(x) x-e^{10} x-2305 e^{10}\right )}{x \left (9 x^4-144 x^3+864 x^2-2304 x+2305\right ) (x+\log (x))^5 \log ^4\left (9 x^4-144 x^3+864 x^2-2304 x+2305\right )}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 4 e^{10} \int \frac {\left (-36 x^2 (x-4)^3-36 x \log (x) (x-4)^3-\left (9 x^5-135 x^4+720 x^3-1440 x^2+x+2305\right ) \log \left (9 x^4-144 x^3+864 x^2-2304 x+2305\right )\right ) \left ((x+\log (x)) \log \left (9 x^4-144 x^3+864 x^2-2304 x+2305\right )+e^{10}\right )^3}{x \left (9 x^4-144 x^3+864 x^2-2304 x+2305\right ) (x+\log (x))^5 \log ^5\left (9 x^4-144 x^3+864 x^2-2304 x+2305\right )}dx\) |
Int[(E^40*(9216*x^2 - 6912*x^3 + 1728*x^4 - 144*x^5) + E^40*(9216*x - 6912 *x^2 + 1728*x^3 - 144*x^4)*Log[x] + (E^40*(-9220 - 4*x + 5760*x^2 - 2880*x ^3 + 540*x^4 - 36*x^5) + E^30*(27648*x^3 - 20736*x^4 + 5184*x^5 - 432*x^6) + E^30*(55296*x^2 - 41472*x^3 + 10368*x^4 - 864*x^5)*Log[x] + E^30*(27648 *x - 20736*x^2 + 5184*x^3 - 432*x^4)*Log[x]^2)*Log[2305 - 2304*x + 864*x^2 - 144*x^3 + 9*x^4] + (E^30*(-27660*x - 12*x^2 + 17280*x^3 - 8640*x^4 + 16 20*x^5 - 108*x^6) + E^20*(27648*x^4 - 20736*x^5 + 5184*x^6 - 432*x^7) + (E ^30*(-27660 - 12*x + 17280*x^2 - 8640*x^3 + 1620*x^4 - 108*x^5) + E^20*(82 944*x^3 - 62208*x^4 + 15552*x^5 - 1296*x^6))*Log[x] + E^20*(82944*x^2 - 62 208*x^3 + 15552*x^4 - 1296*x^5)*Log[x]^2 + E^20*(27648*x - 20736*x^2 + 518 4*x^3 - 432*x^4)*Log[x]^3)*Log[2305 - 2304*x + 864*x^2 - 144*x^3 + 9*x^4]^ 2 + (E^20*(-27660*x^2 - 12*x^3 + 17280*x^4 - 8640*x^5 + 1620*x^6 - 108*x^7 ) + E^10*(9216*x^5 - 6912*x^6 + 1728*x^7 - 144*x^8) + (E^20*(-55320*x - 24 *x^2 + 34560*x^3 - 17280*x^4 + 3240*x^5 - 216*x^6) + E^10*(36864*x^4 - 276 48*x^5 + 6912*x^6 - 576*x^7))*Log[x] + (E^20*(-27660 - 12*x + 17280*x^2 - 8640*x^3 + 1620*x^4 - 108*x^5) + E^10*(55296*x^3 - 41472*x^4 + 10368*x^5 - 864*x^6))*Log[x]^2 + E^10*(36864*x^2 - 27648*x^3 + 6912*x^4 - 576*x^5)*Lo g[x]^3 + E^10*(9216*x - 6912*x^2 + 1728*x^3 - 144*x^4)*Log[x]^4)*Log[2305 - 2304*x + 864*x^2 - 144*x^3 + 9*x^4]^3 + (E^10*(-9220*x^3 - 4*x^4 + 5760* x^5 - 2880*x^6 + 540*x^7 - 36*x^8) + E^10*(-27660*x^2 - 12*x^3 + 17280*x^4 - 8640*x^5 + 1620*x^6 - 108*x^7)*Log[x] + E^10*(-27660*x - 12*x^2 + 17280 *x^3 - 8640*x^4 + 1620*x^5 - 108*x^6)*Log[x]^2 + E^10*(-9220 - 4*x + 5760* x^2 - 2880*x^3 + 540*x^4 - 36*x^5)*Log[x]^3)*Log[2305 - 2304*x + 864*x^2 - 144*x^3 + 9*x^4]^4)/((2305*x^6 - 2304*x^7 + 864*x^8 - 144*x^9 + 9*x^10 + (11525*x^5 - 11520*x^6 + 4320*x^7 - 720*x^8 + 45*x^9)*Log[x] + (23050*x^4 - 23040*x^5 + 8640*x^6 - 1440*x^7 + 90*x^8)*Log[x]^2 + (23050*x^3 - 23040* x^4 + 8640*x^5 - 1440*x^6 + 90*x^7)*Log[x]^3 + (11525*x^2 - 11520*x^3 + 43 20*x^4 - 720*x^5 + 45*x^6)*Log[x]^4 + (2305*x - 2304*x^2 + 864*x^3 - 144*x ^4 + 9*x^5)*Log[x]^5)*Log[2305 - 2304*x + 864*x^2 - 144*x^3 + 9*x^4]^5),x]
3.13.10.3.1 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. \(323\) vs. \(2(27)=54\).
Time = 239.63 (sec) , antiderivative size = 324, normalized size of antiderivative = 12.46
| method | result | size |
| risch | \(\frac {\left ({\mathrm e}^{30}+4 \ln \left (9 x^{4}-144 x^{3}+864 x^{2}-2304 x +2305\right ) {\mathrm e}^{20} x +4 \ln \left (9 x^{4}-144 x^{3}+864 x^{2}-2304 x +2305\right ) \ln \left (x \right ) {\mathrm e}^{20}+6 \,{\mathrm e}^{10} x^{2} \ln \left (9 x^{4}-144 x^{3}+864 x^{2}-2304 x +2305\right )^{2}+12 \,{\mathrm e}^{10} \ln \left (x \right ) x \ln \left (9 x^{4}-144 x^{3}+864 x^{2}-2304 x +2305\right )^{2}+6 \,{\mathrm e}^{10} \ln \left (x \right )^{2} \ln \left (9 x^{4}-144 x^{3}+864 x^{2}-2304 x +2305\right )^{2}+4 \ln \left (9 x^{4}-144 x^{3}+864 x^{2}-2304 x +2305\right )^{3} x^{3}+12 \ln \left (x \right ) \ln \left (9 x^{4}-144 x^{3}+864 x^{2}-2304 x +2305\right )^{3} x^{2}+12 \ln \left (x \right )^{2} \ln \left (9 x^{4}-144 x^{3}+864 x^{2}-2304 x +2305\right )^{3} x +4 \ln \left (x \right )^{3} \ln \left (9 x^{4}-144 x^{3}+864 x^{2}-2304 x +2305\right )^{3}\right ) {\mathrm e}^{10}}{\left (\ln \left (x \right )^{4}+4 x \ln \left (x \right )^{3}+6 x^{2} \ln \left (x \right )^{2}+4 x^{3} \ln \left (x \right )+x^{4}\right ) \ln \left (9 x^{4}-144 x^{3}+864 x^{2}-2304 x +2305\right )^{4}}\) | \(324\) |
| parallelrisch | \(\frac {81 \,{\mathrm e}^{40}+972 \,{\mathrm e}^{20} \ln \left (9 x^{4}-144 x^{3}+864 x^{2}-2304 x +2305\right )^{2} x \ln \left (x \right )+972 \,{\mathrm e}^{10} x^{2} \ln \left (x \right ) \ln \left (9 x^{4}-144 x^{3}+864 x^{2}-2304 x +2305\right )^{3}+972 \,{\mathrm e}^{10} x \ln \left (x \right )^{2} \ln \left (9 x^{4}-144 x^{3}+864 x^{2}-2304 x +2305\right )^{3}+324 \,{\mathrm e}^{30} \ln \left (9 x^{4}-144 x^{3}+864 x^{2}-2304 x +2305\right ) x +324 \,{\mathrm e}^{30} \ln \left (9 x^{4}-144 x^{3}+864 x^{2}-2304 x +2305\right ) \ln \left (x \right )+486 \,{\mathrm e}^{20} \ln \left (9 x^{4}-144 x^{3}+864 x^{2}-2304 x +2305\right )^{2} x^{2}+486 \,{\mathrm e}^{20} \ln \left (x \right )^{2} \ln \left (9 x^{4}-144 x^{3}+864 x^{2}-2304 x +2305\right )^{2}+324 \,{\mathrm e}^{10} x^{3} \ln \left (9 x^{4}-144 x^{3}+864 x^{2}-2304 x +2305\right )^{3}+324 \,{\mathrm e}^{10} \ln \left (x \right )^{3} \ln \left (9 x^{4}-144 x^{3}+864 x^{2}-2304 x +2305\right )^{3}}{81 \left (\ln \left (x \right )^{4}+4 x \ln \left (x \right )^{3}+6 x^{2} \ln \left (x \right )^{2}+4 x^{3} \ln \left (x \right )+x^{4}\right ) \ln \left (9 x^{4}-144 x^{3}+864 x^{2}-2304 x +2305\right )^{4}}\) | \(353\) |
int((((-36*x^5+540*x^4-2880*x^3+5760*x^2-4*x-9220)*exp(5)^2*ln(x)^3+(-108* x^6+1620*x^5-8640*x^4+17280*x^3-12*x^2-27660*x)*exp(5)^2*ln(x)^2+(-108*x^7 +1620*x^6-8640*x^5+17280*x^4-12*x^3-27660*x^2)*exp(5)^2*ln(x)+(-36*x^8+540 *x^7-2880*x^6+5760*x^5-4*x^4-9220*x^3)*exp(5)^2)*ln(9*x^4-144*x^3+864*x^2- 2304*x+2305)^4+((-144*x^4+1728*x^3-6912*x^2+9216*x)*exp(5)^2*ln(x)^4+(-576 *x^5+6912*x^4-27648*x^3+36864*x^2)*exp(5)^2*ln(x)^3+((-108*x^5+1620*x^4-86 40*x^3+17280*x^2-12*x-27660)*exp(5)^4+(-864*x^6+10368*x^5-41472*x^4+55296* x^3)*exp(5)^2)*ln(x)^2+((-216*x^6+3240*x^5-17280*x^4+34560*x^3-24*x^2-5532 0*x)*exp(5)^4+(-576*x^7+6912*x^6-27648*x^5+36864*x^4)*exp(5)^2)*ln(x)+(-10 8*x^7+1620*x^6-8640*x^5+17280*x^4-12*x^3-27660*x^2)*exp(5)^4+(-144*x^8+172 8*x^7-6912*x^6+9216*x^5)*exp(5)^2)*ln(9*x^4-144*x^3+864*x^2-2304*x+2305)^3 +((-432*x^4+5184*x^3-20736*x^2+27648*x)*exp(5)^4*ln(x)^3+(-1296*x^5+15552* x^4-62208*x^3+82944*x^2)*exp(5)^4*ln(x)^2+((-108*x^5+1620*x^4-8640*x^3+172 80*x^2-12*x-27660)*exp(5)^6+(-1296*x^6+15552*x^5-62208*x^4+82944*x^3)*exp( 5)^4)*ln(x)+(-108*x^6+1620*x^5-8640*x^4+17280*x^3-12*x^2-27660*x)*exp(5)^6 +(-432*x^7+5184*x^6-20736*x^5+27648*x^4)*exp(5)^4)*ln(9*x^4-144*x^3+864*x^ 2-2304*x+2305)^2+((-432*x^4+5184*x^3-20736*x^2+27648*x)*exp(5)^6*ln(x)^2+( -864*x^5+10368*x^4-41472*x^3+55296*x^2)*exp(5)^6*ln(x)+(-36*x^5+540*x^4-28 80*x^3+5760*x^2-4*x-9220)*exp(5)^8+(-432*x^6+5184*x^5-20736*x^4+27648*x^3) *exp(5)^6)*ln(9*x^4-144*x^3+864*x^2-2304*x+2305)+(-144*x^4+1728*x^3-6912*x ^2+9216*x)*exp(5)^8*ln(x)+(-144*x^5+1728*x^4-6912*x^3+9216*x^2)*exp(5)^8)/ ((9*x^5-144*x^4+864*x^3-2304*x^2+2305*x)*ln(x)^5+(45*x^6-720*x^5+4320*x^4- 11520*x^3+11525*x^2)*ln(x)^4+(90*x^7-1440*x^6+8640*x^5-23040*x^4+23050*x^3 )*ln(x)^3+(90*x^8-1440*x^7+8640*x^6-23040*x^5+23050*x^4)*ln(x)^2+(45*x^9-7 20*x^8+4320*x^7-11520*x^6+11525*x^5)*ln(x)+9*x^10-144*x^9+864*x^8-2304*x^7 +2305*x^6)/ln(9*x^4-144*x^3+864*x^2-2304*x+2305)^5,x,method=_RETURNVERBOSE )
(exp(30)+4*ln(9*x^4-144*x^3+864*x^2-2304*x+2305)*exp(20)*x+4*ln(9*x^4-144* x^3+864*x^2-2304*x+2305)*ln(x)*exp(20)+6*exp(10)*x^2*ln(9*x^4-144*x^3+864* x^2-2304*x+2305)^2+12*exp(10)*ln(x)*x*ln(9*x^4-144*x^3+864*x^2-2304*x+2305 )^2+6*exp(10)*ln(x)^2*ln(9*x^4-144*x^3+864*x^2-2304*x+2305)^2+4*ln(9*x^4-1 44*x^3+864*x^2-2304*x+2305)^3*x^3+12*ln(x)*ln(9*x^4-144*x^3+864*x^2-2304*x +2305)^3*x^2+12*ln(x)^2*ln(9*x^4-144*x^3+864*x^2-2304*x+2305)^3*x+4*ln(x)^ 3*ln(9*x^4-144*x^3+864*x^2-2304*x+2305)^3)*exp(10)/(ln(x)^4+4*x*ln(x)^3+6* x^2*ln(x)^2+4*x^3*ln(x)+x^4)/ln(9*x^4-144*x^3+864*x^2-2304*x+2305)^4
Leaf count of result is larger than twice the leaf count of optimal. 196 vs. \(2 (25) = 50\).
Time = 0.31 (sec) , antiderivative size = 196, normalized size of antiderivative = 7.54 \[ \text {the integral} =\frac {4 \, {\left (x^{3} e^{10} + 3 \, x^{2} e^{10} \log \left (x\right ) + 3 \, x e^{10} \log \left (x\right )^{2} + e^{10} \log \left (x\right )^{3}\right )} \log \left (9 \, x^{4} - 144 \, x^{3} + 864 \, x^{2} - 2304 \, x + 2305\right )^{3} + 6 \, {\left (x^{2} e^{20} + 2 \, x e^{20} \log \left (x\right ) + e^{20} \log \left (x\right )^{2}\right )} \log \left (9 \, x^{4} - 144 \, x^{3} + 864 \, x^{2} - 2304 \, x + 2305\right )^{2} + 4 \, {\left (x e^{30} + e^{30} \log \left (x\right )\right )} \log \left (9 \, x^{4} - 144 \, x^{3} + 864 \, x^{2} - 2304 \, x + 2305\right ) + e^{40}}{{\left (x^{4} + 4 \, x^{3} \log \left (x\right ) + 6 \, x^{2} \log \left (x\right )^{2} + 4 \, x \log \left (x\right )^{3} + \log \left (x\right )^{4}\right )} \log \left (9 \, x^{4} - 144 \, x^{3} + 864 \, x^{2} - 2304 \, x + 2305\right )^{4}} \]
integrate((((-36*x^5+540*x^4-2880*x^3+5760*x^2-4*x-9220)*exp(5)^2*log(x)^3 +(-108*x^6+1620*x^5-8640*x^4+17280*x^3-12*x^2-27660*x)*exp(5)^2*log(x)^2+( -108*x^7+1620*x^6-8640*x^5+17280*x^4-12*x^3-27660*x^2)*exp(5)^2*log(x)+(-3 6*x^8+540*x^7-2880*x^6+5760*x^5-4*x^4-9220*x^3)*exp(5)^2)*log(9*x^4-144*x^ 3+864*x^2-2304*x+2305)^4+((-144*x^4+1728*x^3-6912*x^2+9216*x)*exp(5)^2*log (x)^4+(-576*x^5+6912*x^4-27648*x^3+36864*x^2)*exp(5)^2*log(x)^3+((-108*x^5 +1620*x^4-8640*x^3+17280*x^2-12*x-27660)*exp(5)^4+(-864*x^6+10368*x^5-4147 2*x^4+55296*x^3)*exp(5)^2)*log(x)^2+((-216*x^6+3240*x^5-17280*x^4+34560*x^ 3-24*x^2-55320*x)*exp(5)^4+(-576*x^7+6912*x^6-27648*x^5+36864*x^4)*exp(5)^ 2)*log(x)+(-108*x^7+1620*x^6-8640*x^5+17280*x^4-12*x^3-27660*x^2)*exp(5)^4 +(-144*x^8+1728*x^7-6912*x^6+9216*x^5)*exp(5)^2)*log(9*x^4-144*x^3+864*x^2 -2304*x+2305)^3+((-432*x^4+5184*x^3-20736*x^2+27648*x)*exp(5)^4*log(x)^3+( -1296*x^5+15552*x^4-62208*x^3+82944*x^2)*exp(5)^4*log(x)^2+((-108*x^5+1620 *x^4-8640*x^3+17280*x^2-12*x-27660)*exp(5)^6+(-1296*x^6+15552*x^5-62208*x^ 4+82944*x^3)*exp(5)^4)*log(x)+(-108*x^6+1620*x^5-8640*x^4+17280*x^3-12*x^2 -27660*x)*exp(5)^6+(-432*x^7+5184*x^6-20736*x^5+27648*x^4)*exp(5)^4)*log(9 *x^4-144*x^3+864*x^2-2304*x+2305)^2+((-432*x^4+5184*x^3-20736*x^2+27648*x) *exp(5)^6*log(x)^2+(-864*x^5+10368*x^4-41472*x^3+55296*x^2)*exp(5)^6*log(x )+(-36*x^5+540*x^4-2880*x^3+5760*x^2-4*x-9220)*exp(5)^8+(-432*x^6+5184*x^5 -20736*x^4+27648*x^3)*exp(5)^6)*log(9*x^4-144*x^3+864*x^2-2304*x+2305)+(-1 44*x^4+1728*x^3-6912*x^2+9216*x)*exp(5)^8*log(x)+(-144*x^5+1728*x^4-6912*x ^3+9216*x^2)*exp(5)^8)/((9*x^5-144*x^4+864*x^3-2304*x^2+2305*x)*log(x)^5+( 45*x^6-720*x^5+4320*x^4-11520*x^3+11525*x^2)*log(x)^4+(90*x^7-1440*x^6+864 0*x^5-23040*x^4+23050*x^3)*log(x)^3+(90*x^8-1440*x^7+8640*x^6-23040*x^5+23 050*x^4)*log(x)^2+(45*x^9-720*x^8+4320*x^7-11520*x^6+11525*x^5)*log(x)+9*x ^10-144*x^9+864*x^8-2304*x^7+2305*x^6)/log(9*x^4-144*x^3+864*x^2-2304*x+23 05)^5,x, algorithm=\
(4*(x^3*e^10 + 3*x^2*e^10*log(x) + 3*x*e^10*log(x)^2 + e^10*log(x)^3)*log( 9*x^4 - 144*x^3 + 864*x^2 - 2304*x + 2305)^3 + 6*(x^2*e^20 + 2*x*e^20*log( x) + e^20*log(x)^2)*log(9*x^4 - 144*x^3 + 864*x^2 - 2304*x + 2305)^2 + 4*( x*e^30 + e^30*log(x))*log(9*x^4 - 144*x^3 + 864*x^2 - 2304*x + 2305) + e^4 0)/((x^4 + 4*x^3*log(x) + 6*x^2*log(x)^2 + 4*x*log(x)^3 + log(x)^4)*log(9* x^4 - 144*x^3 + 864*x^2 - 2304*x + 2305)^4)
Leaf count of result is larger than twice the leaf count of optimal. 218 vs. \(2 (20) = 40\).
Time = 2.23 (sec) , antiderivative size = 218, normalized size of antiderivative = 8.38 \[ \text {the integral} =\frac {\left (4 x e^{30} + 4 e^{30} \log {\left (x \right )}\right ) \log {\left (9 x^{4} - 144 x^{3} + 864 x^{2} - 2304 x + 2305 \right )} + \left (6 x^{2} e^{20} + 12 x e^{20} \log {\left (x \right )} + 6 e^{20} \log {\left (x \right )}^{2}\right ) \log {\left (9 x^{4} - 144 x^{3} + 864 x^{2} - 2304 x + 2305 \right )}^{2} + \left (4 x^{3} e^{10} + 12 x^{2} e^{10} \log {\left (x \right )} + 12 x e^{10} \log {\left (x \right )}^{2} + 4 e^{10} \log {\left (x \right )}^{3}\right ) \log {\left (9 x^{4} - 144 x^{3} + 864 x^{2} - 2304 x + 2305 \right )}^{3} + e^{40}}{\left (x^{4} + 4 x^{3} \log {\left (x \right )} + 6 x^{2} \log {\left (x \right )}^{2} + 4 x \log {\left (x \right )}^{3} + \log {\left (x \right )}^{4}\right ) \log {\left (9 x^{4} - 144 x^{3} + 864 x^{2} - 2304 x + 2305 \right )}^{4}} \]
integrate((((-36*x**5+540*x**4-2880*x**3+5760*x**2-4*x-9220)*exp(5)**2*ln( x)**3+(-108*x**6+1620*x**5-8640*x**4+17280*x**3-12*x**2-27660*x)*exp(5)**2 *ln(x)**2+(-108*x**7+1620*x**6-8640*x**5+17280*x**4-12*x**3-27660*x**2)*ex p(5)**2*ln(x)+(-36*x**8+540*x**7-2880*x**6+5760*x**5-4*x**4-9220*x**3)*exp (5)**2)*ln(9*x**4-144*x**3+864*x**2-2304*x+2305)**4+((-144*x**4+1728*x**3- 6912*x**2+9216*x)*exp(5)**2*ln(x)**4+(-576*x**5+6912*x**4-27648*x**3+36864 *x**2)*exp(5)**2*ln(x)**3+((-108*x**5+1620*x**4-8640*x**3+17280*x**2-12*x- 27660)*exp(5)**4+(-864*x**6+10368*x**5-41472*x**4+55296*x**3)*exp(5)**2)*l n(x)**2+((-216*x**6+3240*x**5-17280*x**4+34560*x**3-24*x**2-55320*x)*exp(5 )**4+(-576*x**7+6912*x**6-27648*x**5+36864*x**4)*exp(5)**2)*ln(x)+(-108*x* *7+1620*x**6-8640*x**5+17280*x**4-12*x**3-27660*x**2)*exp(5)**4+(-144*x**8 +1728*x**7-6912*x**6+9216*x**5)*exp(5)**2)*ln(9*x**4-144*x**3+864*x**2-230 4*x+2305)**3+((-432*x**4+5184*x**3-20736*x**2+27648*x)*exp(5)**4*ln(x)**3+ (-1296*x**5+15552*x**4-62208*x**3+82944*x**2)*exp(5)**4*ln(x)**2+((-108*x* *5+1620*x**4-8640*x**3+17280*x**2-12*x-27660)*exp(5)**6+(-1296*x**6+15552* x**5-62208*x**4+82944*x**3)*exp(5)**4)*ln(x)+(-108*x**6+1620*x**5-8640*x** 4+17280*x**3-12*x**2-27660*x)*exp(5)**6+(-432*x**7+5184*x**6-20736*x**5+27 648*x**4)*exp(5)**4)*ln(9*x**4-144*x**3+864*x**2-2304*x+2305)**2+((-432*x* *4+5184*x**3-20736*x**2+27648*x)*exp(5)**6*ln(x)**2+(-864*x**5+10368*x**4- 41472*x**3+55296*x**2)*exp(5)**6*ln(x)+(-36*x**5+540*x**4-2880*x**3+5760*x **2-4*x-9220)*exp(5)**8+(-432*x**6+5184*x**5-20736*x**4+27648*x**3)*exp(5) **6)*ln(9*x**4-144*x**3+864*x**2-2304*x+2305)+(-144*x**4+1728*x**3-6912*x* *2+9216*x)*exp(5)**8*ln(x)+(-144*x**5+1728*x**4-6912*x**3+9216*x**2)*exp(5 )**8)/((9*x**5-144*x**4+864*x**3-2304*x**2+2305*x)*ln(x)**5+(45*x**6-720*x **5+4320*x**4-11520*x**3+11525*x**2)*ln(x)**4+(90*x**7-1440*x**6+8640*x**5 -23040*x**4+23050*x**3)*ln(x)**3+(90*x**8-1440*x**7+8640*x**6-23040*x**5+2 3050*x**4)*ln(x)**2+(45*x**9-720*x**8+4320*x**7-11520*x**6+11525*x**5)*ln( x)+9*x**10-144*x**9+864*x**8-2304*x**7+2305*x**6)/ln(9*x**4-144*x**3+864*x **2-2304*x+2305)**5,x)
((4*x*exp(30) + 4*exp(30)*log(x))*log(9*x**4 - 144*x**3 + 864*x**2 - 2304* x + 2305) + (6*x**2*exp(20) + 12*x*exp(20)*log(x) + 6*exp(20)*log(x)**2)*l og(9*x**4 - 144*x**3 + 864*x**2 - 2304*x + 2305)**2 + (4*x**3*exp(10) + 12 *x**2*exp(10)*log(x) + 12*x*exp(10)*log(x)**2 + 4*exp(10)*log(x)**3)*log(9 *x**4 - 144*x**3 + 864*x**2 - 2304*x + 2305)**3 + exp(40))/((x**4 + 4*x**3 *log(x) + 6*x**2*log(x)**2 + 4*x*log(x)**3 + log(x)**4)*log(9*x**4 - 144*x **3 + 864*x**2 - 2304*x + 2305)**4)
Leaf count of result is larger than twice the leaf count of optimal. 196 vs. \(2 (25) = 50\).
Time = 1.12 (sec) , antiderivative size = 196, normalized size of antiderivative = 7.54 \[ \text {the integral} =\frac {4 \, {\left (x^{3} e^{10} + 3 \, x^{2} e^{10} \log \left (x\right ) + 3 \, x e^{10} \log \left (x\right )^{2} + e^{10} \log \left (x\right )^{3}\right )} \log \left (9 \, x^{4} - 144 \, x^{3} + 864 \, x^{2} - 2304 \, x + 2305\right )^{3} + 6 \, {\left (x^{2} e^{20} + 2 \, x e^{20} \log \left (x\right ) + e^{20} \log \left (x\right )^{2}\right )} \log \left (9 \, x^{4} - 144 \, x^{3} + 864 \, x^{2} - 2304 \, x + 2305\right )^{2} + 4 \, {\left (x e^{30} + e^{30} \log \left (x\right )\right )} \log \left (9 \, x^{4} - 144 \, x^{3} + 864 \, x^{2} - 2304 \, x + 2305\right ) + e^{40}}{{\left (x^{4} + 4 \, x^{3} \log \left (x\right ) + 6 \, x^{2} \log \left (x\right )^{2} + 4 \, x \log \left (x\right )^{3} + \log \left (x\right )^{4}\right )} \log \left (9 \, x^{4} - 144 \, x^{3} + 864 \, x^{2} - 2304 \, x + 2305\right )^{4}} \]
integrate((((-36*x^5+540*x^4-2880*x^3+5760*x^2-4*x-9220)*exp(5)^2*log(x)^3 +(-108*x^6+1620*x^5-8640*x^4+17280*x^3-12*x^2-27660*x)*exp(5)^2*log(x)^2+( -108*x^7+1620*x^6-8640*x^5+17280*x^4-12*x^3-27660*x^2)*exp(5)^2*log(x)+(-3 6*x^8+540*x^7-2880*x^6+5760*x^5-4*x^4-9220*x^3)*exp(5)^2)*log(9*x^4-144*x^ 3+864*x^2-2304*x+2305)^4+((-144*x^4+1728*x^3-6912*x^2+9216*x)*exp(5)^2*log (x)^4+(-576*x^5+6912*x^4-27648*x^3+36864*x^2)*exp(5)^2*log(x)^3+((-108*x^5 +1620*x^4-8640*x^3+17280*x^2-12*x-27660)*exp(5)^4+(-864*x^6+10368*x^5-4147 2*x^4+55296*x^3)*exp(5)^2)*log(x)^2+((-216*x^6+3240*x^5-17280*x^4+34560*x^ 3-24*x^2-55320*x)*exp(5)^4+(-576*x^7+6912*x^6-27648*x^5+36864*x^4)*exp(5)^ 2)*log(x)+(-108*x^7+1620*x^6-8640*x^5+17280*x^4-12*x^3-27660*x^2)*exp(5)^4 +(-144*x^8+1728*x^7-6912*x^6+9216*x^5)*exp(5)^2)*log(9*x^4-144*x^3+864*x^2 -2304*x+2305)^3+((-432*x^4+5184*x^3-20736*x^2+27648*x)*exp(5)^4*log(x)^3+( -1296*x^5+15552*x^4-62208*x^3+82944*x^2)*exp(5)^4*log(x)^2+((-108*x^5+1620 *x^4-8640*x^3+17280*x^2-12*x-27660)*exp(5)^6+(-1296*x^6+15552*x^5-62208*x^ 4+82944*x^3)*exp(5)^4)*log(x)+(-108*x^6+1620*x^5-8640*x^4+17280*x^3-12*x^2 -27660*x)*exp(5)^6+(-432*x^7+5184*x^6-20736*x^5+27648*x^4)*exp(5)^4)*log(9 *x^4-144*x^3+864*x^2-2304*x+2305)^2+((-432*x^4+5184*x^3-20736*x^2+27648*x) *exp(5)^6*log(x)^2+(-864*x^5+10368*x^4-41472*x^3+55296*x^2)*exp(5)^6*log(x )+(-36*x^5+540*x^4-2880*x^3+5760*x^2-4*x-9220)*exp(5)^8+(-432*x^6+5184*x^5 -20736*x^4+27648*x^3)*exp(5)^6)*log(9*x^4-144*x^3+864*x^2-2304*x+2305)+(-1 44*x^4+1728*x^3-6912*x^2+9216*x)*exp(5)^8*log(x)+(-144*x^5+1728*x^4-6912*x ^3+9216*x^2)*exp(5)^8)/((9*x^5-144*x^4+864*x^3-2304*x^2+2305*x)*log(x)^5+( 45*x^6-720*x^5+4320*x^4-11520*x^3+11525*x^2)*log(x)^4+(90*x^7-1440*x^6+864 0*x^5-23040*x^4+23050*x^3)*log(x)^3+(90*x^8-1440*x^7+8640*x^6-23040*x^5+23 050*x^4)*log(x)^2+(45*x^9-720*x^8+4320*x^7-11520*x^6+11525*x^5)*log(x)+9*x ^10-144*x^9+864*x^8-2304*x^7+2305*x^6)/log(9*x^4-144*x^3+864*x^2-2304*x+23 05)^5,x, algorithm=\
(4*(x^3*e^10 + 3*x^2*e^10*log(x) + 3*x*e^10*log(x)^2 + e^10*log(x)^3)*log( 9*x^4 - 144*x^3 + 864*x^2 - 2304*x + 2305)^3 + 6*(x^2*e^20 + 2*x*e^20*log( x) + e^20*log(x)^2)*log(9*x^4 - 144*x^3 + 864*x^2 - 2304*x + 2305)^2 + 4*( x*e^30 + e^30*log(x))*log(9*x^4 - 144*x^3 + 864*x^2 - 2304*x + 2305) + e^4 0)/((x^4 + 4*x^3*log(x) + 6*x^2*log(x)^2 + 4*x*log(x)^3 + log(x)^4)*log(9* x^4 - 144*x^3 + 864*x^2 - 2304*x + 2305)^4)
Timed out. \[ \text {the integral} =\text {Timed out} \]
integrate((((-36*x^5+540*x^4-2880*x^3+5760*x^2-4*x-9220)*exp(5)^2*log(x)^3 +(-108*x^6+1620*x^5-8640*x^4+17280*x^3-12*x^2-27660*x)*exp(5)^2*log(x)^2+( -108*x^7+1620*x^6-8640*x^5+17280*x^4-12*x^3-27660*x^2)*exp(5)^2*log(x)+(-3 6*x^8+540*x^7-2880*x^6+5760*x^5-4*x^4-9220*x^3)*exp(5)^2)*log(9*x^4-144*x^ 3+864*x^2-2304*x+2305)^4+((-144*x^4+1728*x^3-6912*x^2+9216*x)*exp(5)^2*log (x)^4+(-576*x^5+6912*x^4-27648*x^3+36864*x^2)*exp(5)^2*log(x)^3+((-108*x^5 +1620*x^4-8640*x^3+17280*x^2-12*x-27660)*exp(5)^4+(-864*x^6+10368*x^5-4147 2*x^4+55296*x^3)*exp(5)^2)*log(x)^2+((-216*x^6+3240*x^5-17280*x^4+34560*x^ 3-24*x^2-55320*x)*exp(5)^4+(-576*x^7+6912*x^6-27648*x^5+36864*x^4)*exp(5)^ 2)*log(x)+(-108*x^7+1620*x^6-8640*x^5+17280*x^4-12*x^3-27660*x^2)*exp(5)^4 +(-144*x^8+1728*x^7-6912*x^6+9216*x^5)*exp(5)^2)*log(9*x^4-144*x^3+864*x^2 -2304*x+2305)^3+((-432*x^4+5184*x^3-20736*x^2+27648*x)*exp(5)^4*log(x)^3+( -1296*x^5+15552*x^4-62208*x^3+82944*x^2)*exp(5)^4*log(x)^2+((-108*x^5+1620 *x^4-8640*x^3+17280*x^2-12*x-27660)*exp(5)^6+(-1296*x^6+15552*x^5-62208*x^ 4+82944*x^3)*exp(5)^4)*log(x)+(-108*x^6+1620*x^5-8640*x^4+17280*x^3-12*x^2 -27660*x)*exp(5)^6+(-432*x^7+5184*x^6-20736*x^5+27648*x^4)*exp(5)^4)*log(9 *x^4-144*x^3+864*x^2-2304*x+2305)^2+((-432*x^4+5184*x^3-20736*x^2+27648*x) *exp(5)^6*log(x)^2+(-864*x^5+10368*x^4-41472*x^3+55296*x^2)*exp(5)^6*log(x )+(-36*x^5+540*x^4-2880*x^3+5760*x^2-4*x-9220)*exp(5)^8+(-432*x^6+5184*x^5 -20736*x^4+27648*x^3)*exp(5)^6)*log(9*x^4-144*x^3+864*x^2-2304*x+2305)+(-1 44*x^4+1728*x^3-6912*x^2+9216*x)*exp(5)^8*log(x)+(-144*x^5+1728*x^4-6912*x ^3+9216*x^2)*exp(5)^8)/((9*x^5-144*x^4+864*x^3-2304*x^2+2305*x)*log(x)^5+( 45*x^6-720*x^5+4320*x^4-11520*x^3+11525*x^2)*log(x)^4+(90*x^7-1440*x^6+864 0*x^5-23040*x^4+23050*x^3)*log(x)^3+(90*x^8-1440*x^7+8640*x^6-23040*x^5+23 050*x^4)*log(x)^2+(45*x^9-720*x^8+4320*x^7-11520*x^6+11525*x^5)*log(x)+9*x ^10-144*x^9+864*x^8-2304*x^7+2305*x^6)/log(9*x^4-144*x^3+864*x^2-2304*x+23 05)^5,x, algorithm=\
Time = 142.25 (sec) , antiderivative size = 117946, normalized size of antiderivative = 4536.38 \[ \text {the integral} =\text {Too large to display} \]
int((log(864*x^2 - 2304*x - 144*x^3 + 9*x^4 + 2305)^2*(exp(20)*(27648*x^4 - 20736*x^5 + 5184*x^6 - 432*x^7) - log(x)*(exp(30)*(12*x - 17280*x^2 + 86 40*x^3 - 1620*x^4 + 108*x^5 + 27660) - exp(20)*(82944*x^3 - 62208*x^4 + 15 552*x^5 - 1296*x^6)) - exp(30)*(27660*x + 12*x^2 - 17280*x^3 + 8640*x^4 - 1620*x^5 + 108*x^6) + exp(20)*log(x)^2*(82944*x^2 - 62208*x^3 + 15552*x^4 - 1296*x^5) + exp(20)*log(x)^3*(27648*x - 20736*x^2 + 5184*x^3 - 432*x^4)) - log(864*x^2 - 2304*x - 144*x^3 + 9*x^4 + 2305)^3*(exp(20)*(27660*x^2 + 12*x^3 - 17280*x^4 + 8640*x^5 - 1620*x^6 + 108*x^7) + log(x)*(exp(20)*(553 20*x + 24*x^2 - 34560*x^3 + 17280*x^4 - 3240*x^5 + 216*x^6) - exp(10)*(368 64*x^4 - 27648*x^5 + 6912*x^6 - 576*x^7)) + log(x)^2*(exp(20)*(12*x - 1728 0*x^2 + 8640*x^3 - 1620*x^4 + 108*x^5 + 27660) - exp(10)*(55296*x^3 - 4147 2*x^4 + 10368*x^5 - 864*x^6)) - exp(10)*(9216*x^5 - 6912*x^6 + 1728*x^7 - 144*x^8) - exp(10)*log(x)^3*(36864*x^2 - 27648*x^3 + 6912*x^4 - 576*x^5) - exp(10)*log(x)^4*(9216*x - 6912*x^2 + 1728*x^3 - 144*x^4)) - log(864*x^2 - 2304*x - 144*x^3 + 9*x^4 + 2305)^4*(exp(10)*(9220*x^3 + 4*x^4 - 5760*x^5 + 2880*x^6 - 540*x^7 + 36*x^8) + exp(10)*log(x)^3*(4*x - 5760*x^2 + 2880* x^3 - 540*x^4 + 36*x^5 + 9220) + exp(10)*log(x)^2*(27660*x + 12*x^2 - 1728 0*x^3 + 8640*x^4 - 1620*x^5 + 108*x^6) + exp(10)*log(x)*(27660*x^2 + 12*x^ 3 - 17280*x^4 + 8640*x^5 - 1620*x^6 + 108*x^7)) + log(864*x^2 - 2304*x - 1 44*x^3 + 9*x^4 + 2305)*(exp(30)*(27648*x^3 - 20736*x^4 + 5184*x^5 - 432*x^ 6) - exp(40)*(4*x - 5760*x^2 + 2880*x^3 - 540*x^4 + 36*x^5 + 9220) + exp(3 0)*log(x)^2*(27648*x - 20736*x^2 + 5184*x^3 - 432*x^4) + exp(30)*log(x)*(5 5296*x^2 - 41472*x^3 + 10368*x^4 - 864*x^5)) + exp(40)*(9216*x^2 - 6912*x^ 3 + 1728*x^4 - 144*x^5) + exp(40)*log(x)*(9216*x - 6912*x^2 + 1728*x^3 - 1 44*x^4))/(log(864*x^2 - 2304*x - 144*x^3 + 9*x^4 + 2305)^5*(log(x)^4*(1152 5*x^2 - 11520*x^3 + 4320*x^4 - 720*x^5 + 45*x^6) + log(x)^3*(23050*x^3 - 2 3040*x^4 + 8640*x^5 - 1440*x^6 + 90*x^7) + log(x)^2*(23050*x^4 - 23040*x^5 + 8640*x^6 - 1440*x^7 + 90*x^8) + log(x)^5*(2305*x - 2304*x^2 + 864*x^3 - 144*x^4 + 9*x^5) + log(x)*(11525*x^5 - 11520*x^6 + 4320*x^7 - 720*x^8 + 4 5*x^9) + 2305*x^6 - 2304*x^7 + 864*x^8 - 144*x^9 + 9*x^10)),x)
((14068988282011852800000*exp(40) + 7988384151172546560000*x*exp(30) + 409 45052556083988480000*x*exp(40) - 2660484767292378316800*x^6*exp(10) - 8315 169121115056373760*x^7*exp(10) + 910357579198648811520*x^8*exp(10) + 20011 037324650563502080*x^9*exp(10) - 790089161774915911680*x^10*exp(10) - 2472 0238100206539767808*x^11*exp(10) + 8868982690649707905024*x^12*exp(10) - 4 790951084850728140800*x^3*exp(20) + 13315940124598896427008*x^13*exp(10) - 12580403605182055710720*x^4*exp(20) - 10386249964596838268928*x^14*exp(10 ) + 6172462325296307109888*x^5*exp(20) + 1320732171062923493376*x^15*exp(1 0) + 30103148966667437998080*x^6*exp(20) - 1648416955872565002240*x^16*exp (10) - 8277689906736610148352*x^7*exp(20) + 4264193441123474079744*x^17*ex p(10) - 32109838454169985351680*x^8*exp(20) - 3092185320073234219008*x^18* exp(10) + 14659075272269900021760*x^9*exp(20) + 599150950931310575616*x^19 *exp(10) + 13884863860552539045888*x^10*exp(20) + 479393099688666267648*x^ 20*exp(10) - 13201318078222178451456*x^11*exp(20) - 373940458411145674752* x^21*exp(10) + 16116839391040634880000*x^2*exp(30) + 676915998482394906624 0*x^12*exp(20) + 83644475413063200768*x^22*exp(10) - 261467942571995037696 00*x^3*exp(30) - 1623379224423161659392*x^13*exp(20) + 3051132719744349388 8*x^23*exp(10) - 45567491886392845271040*x^4*exp(30) - 1029230814006980237 7216*x^14*exp(20) - 32294536155824845824*x^24*exp(10) + 620280107798080625 04960*x^5*exp(30) + 19175253433638693249024*x^15*exp(20) + 141238248584...