Integrand size = 1697, antiderivative size = 28 \[ \text {the integral} =\left (-2+\left (x+\frac {x^2}{\left (x+x^2\right ) (1+x-\log (5))}\right )^4\right )^2 \]
Leaf count is larger than twice the leaf count of optimal. \(1517\) vs. \(2(28)=56\).
Time = 2.76 (sec) , antiderivative size = 1517, normalized size of antiderivative = 54.18 \[ \text {the integral} =\text {Too large to display} \]
Integrate[(256*x^3 + 3328*x^4 + 20736*x^5 + 82560*x^6 + 233984*x^7 + 49708 8*x^8 + 808320*x^9 + 996512*x^10 + 866544*x^11 + 356640*x^12 - 369072*x^13 - 1002816*x^14 - 1296032*x^15 - 1207680*x^16 - 884448*x^17 - 523680*x^18 - 252432*x^19 - 98496*x^20 - 30576*x^21 - 7312*x^22 - 1272*x^23 - 144*x^24 - 8*x^25 + (-1792*x^3 - 22272*x^4 - 132480*x^5 - 502336*x^6 - 1352576*x^7 - 2718720*x^8 - 4151456*x^9 - 4734416*x^10 - 3653904*x^11 - 952528*x^12 + 2287104*x^13 + 4629792*x^14 + 5263520*x^15 + 4403552*x^16 + 2894688*x^17 + 1525072*x^18 + 644016*x^19 + 214896*x^20 + 54960*x^21 + 10184*x^22 + 122 4*x^23 + 72*x^24)*Log[5] + (5504*x^3 + 65408*x^4 + 371136*x^5 + 1337760*x^ 6 + 3411200*x^7 + 6457392*x^8 + 9198320*x^9 + 9595520*x^10 + 6366336*x^11 + 375072*x^12 - 5659552*x^13 - 9084192*x^14 - 9080256*x^15 - 6771984*x^16 - 3951792*x^17 - 1823216*x^18 - 658768*x^19 - 181272*x^20 - 35960*x^21 - 4 608*x^22 - 288*x^23)*Log[5]^2 + (-9728*x^3 - 110592*x^4 - 598176*x^5 - 204 5488*x^6 - 4921888*x^7 - 8728272*x^8 - 11506656*x^9 - 10817504*x^10 - 5840 736*x^11 + 1446496*x^12 + 7517632*x^13 + 9906576*x^14 + 8684032*x^15 + 571 8832*x^16 + 2918160*x^17 + 1152200*x^18 + 343616*x^19 + 73416*x^20 + 10080 *x^21 + 672*x^22)*Log[5]^3 + (10896*x^3 + 118608*x^4 + 611136*x^5 + 197806 4*x^6 + 4472960*x^7 + 7384608*x^8 + 8921456*x^9 + 7401248*x^10 + 2904672*x ^11 - 2422544*x^12 - 5968528*x^13 - 6586272*x^14 - 5036528*x^15 - 2889992* x^16 - 1261512*x^17 - 411432*x^18 - 95368*x^19 - 14112*x^20 - 1008*x^21)*L og[5]^4 + (-8016*x^3 - 83664*x^4 - 410400*x^5 - 1254016*x^6 - 2651952*x^7 - 4045104*x^8 - 4421536*x^9 - 3134704*x^10 - 636096*x^11 + 1765856*x^12 + 2948848*x^13 + 2752008*x^14 + 1818768*x^15 + 891296*x^16 + 321552*x^17 + 8 1592*x^18 + 13104*x^19 + 1008*x^20)*Log[5]^5 + (3872*x^3 + 38816*x^4 + 181 152*x^5 + 520928*x^6 + 1024160*x^7 + 1429488*x^8 + 1389264*x^9 + 796656*x^ 10 - 58512*x^11 - 713944*x^12 - 906808*x^13 - 717024*x^14 - 402976*x^15 - 163240*x^16 - 45864*x^17 - 8064*x^18 - 672*x^19)*Log[5]^6 + (-1184*x^3 - 1 1424*x^4 - 50688*x^5 - 136656*x^6 - 247904*x^7 - 312624*x^8 - 263376*x^9 - 109016*x^10 + 63744*x^11 + 164344*x^12 + 166928*x^13 + 111048*x^14 + 5155 2*x^15 + 16280*x^16 + 3168*x^17 + 288*x^18)*Log[5]^7 + (208*x^3 + 1936*x^4 + 8160*x^5 + 20528*x^6 + 34024*x^7 + 38088*x^8 + 26720*x^9 + 5624*x^10 - 12792*x^11 - 20008*x^12 - 16600*x^13 - 9096*x^14 - 3296*x^15 - 720*x^16 - 72*x^17)*Log[5]^8 + (-16*x^3 - 144*x^4 - 576*x^5 - 1344*x^6 - 2008*x^7 - 1 944*x^8 - 1056*x^9 + 96*x^10 + 864*x^11 + 992*x^12 + 672*x^13 + 288*x^14 + 72*x^15 + 8*x^16)*Log[5]^9)/(-1 - 18*x - 153*x^2 - 816*x^3 - 3060*x^4 - 8 568*x^5 - 18564*x^6 - 31824*x^7 - 43758*x^8 - 48620*x^9 - 43758*x^10 - 318 24*x^11 - 18564*x^12 - 8568*x^13 - 3060*x^14 - 816*x^15 - 153*x^16 - 18*x^ 17 - x^18 + (9 + 153*x + 1224*x^2 + 6120*x^3 + 21420*x^4 + 55692*x^5 + 111 384*x^6 + 175032*x^7 + 218790*x^8 + 218790*x^9 + 175032*x^10 + 111384*x^11 + 55692*x^12 + 21420*x^13 + 6120*x^14 + 1224*x^15 + 153*x^16 + 9*x^17)*Lo g[5] + (-36 - 576*x - 4320*x^2 - 20160*x^3 - 65520*x^4 - 157248*x^5 - 2882 88*x^6 - 411840*x^7 - 463320*x^8 - 411840*x^9 - 288288*x^10 - 157248*x^11 - 65520*x^12 - 20160*x^13 - 4320*x^14 - 576*x^15 - 36*x^16)*Log[5]^2 + (84 + 1260*x + 8820*x^2 + 38220*x^3 + 114660*x^4 + 252252*x^5 + 420420*x^6 + 540540*x^7 + 540540*x^8 + 420420*x^9 + 252252*x^10 + 114660*x^11 + 38220*x ^12 + 8820*x^13 + 1260*x^14 + 84*x^15)*Log[5]^3 + (-126 - 1764*x - 11466*x ^2 - 45864*x^3 - 126126*x^4 - 252252*x^5 - 378378*x^6 - 432432*x^7 - 37837 8*x^8 - 252252*x^9 - 126126*x^10 - 45864*x^11 - 11466*x^12 - 1764*x^13 - 1 26*x^14)*Log[5]^4 + (126 + 1638*x + 9828*x^2 + 36036*x^3 + 90090*x^4 + 162 162*x^5 + 216216*x^6 + 216216*x^7 + 162162*x^8 + 90090*x^9 + 36036*x^10 + 9828*x^11 + 1638*x^12 + 126*x^13)*Log[5]^5 + (-84 - 1008*x - 5544*x^2 - 18 480*x^3 - 41580*x^4 - 66528*x^5 - 77616*x^6 - 66528*x^7 - 41580*x^8 - 1848 0*x^9 - 5544*x^10 - 1008*x^11 - 84*x^12)*Log[5]^6 + (36 + 396*x + 1980*x^2 + 5940*x^3 + 11880*x^4 + 16632*x^5 + 16632*x^6 + 11880*x^7 + 5940*x^8 + 1 980*x^9 + 396*x^10 + 36*x^11)*Log[5]^7 + (-9 - 90*x - 405*x^2 - 1080*x^3 - 1890*x^4 - 2268*x^5 - 1890*x^6 - 1080*x^7 - 405*x^8 - 90*x^9 - 9*x^10)*Lo g[5]^8 + (1 + 9*x + 36*x^2 + 84*x^3 + 126*x^4 + 126*x^5 + 84*x^6 + 36*x^7 + 9*x^8 + x^9)*Log[5]^9),x]
-((-x^24 + 8*x^23*(-2 + Log[5]) + 56*x^21*(-3 + Log[5])*(-2 + Log[5])^2 - 4*x^22*(32 - 30*Log[5] + 7*Log[5]^2) + x^20*(-2572 + 4368*Log[5] - 2716*Lo g[5]^2 + 728*Log[5]^3 - 70*Log[5]^4) + 8*x^19*(-944 + 1928*Log[5] - 1526*L og[5]^2 + 581*Log[5]^3 - 105*Log[5]^4 + 7*Log[5]^5) - 4*x^18*(4356 - 10352 *Log[5] + 9856*Log[5]^2 - 4774*Log[5]^3 + 1225*Log[5]^4 - 154*Log[5]^5 + 7 *Log[5]^6) + 8*x^17*(-3964 + 10766*Log[5] - 11956*Log[5]^2 + 6972*Log[5]^3 - 2275*Log[5]^4 + 406*Log[5]^5 - 35*Log[5]^6 + Log[5]^7) + x^16*(-40885 + 130520*Log[5] - 169276*Log[5]^2 + 116328*Log[5]^3 - 45784*Log[5]^4 + 1031 2*Log[5]^5 - 1232*Log[5]^6 + 64*Log[5]^7) + (-1 + Log[5])^8*(3699 - 7256*L og[5] + 6900*Log[5]^2 - 4072*Log[5]^3 + 1606*Log[5]^4 - 440*Log[5]^5 + 84* Log[5]^6 - 8*Log[5]^7 + Log[5]^8) + 8*x*(-1 + Log[5])^7*(-7398 + 18211*Log [5] - 21056*Log[5]^2 + 15044*Log[5]^3 - 7284*Log[5]^4 + 2486*Log[5]^5 - 60 8*Log[5]^6 + 100*Log[5]^7 - 10*Log[5]^8 + Log[5]^9) - 8*x^15*(-1802 - 1891 *Log[5] + 8848*Log[5]^2 - 8854*Log[5]^3 + 3846*Log[5]^4 - 573*Log[5]^5 - 1 32*Log[5]^6 + 63*Log[5]^7 - 9*Log[5]^8 + Log[5]^9) + 4*x^14*(105462 - 3012 70*Log[5] + 398331*Log[5]^2 - 328404*Log[5]^3 + 189520*Log[5]^4 - 80210*Lo g[5]^5 + 25121*Log[5]^6 - 5658*Log[5]^7 + 851*Log[5]^8 - 86*Log[5]^9 + 7*L og[5]^10) + 4*x^2*(-1 + Log[5])^6*(110970 - 328650*Log[5] + 450573*Log[5]^ 2 - 379952*Log[5]^3 + 218640*Log[5]^4 - 89884*Log[5]^5 + 26962*Log[5]^6 - 5840*Log[5]^7 + 858*Log[5]^8 - 86*Log[5]^9 + 7*Log[5]^10) + 56*x^3*(-1 ...
Leaf count is larger than twice the leaf count of optimal. \(1192\) vs. \(2(28)=56\).
Time = 18.60 (sec) , antiderivative size = 1192, normalized size of antiderivative = 42.57, number of steps used = 2, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.001, Rules used = {2462, 2009}
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 {-8 x^{25}-144 x^{24}-1272 x^{23}-7312 x^{22}-30576 x^{21}-98496 x^{20}-252432 x^{19}-523680 x^{18}-884448 x^{17}-1207680 x^{16}-1296032 x^{15}-1002816 x^{14}-369072 x^{13}+356640 x^{12}+866544 x^{11}+996512 x^{10}+808320 x^9+497088 x^8+233984 x^7+82560 x^6+20736 x^5+3328 x^4+256 x^3+\left (8 x^{16}+72 x^{15}+288 x^{14}+672 x^{13}+992 x^{12}+864 x^{11}+96 x^{10}-1056 x^9-1944 x^8-2008 x^7-1344 x^6-576 x^5-144 x^4-16 x^3\right ) \log ^9(5)+\left (-72 x^{17}-720 x^{16}-3296 x^{15}-9096 x^{14}-16600 x^{13}-20008 x^{12}-12792 x^{11}+5624 x^{10}+26720 x^9+38088 x^8+34024 x^7+20528 x^6+8160 x^5+1936 x^4+208 x^3\right ) \log ^8(5)+\left (288 x^{18}+3168 x^{17}+16280 x^{16}+51552 x^{15}+111048 x^{14}+166928 x^{13}+164344 x^{12}+63744 x^{11}-109016 x^{10}-263376 x^9-312624 x^8-247904 x^7-136656 x^6-50688 x^5-11424 x^4-1184 x^3\right ) \log ^7(5)+\left (-672 x^{19}-8064 x^{18}-45864 x^{17}-163240 x^{16}-402976 x^{15}-717024 x^{14}-906808 x^{13}-713944 x^{12}-58512 x^{11}+796656 x^{10}+1389264 x^9+1429488 x^8+1024160 x^7+520928 x^6+181152 x^5+38816 x^4+3872 x^3\right ) \log ^6(5)+\left (1008 x^{20}+13104 x^{19}+81592 x^{18}+321552 x^{17}+891296 x^{16}+1818768 x^{15}+2752008 x^{14}+2948848 x^{13}+1765856 x^{12}-636096 x^{11}-3134704 x^{10}-4421536 x^9-4045104 x^8-2651952 x^7-1254016 x^6-410400 x^5-83664 x^4-8016 x^3\right ) \log ^5(5)+\left (-1008 x^{21}-14112 x^{20}-95368 x^{19}-411432 x^{18}-1261512 x^{17}-2889992 x^{16}-5036528 x^{15}-6586272 x^{14}-5968528 x^{13}-2422544 x^{12}+2904672 x^{11}+7401248 x^{10}+8921456 x^9+7384608 x^8+4472960 x^7+1978064 x^6+611136 x^5+118608 x^4+10896 x^3\right ) \log ^4(5)+\left (672 x^{22}+10080 x^{21}+73416 x^{20}+343616 x^{19}+1152200 x^{18}+2918160 x^{17}+5718832 x^{16}+8684032 x^{15}+9906576 x^{14}+7517632 x^{13}+1446496 x^{12}-5840736 x^{11}-10817504 x^{10}-11506656 x^9-8728272 x^8-4921888 x^7-2045488 x^6-598176 x^5-110592 x^4-9728 x^3\right ) \log ^3(5)+\left (-288 x^{23}-4608 x^{22}-35960 x^{21}-181272 x^{20}-658768 x^{19}-1823216 x^{18}-3951792 x^{17}-6771984 x^{16}-9080256 x^{15}-9084192 x^{14}-5659552 x^{13}+375072 x^{12}+6366336 x^{11}+9595520 x^{10}+9198320 x^9+6457392 x^8+3411200 x^7+1337760 x^6+371136 x^5+65408 x^4+5504 x^3\right ) \log ^2(5)+\left (72 x^{24}+1224 x^{23}+10184 x^{22}+54960 x^{21}+214896 x^{20}+644016 x^{19}+1525072 x^{18}+2894688 x^{17}+4403552 x^{16}+5263520 x^{15}+4629792 x^{14}+2287104 x^{13}-952528 x^{12}-3653904 x^{11}-4734416 x^{10}-4151456 x^9-2718720 x^8-1352576 x^7-502336 x^6-132480 x^5-22272 x^4-1792 x^3\right ) \log (5)}{-x^{18}-18 x^{17}-153 x^{16}-816 x^{15}-3060 x^{14}-8568 x^{13}-18564 x^{12}-31824 x^{11}-43758 x^{10}-48620 x^9-43758 x^8-31824 x^7-18564 x^6-8568 x^5-3060 x^4-816 x^3-153 x^2-18 x+\left (x^9+9 x^8+36 x^7+84 x^6+126 x^5+126 x^4+84 x^3+36 x^2+9 x+1\right ) \log ^9(5)+\left (-9 x^{10}-90 x^9-405 x^8-1080 x^7-1890 x^6-2268 x^5-1890 x^4-1080 x^3-405 x^2-90 x-9\right ) \log ^8(5)+\left (36 x^{11}+396 x^{10}+1980 x^9+5940 x^8+11880 x^7+16632 x^6+16632 x^5+11880 x^4+5940 x^3+1980 x^2+396 x+36\right ) \log ^7(5)+\left (-84 x^{12}-1008 x^{11}-5544 x^{10}-18480 x^9-41580 x^8-66528 x^7-77616 x^6-66528 x^5-41580 x^4-18480 x^3-5544 x^2-1008 x-84\right ) \log ^6(5)+\left (126 x^{13}+1638 x^{12}+9828 x^{11}+36036 x^{10}+90090 x^9+162162 x^8+216216 x^7+216216 x^6+162162 x^5+90090 x^4+36036 x^3+9828 x^2+1638 x+126\right ) \log ^5(5)+\left (-126 x^{14}-1764 x^{13}-11466 x^{12}-45864 x^{11}-126126 x^{10}-252252 x^9-378378 x^8-432432 x^7-378378 x^6-252252 x^5-126126 x^4-45864 x^3-11466 x^2-1764 x-126\right ) \log ^4(5)+\left (84 x^{15}+1260 x^{14}+8820 x^{13}+38220 x^{12}+114660 x^{11}+252252 x^{10}+420420 x^9+540540 x^8+540540 x^7+420420 x^6+252252 x^5+114660 x^4+38220 x^3+8820 x^2+1260 x+84\right ) \log ^3(5)+\left (-36 x^{16}-576 x^{15}-4320 x^{14}-20160 x^{13}-65520 x^{12}-157248 x^{11}-288288 x^{10}-411840 x^9-463320 x^8-411840 x^7-288288 x^6-157248 x^5-65520 x^4-20160 x^3-4320 x^2-576 x-36\right ) \log ^2(5)+\left (9 x^{17}+153 x^{16}+1224 x^{15}+6120 x^{14}+21420 x^{13}+55692 x^{12}+111384 x^{11}+175032 x^{10}+218790 x^9+218790 x^8+175032 x^7+111384 x^6+55692 x^5+21420 x^4+6120 x^3+1224 x^2+153 x+9\right ) \log (5)-1} \, dx\) |
| \(\Big \downarrow \) 2462 |
| \(\displaystyle \int \left (8 x^7+48 x^5+40 (-2+\log (5)) x^4+32 \left (6-3 \log (5)+\log ^2(5)\right ) x^3+24 (2-\log (5)) \left (-9+2 \log (5)-\log ^2(5)\right ) x^2+8 \left (90-90 \log (5)+41 \log ^2(5)-10 \log ^3(5)+2 \log ^4(5)\right ) x+\frac {8 (1-\log (5)) \left (429-1287 \log (5)+561 \log ^2(5)+1947 \log ^3(5)-2001 \log ^4(5)-1077 \log ^5(5)+1989 \log ^6(5)+224 \log ^7(5)-1109 \log ^8(5)-25 \log ^9(5)+423 \log ^{10}(5)+79 \log ^{11}(5)-104 \log ^{12}(5)-120 \log ^{13}(5)-119 \log ^{14}(5)+527 \log ^{15}(5)-596 \log ^{16}(5)+376 \log ^{17}(5)-154 \log ^{18}(5)+42 \log ^{19}(5)-7 \log ^{20}(5)+\log ^{21}(5)\right )}{(x-\log (5)+1)^2 \log ^{15}(5)}-\frac {8 (-1+\log (5))^2 \left (429-990 \log (5)-99 \log ^2(5)+1884 \log ^3(5)-837 \log ^4(5)-1598 \log ^5(5)+1120 \log ^6(5)+868 \log ^7(5)-745 \log ^8(5)-430 \log ^9(5)+327 \log ^{10}(5)+300 \log ^{11}(5)-94 \log ^{12}(5)-520 \log ^{13}(5)+694 \log ^{14}(5)-448 \log ^{15}(5)+175 \log ^{16}(5)-42 \log ^{17}(5)+7 \log ^{18}(5)\right )}{(x-\log (5)+1)^3 \log ^{14}(5)}-\frac {24 (-1+\log (5))^3 \left (99-165 \log (5)-120 \log ^2(5)+360 \log ^3(5)+\log ^4(5)-364 \log ^5(5)+91 \log ^6(5)+245 \log ^7(5)-93 \log ^8(5)-147 \log ^9(5)+72 \log ^{10}(5)+124 \log ^{11}(5)-175 \log ^{12}(5)+105 \log ^{13}(5)-35 \log ^{14}(5)+7 \log ^{15}(5)\right )}{(x-\log (5)+1)^4 \log ^{13}(5)}-\frac {8 \left (429-1716 \log (5)+1848 \log ^2(5)+1386 \log ^3(5)-3948 \log ^4(5)+924 \log ^5(5)+3066 \log ^6(5)-1765 \log ^7(5)-1333 \log ^8(5)+1084 \log ^9(5)+448 \log ^{10}(5)-344 \log ^{11}(5)-183 \log ^{12}(5)-16 \log ^{13}(5)+\log ^{14}(5)\right )}{(x+1)^2 \log ^{15}(5)}-\frac {8 (-1+\log (5))^4 \left (165-180 \log (5)-282 \log ^2(5)+444 \log ^3(5)+182 \log ^4(5)-504 \log ^5(5)+392 \log ^7(5)-121 \log ^8(5)-252 \log ^9(5)+294 \log ^{10}(5)-140 \log ^{11}(5)+35 \log ^{12}(5)\right )}{(x-\log (5)+1)^5 \log ^{12}(5)}-\frac {8 \left (429-1584 \log (5)+1386 \log ^2(5)+1680 \log ^3(5)-3192 \log ^4(5)-112 \log ^5(5)+2653 \log ^6(5)-560 \log ^7(5)-1305 \log ^8(5)+240 \log ^9(5)+454 \log ^{10}(5)+96 \log ^{11}(5)+\log ^{12}(5)\right )}{(x+1)^3 \log ^{14}(5)}+\frac {24 \left (-99+330 \log (5)-210 \log ^2(5)-420 \log ^3(5)+518 \log ^4(5)+203 \log ^5(5)-413 \log ^6(5)-84 \log ^7(5)+163 \log ^8(5)+68 \log ^9(5)+5 \log ^{10}(5)\right )}{(x+1)^4 \log ^{13}(5)}-\frac {40 (-1+\log (5))^5 \left (15-9 \log (5)-27 \log ^2(5)+28 \log ^3(5)+21 \log ^4(5)-35 \log ^5(5)+28 \log ^7(5)-21 \log ^8(5)+7 \log ^9(5)\right )}{(x-\log (5)+1)^6 \log ^{11}(5)}-\frac {8 \left (165-480 \log (5)+168 \log ^2(5)+672 \log ^3(5)-455 \log ^4(5)-448 \log ^5(5)+252 \log ^6(5)+224 \log ^7(5)+33 \log ^8(5)\right )}{(x+1)^5 \log ^{12}(5)}+\frac {40 \left (-15+36 \log (5)-49 \log ^3(5)+7 \log ^4(5)+28 \log ^5(5)+7 \log ^6(5)\right )}{(x+1)^6 \log ^{11}(5)}-\frac {24 (-1+\log (5))^6 \left (9-2 \log (5)-14 \log ^2(5)+12 \log ^3(5)+9 \log ^4(5)-14 \log ^5(5)+7 \log ^6(5)\right )}{(x-\log (5)+1)^7 \log ^{10}(5)}-\frac {24 \left (9-16 \log (5)-7 \log ^2(5)+16 \log ^3(5)+7 \log ^4(5)\right )}{(x+1)^7 \log ^{10}(5)}+8 (2-\log (5)) \left (-57+41 \log (5)-21 \log ^2(5)+4 \log ^3(5)-\log ^4(5)\right )-\frac {56 (-1+\log (5))^7 \left (1-\log ^2(5)+\log ^3(5)\right )}{(x-\log (5)+1)^8 \log ^9(5)}+\frac {56 \left (-1+\log (5)+\log ^2(5)\right )}{(x+1)^8 \log ^9(5)}-\frac {8}{(x+1)^9 \log ^8(5)}-\frac {8 (-1+\log (5))^8}{(x-\log (5)+1)^9 \log ^8(5)}\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle x^8+8 x^6-8 (2-\log (5)) x^5+8 \left (6-3 \log (5)+\log ^2(5)\right ) x^4-8 (2-\log (5)) \left (9-2 \log (5)+\log ^2(5)\right ) x^3+4 \left (90-90 \log (5)+41 \log ^2(5)-10 \log ^3(5)+2 \log ^4(5)\right ) x^2-8 (2-\log (5)) \left (57-41 \log (5)+21 \log ^2(5)-4 \log ^3(5)+\log ^4(5)\right ) x-\frac {8 (1-\log (5)) \left (429-1287 \log (5)+561 \log ^2(5)+1947 \log ^3(5)-2001 \log ^4(5)-1077 \log ^5(5)+1989 \log ^6(5)+224 \log ^7(5)-1109 \log ^8(5)-25 \log ^9(5)+423 \log ^{10}(5)+79 \log ^{11}(5)-104 \log ^{12}(5)-120 \log ^{13}(5)-119 \log ^{14}(5)+527 \log ^{15}(5)-596 \log ^{16}(5)+376 \log ^{17}(5)-154 \log ^{18}(5)+42 \log ^{19}(5)-7 \log ^{20}(5)+\log ^{21}(5)\right )}{(x-\log (5)+1) \log ^{15}(5)}+\frac {4 (1-\log (5))^2 \left (429-990 \log (5)-99 \log ^2(5)+1884 \log ^3(5)-837 \log ^4(5)-1598 \log ^5(5)+1120 \log ^6(5)+868 \log ^7(5)-745 \log ^8(5)-430 \log ^9(5)+327 \log ^{10}(5)+300 \log ^{11}(5)-94 \log ^{12}(5)-520 \log ^{13}(5)+694 \log ^{14}(5)-448 \log ^{15}(5)+175 \log ^{16}(5)-42 \log ^{17}(5)+7 \log ^{18}(5)\right )}{(x-\log (5)+1)^2 \log ^{14}(5)}-\frac {8 (1-\log (5))^3 \left (99-165 \log (5)-120 \log ^2(5)+360 \log ^3(5)+\log ^4(5)-364 \log ^5(5)+91 \log ^6(5)+245 \log ^7(5)-93 \log ^8(5)-147 \log ^9(5)+72 \log ^{10}(5)+124 \log ^{11}(5)-175 \log ^{12}(5)+105 \log ^{13}(5)-35 \log ^{14}(5)+7 \log ^{15}(5)\right )}{(x-\log (5)+1)^3 \log ^{13}(5)}+\frac {8 \left (429-1716 \log (5)+1848 \log ^2(5)+1386 \log ^3(5)-3948 \log ^4(5)+924 \log ^5(5)+3066 \log ^6(5)-1765 \log ^7(5)-1333 \log ^8(5)+1084 \log ^9(5)+448 \log ^{10}(5)-344 \log ^{11}(5)-183 \log ^{12}(5)-16 \log ^{13}(5)+\log ^{14}(5)\right )}{(x+1) \log ^{15}(5)}+\frac {2 (1-\log (5))^4 \left (165-180 \log (5)-282 \log ^2(5)+444 \log ^3(5)+182 \log ^4(5)-504 \log ^5(5)+392 \log ^7(5)-121 \log ^8(5)-252 \log ^9(5)+294 \log ^{10}(5)-140 \log ^{11}(5)+35 \log ^{12}(5)\right )}{(x-\log (5)+1)^4 \log ^{12}(5)}+\frac {4 \left (429-1584 \log (5)+1386 \log ^2(5)+1680 \log ^3(5)-3192 \log ^4(5)-112 \log ^5(5)+2653 \log ^6(5)-560 \log ^7(5)-1305 \log ^8(5)+240 \log ^9(5)+454 \log ^{10}(5)+96 \log ^{11}(5)+\log ^{12}(5)\right )}{(x+1)^2 \log ^{14}(5)}+\frac {8 \left (99-330 \log (5)+210 \log ^2(5)+420 \log ^3(5)-518 \log ^4(5)-203 \log ^5(5)+413 \log ^6(5)+84 \log ^7(5)-163 \log ^8(5)-68 \log ^9(5)-5 \log ^{10}(5)\right )}{(x+1)^3 \log ^{13}(5)}-\frac {8 (1-\log (5))^5 \left (15-9 \log (5)-27 \log ^2(5)+28 \log ^3(5)+21 \log ^4(5)-35 \log ^5(5)+28 \log ^7(5)-21 \log ^8(5)+7 \log ^9(5)\right )}{(x-\log (5)+1)^5 \log ^{11}(5)}+\frac {2 \left (165-480 \log (5)+168 \log ^2(5)+672 \log ^3(5)-455 \log ^4(5)-448 \log ^5(5)+252 \log ^6(5)+224 \log ^7(5)+33 \log ^8(5)\right )}{(x+1)^4 \log ^{12}(5)}+\frac {4 (1-\log (5))^6 \left (9-2 \log (5)-14 \log ^2(5)+12 \log ^3(5)+9 \log ^4(5)-14 \log ^5(5)+7 \log ^6(5)\right )}{(x-\log (5)+1)^6 \log ^{10}(5)}+\frac {8 \left (15-36 \log (5)+49 \log ^3(5)-7 \log ^4(5)-28 \log ^5(5)-7 \log ^6(5)\right )}{(x+1)^5 \log ^{11}(5)}+\frac {4 \left (9-16 \log (5)-7 \log ^2(5)+16 \log ^3(5)+7 \log ^4(5)\right )}{(x+1)^6 \log ^{10}(5)}-\frac {8 (1-\log (5))^7 \left (1-\log ^2(5)+\log ^3(5)\right )}{(x-\log (5)+1)^7 \log ^9(5)}+\frac {8 \left (1-\log (5)-\log ^2(5)\right )}{(x+1)^7 \log ^9(5)}+\frac {1}{(x+1)^8 \log ^8(5)}+\frac {(1-\log (5))^8}{(x-\log (5)+1)^8 \log ^8(5)}\) |
Int[(256*x^3 + 3328*x^4 + 20736*x^5 + 82560*x^6 + 233984*x^7 + 497088*x^8 + 808320*x^9 + 996512*x^10 + 866544*x^11 + 356640*x^12 - 369072*x^13 - 100 2816*x^14 - 1296032*x^15 - 1207680*x^16 - 884448*x^17 - 523680*x^18 - 2524 32*x^19 - 98496*x^20 - 30576*x^21 - 7312*x^22 - 1272*x^23 - 144*x^24 - 8*x ^25 + (-1792*x^3 - 22272*x^4 - 132480*x^5 - 502336*x^6 - 1352576*x^7 - 271 8720*x^8 - 4151456*x^9 - 4734416*x^10 - 3653904*x^11 - 952528*x^12 + 22871 04*x^13 + 4629792*x^14 + 5263520*x^15 + 4403552*x^16 + 2894688*x^17 + 1525 072*x^18 + 644016*x^19 + 214896*x^20 + 54960*x^21 + 10184*x^22 + 1224*x^23 + 72*x^24)*Log[5] + (5504*x^3 + 65408*x^4 + 371136*x^5 + 1337760*x^6 + 34 11200*x^7 + 6457392*x^8 + 9198320*x^9 + 9595520*x^10 + 6366336*x^11 + 3750 72*x^12 - 5659552*x^13 - 9084192*x^14 - 9080256*x^15 - 6771984*x^16 - 3951 792*x^17 - 1823216*x^18 - 658768*x^19 - 181272*x^20 - 35960*x^21 - 4608*x^ 22 - 288*x^23)*Log[5]^2 + (-9728*x^3 - 110592*x^4 - 598176*x^5 - 2045488*x ^6 - 4921888*x^7 - 8728272*x^8 - 11506656*x^9 - 10817504*x^10 - 5840736*x^ 11 + 1446496*x^12 + 7517632*x^13 + 9906576*x^14 + 8684032*x^15 + 5718832*x ^16 + 2918160*x^17 + 1152200*x^18 + 343616*x^19 + 73416*x^20 + 10080*x^21 + 672*x^22)*Log[5]^3 + (10896*x^3 + 118608*x^4 + 611136*x^5 + 1978064*x^6 + 4472960*x^7 + 7384608*x^8 + 8921456*x^9 + 7401248*x^10 + 2904672*x^11 - 2422544*x^12 - 5968528*x^13 - 6586272*x^14 - 5036528*x^15 - 2889992*x^16 - 1261512*x^17 - 411432*x^18 - 95368*x^19 - 14112*x^20 - 1008*x^21)*Log[5]^ 4 + (-8016*x^3 - 83664*x^4 - 410400*x^5 - 1254016*x^6 - 2651952*x^7 - 4045 104*x^8 - 4421536*x^9 - 3134704*x^10 - 636096*x^11 + 1765856*x^12 + 294884 8*x^13 + 2752008*x^14 + 1818768*x^15 + 891296*x^16 + 321552*x^17 + 81592*x ^18 + 13104*x^19 + 1008*x^20)*Log[5]^5 + (3872*x^3 + 38816*x^4 + 181152*x^ 5 + 520928*x^6 + 1024160*x^7 + 1429488*x^8 + 1389264*x^9 + 796656*x^10 - 5 8512*x^11 - 713944*x^12 - 906808*x^13 - 717024*x^14 - 402976*x^15 - 163240 *x^16 - 45864*x^17 - 8064*x^18 - 672*x^19)*Log[5]^6 + (-1184*x^3 - 11424*x ^4 - 50688*x^5 - 136656*x^6 - 247904*x^7 - 312624*x^8 - 263376*x^9 - 10901 6*x^10 + 63744*x^11 + 164344*x^12 + 166928*x^13 + 111048*x^14 + 51552*x^15 + 16280*x^16 + 3168*x^17 + 288*x^18)*Log[5]^7 + (208*x^3 + 1936*x^4 + 816 0*x^5 + 20528*x^6 + 34024*x^7 + 38088*x^8 + 26720*x^9 + 5624*x^10 - 12792* x^11 - 20008*x^12 - 16600*x^13 - 9096*x^14 - 3296*x^15 - 720*x^16 - 72*x^1 7)*Log[5]^8 + (-16*x^3 - 144*x^4 - 576*x^5 - 1344*x^6 - 2008*x^7 - 1944*x^ 8 - 1056*x^9 + 96*x^10 + 864*x^11 + 992*x^12 + 672*x^13 + 288*x^14 + 72*x^ 15 + 8*x^16)*Log[5]^9)/(-1 - 18*x - 153*x^2 - 816*x^3 - 3060*x^4 - 8568*x^ 5 - 18564*x^6 - 31824*x^7 - 43758*x^8 - 48620*x^9 - 43758*x^10 - 31824*x^1 1 - 18564*x^12 - 8568*x^13 - 3060*x^14 - 816*x^15 - 153*x^16 - 18*x^17 - x ^18 + (9 + 153*x + 1224*x^2 + 6120*x^3 + 21420*x^4 + 55692*x^5 + 111384*x^ 6 + 175032*x^7 + 218790*x^8 + 218790*x^9 + 175032*x^10 + 111384*x^11 + 556 92*x^12 + 21420*x^13 + 6120*x^14 + 1224*x^15 + 153*x^16 + 9*x^17)*Log[5] + (-36 - 576*x - 4320*x^2 - 20160*x^3 - 65520*x^4 - 157248*x^5 - 288288*x^6 - 411840*x^7 - 463320*x^8 - 411840*x^9 - 288288*x^10 - 157248*x^11 - 6552 0*x^12 - 20160*x^13 - 4320*x^14 - 576*x^15 - 36*x^16)*Log[5]^2 + (84 + 126 0*x + 8820*x^2 + 38220*x^3 + 114660*x^4 + 252252*x^5 + 420420*x^6 + 540540 *x^7 + 540540*x^8 + 420420*x^9 + 252252*x^10 + 114660*x^11 + 38220*x^12 + 8820*x^13 + 1260*x^14 + 84*x^15)*Log[5]^3 + (-126 - 1764*x - 11466*x^2 - 4 5864*x^3 - 126126*x^4 - 252252*x^5 - 378378*x^6 - 432432*x^7 - 378378*x^8 - 252252*x^9 - 126126*x^10 - 45864*x^11 - 11466*x^12 - 1764*x^13 - 126*x^1 4)*Log[5]^4 + (126 + 1638*x + 9828*x^2 + 36036*x^3 + 90090*x^4 + 162162*x^ 5 + 216216*x^6 + 216216*x^7 + 162162*x^8 + 90090*x^9 + 36036*x^10 + 9828*x ^11 + 1638*x^12 + 126*x^13)*Log[5]^5 + (-84 - 1008*x - 5544*x^2 - 18480*x^ 3 - 41580*x^4 - 66528*x^5 - 77616*x^6 - 66528*x^7 - 41580*x^8 - 18480*x^9 - 5544*x^10 - 1008*x^11 - 84*x^12)*Log[5]^6 + (36 + 396*x + 1980*x^2 + 594 0*x^3 + 11880*x^4 + 16632*x^5 + 16632*x^6 + 11880*x^7 + 5940*x^8 + 1980*x^ 9 + 396*x^10 + 36*x^11)*Log[5]^7 + (-9 - 90*x - 405*x^2 - 1080*x^3 - 1890* x^4 - 2268*x^5 - 1890*x^6 - 1080*x^7 - 405*x^8 - 90*x^9 - 9*x^10)*Log[5]^8 + (1 + 9*x + 36*x^2 + 84*x^3 + 126*x^4 + 126*x^5 + 84*x^6 + 36*x^7 + 9*x^ 8 + x^9)*Log[5]^9),x]
8*x^6 + x^8 - 8*x^5*(2 - Log[5]) + 1/((1 + x)^8*Log[5]^8) + (1 - Log[5])^8 /((1 + x - Log[5])^8*Log[5]^8) + (8*(1 - Log[5] - Log[5]^2))/((1 + x)^7*Lo g[5]^9) + 8*x^4*(6 - 3*Log[5] + Log[5]^2) - 8*x^3*(2 - Log[5])*(9 - 2*Log[ 5] + Log[5]^2) - (8*(1 - Log[5])^7*(1 - Log[5]^2 + Log[5]^3))/((1 + x - Lo g[5])^7*Log[5]^9) - 8*x*(2 - Log[5])*(57 - 41*Log[5] + 21*Log[5]^2 - 4*Log [5]^3 + Log[5]^4) + 4*x^2*(90 - 90*Log[5] + 41*Log[5]^2 - 10*Log[5]^3 + 2* Log[5]^4) + (4*(9 - 16*Log[5] - 7*Log[5]^2 + 16*Log[5]^3 + 7*Log[5]^4))/(( 1 + x)^6*Log[5]^10) + (8*(15 - 36*Log[5] + 49*Log[5]^3 - 7*Log[5]^4 - 28*L og[5]^5 - 7*Log[5]^6))/((1 + x)^5*Log[5]^11) + (4*(1 - Log[5])^6*(9 - 2*Lo g[5] - 14*Log[5]^2 + 12*Log[5]^3 + 9*Log[5]^4 - 14*Log[5]^5 + 7*Log[5]^6)) /((1 + x - Log[5])^6*Log[5]^10) + (2*(165 - 480*Log[5] + 168*Log[5]^2 + 67 2*Log[5]^3 - 455*Log[5]^4 - 448*Log[5]^5 + 252*Log[5]^6 + 224*Log[5]^7 + 3 3*Log[5]^8))/((1 + x)^4*Log[5]^12) - (8*(1 - Log[5])^5*(15 - 9*Log[5] - 27 *Log[5]^2 + 28*Log[5]^3 + 21*Log[5]^4 - 35*Log[5]^5 + 28*Log[5]^7 - 21*Log [5]^8 + 7*Log[5]^9))/((1 + x - Log[5])^5*Log[5]^11) + (8*(99 - 330*Log[5] + 210*Log[5]^2 + 420*Log[5]^3 - 518*Log[5]^4 - 203*Log[5]^5 + 413*Log[5]^6 + 84*Log[5]^7 - 163*Log[5]^8 - 68*Log[5]^9 - 5*Log[5]^10))/((1 + x)^3*Log [5]^13) + (4*(429 - 1584*Log[5] + 1386*Log[5]^2 + 1680*Log[5]^3 - 3192*Log [5]^4 - 112*Log[5]^5 + 2653*Log[5]^6 - 560*Log[5]^7 - 1305*Log[5]^8 + 240* Log[5]^9 + 454*Log[5]^10 + 96*Log[5]^11 + Log[5]^12))/((1 + x)^2*Log[5]...
3.13.61.3.1 Defintions of rubi rules used
Int[(u_.)*(Px_)^(p_), x_Symbol] :> With[{Qx = Factor[Px]}, Int[ExpandIntegr and[u*Qx^p, x], x] /; !SumQ[NonfreeFactors[Qx, x]]] /; PolyQ[Px, x] && GtQ [Expon[Px, x], 2] && !BinomialQ[Px, x] && !TrinomialQ[Px, x] && ILtQ[p, 0 ] && RationalFunctionQ[u, x]
Leaf count of result is larger than twice the leaf count of optimal. \(1402\) vs. \(2(28)=56\).
Time = 3.09 (sec) , antiderivative size = 1403, normalized size of antiderivative = 50.11
| method | result | size |
| default | \(\text {Expression too large to display}\) | \(1403\) |
| norman | \(\text {Expression too large to display}\) | \(1641\) |
| risch | \(\text {Expression too large to display}\) | \(2288\) |
| gosper | \(\text {Expression too large to display}\) | \(3198\) |
| parallelrisch | \(\text {Expression too large to display}\) | \(3198\) |
int(((-1008*x^21-14112*x^20-95368*x^19-411432*x^18-1261512*x^17-2889992*x^ 16-5036528*x^15-6586272*x^14-5968528*x^13-2422544*x^12+2904672*x^11+740124 8*x^10+8921456*x^9+7384608*x^8+4472960*x^7+1978064*x^6+611136*x^5+118608*x ^4+10896*x^3)*ln(5)^4+(672*x^22+10080*x^21+73416*x^20+343616*x^19+1152200* x^18+2918160*x^17+5718832*x^16+8684032*x^15+9906576*x^14+7517632*x^13+1446 496*x^12-5840736*x^11-10817504*x^10-11506656*x^9-8728272*x^8-4921888*x^7-2 045488*x^6-598176*x^5-110592*x^4-9728*x^3)*ln(5)^3+(-288*x^23-4608*x^22-35 960*x^21-181272*x^20-658768*x^19-1823216*x^18-3951792*x^17-6771984*x^16-90 80256*x^15-9084192*x^14-5659552*x^13+375072*x^12+6366336*x^11+9595520*x^10 +9198320*x^9+6457392*x^8+3411200*x^7+1337760*x^6+371136*x^5+65408*x^4+5504 *x^3)*ln(5)^2+(72*x^24+1224*x^23+10184*x^22+54960*x^21+214896*x^20+644016* x^19+1525072*x^18+2894688*x^17+4403552*x^16+5263520*x^15+4629792*x^14+2287 104*x^13-952528*x^12-3653904*x^11-4734416*x^10-4151456*x^9-2718720*x^8-135 2576*x^7-502336*x^6-132480*x^5-22272*x^4-1792*x^3)*ln(5)+(8*x^16+72*x^15+2 88*x^14+672*x^13+992*x^12+864*x^11+96*x^10-1056*x^9-1944*x^8-2008*x^7-1344 *x^6-576*x^5-144*x^4-16*x^3)*ln(5)^9+(-72*x^17-720*x^16-3296*x^15-9096*x^1 4-16600*x^13-20008*x^12-12792*x^11+5624*x^10+26720*x^9+38088*x^8+34024*x^7 +20528*x^6+8160*x^5+1936*x^4+208*x^3)*ln(5)^8+(288*x^18+3168*x^17+16280*x^ 16+51552*x^15+111048*x^14+166928*x^13+164344*x^12+63744*x^11-109016*x^10-2 63376*x^9-312624*x^8-247904*x^7-136656*x^6-50688*x^5-11424*x^4-1184*x^3)*l n(5)^7+(-672*x^19-8064*x^18-45864*x^17-163240*x^16-402976*x^15-717024*x^14 -906808*x^13-713944*x^12-58512*x^11+796656*x^10+1389264*x^9+1429488*x^8+10 24160*x^7+520928*x^6+181152*x^5+38816*x^4+3872*x^3)*ln(5)^6+(1008*x^20+131 04*x^19+81592*x^18+321552*x^17+891296*x^16+1818768*x^15+2752008*x^14+29488 48*x^13+1765856*x^12-636096*x^11-3134704*x^10-4421536*x^9-4045104*x^8-2651 952*x^7-1254016*x^6-410400*x^5-83664*x^4-8016*x^3)*ln(5)^5-8*x^25-144*x^24 -30576*x^21-7312*x^22-1272*x^23-98496*x^20-252432*x^19-523680*x^18-884448* x^17+866544*x^11+356640*x^12-369072*x^13-1002816*x^14-1207680*x^16-1296032 *x^15+233984*x^7+497088*x^8+996512*x^10+808320*x^9+82560*x^6+20736*x^5+332 8*x^4+256*x^3)/(-1-18*x+(84*x^15+1260*x^14+8820*x^13+38220*x^12+114660*x^1 1+252252*x^10+420420*x^9+540540*x^8+540540*x^7+420420*x^6+252252*x^5+11466 0*x^4+38220*x^3+8820*x^2+1260*x+84)*ln(5)^3+(-36*x^16-576*x^15-4320*x^14-2 0160*x^13-65520*x^12-157248*x^11-288288*x^10-411840*x^9-463320*x^8-411840* x^7-288288*x^6-157248*x^5-65520*x^4-20160*x^3-4320*x^2-576*x-36)*ln(5)^2+( x^9+9*x^8+36*x^7+84*x^6+126*x^5+126*x^4+84*x^3+36*x^2+9*x+1)*ln(5)^9+(9*x^ 17+153*x^16+1224*x^15+6120*x^14+21420*x^13+55692*x^12+111384*x^11+175032*x ^10+218790*x^9+218790*x^8+175032*x^7+111384*x^6+55692*x^5+21420*x^4+6120*x ^3+1224*x^2+153*x+9)*ln(5)+(-9*x^10-90*x^9-405*x^8-1080*x^7-1890*x^6-2268* x^5-1890*x^4-1080*x^3-405*x^2-90*x-9)*ln(5)^8+(36*x^11+396*x^10+1980*x^9+5 940*x^8+11880*x^7+16632*x^6+16632*x^5+11880*x^4+5940*x^3+1980*x^2+396*x+36 )*ln(5)^7+(-84*x^12-1008*x^11-5544*x^10-18480*x^9-41580*x^8-66528*x^7-7761 6*x^6-66528*x^5-41580*x^4-18480*x^3-5544*x^2-1008*x-84)*ln(5)^6+(126*x^13+ 1638*x^12+9828*x^11+36036*x^10+90090*x^9+162162*x^8+216216*x^7+216216*x^6+ 162162*x^5+90090*x^4+36036*x^3+9828*x^2+1638*x+126)*ln(5)^5+(-126*x^14-176 4*x^13-11466*x^12-45864*x^11-126126*x^10-252252*x^9-378378*x^8-432432*x^7- 378378*x^6-252252*x^5-126126*x^4-45864*x^3-11466*x^2-1764*x-126)*ln(5)^4-x ^18-18*x^17-31824*x^11-18564*x^12-8568*x^13-3060*x^14-153*x^16-816*x^15-31 824*x^7-43758*x^8-43758*x^10-48620*x^9-18564*x^6-8568*x^5-3060*x^4-816*x^3 -153*x^2),x,method=_RETURNVERBOSE)
-8/ln(5)^15*(-ln(5)^14+16*ln(5)^13+183*ln(5)^12+344*ln(5)^11-448*ln(5)^10- 1084*ln(5)^9+1333*ln(5)^8+1765*ln(5)^7-3066*ln(5)^6-924*ln(5)^5+3948*ln(5) ^4-1386*ln(5)^3-1848*ln(5)^2+1716*ln(5)-429)/(1+x)-2*(-35*ln(5)^16+280*ln( 5)^15-1064*ln(5)^14+2408*ln(5)^13-3246*ln(5)^12+1952*ln(5)^11+992*ln(5)^10 -2080*ln(5)^9-509*ln(5)^8+2916*ln(5)^7-1050*ln(5)^6-2380*ln(5)^5+2401*ln(5 )^4+168*ln(5)^3-1428*ln(5)^2+840*ln(5)-165)/ln(5)^12/(1+x-ln(5))^4-8*(-ln( 5)^22+8*ln(5)^21-49*ln(5)^20+196*ln(5)^19-530*ln(5)^18+972*ln(5)^17-1123*l n(5)^16+646*ln(5)^15+ln(5)^14-16*ln(5)^13-183*ln(5)^12-344*ln(5)^11+448*ln (5)^10+1084*ln(5)^9-1333*ln(5)^8-1765*ln(5)^7+3066*ln(5)^6+924*ln(5)^5-394 8*ln(5)^4+1386*ln(5)^3+1848*ln(5)^2-1716*ln(5)+429)/ln(5)^15/(1+x-ln(5))-8 /7*(7*ln(5)^2+7*ln(5)-7)/ln(5)^9/(1+x)^7-8/5*(-35*ln(5)^14+280*ln(5)^13-10 15*ln(5)^12+2100*ln(5)^11-2450*ln(5)^10+980*ln(5)^9+1330*ln(5)^8-1825*ln(5 )^7-105*ln(5)^6+1750*ln(5)^5-1120*ln(5)^4-385*ln(5)^3+840*ln(5)^2-420*ln(5 )+75)/ln(5)^11/(1+x-ln(5))^5-912*x-32*x^3*ln(5)^2+8*x^3*ln(5)^3+8*x^5*ln(5 )-48*x*ln(5)^4+1112*x*ln(5)+164*x^2*ln(5)^2+104*x^3*ln(5)+8*x^4*ln(5)^2-66 4*x*ln(5)^2-24*x^4*ln(5)-40*x^2*ln(5)^3-360*x^2*ln(5)+x^8+8*x^6-16*x^5+48* x^4-144*x^3+360*x^2+8*ln(5)^5*x-8/5*(35*ln(5)^6+140*ln(5)^5+35*ln(5)^4-245 *ln(5)^3+180*ln(5)-75)/ln(5)^11/(1+x)^5-8/3*(-21*ln(5)^18+168*ln(5)^17-693 *ln(5)^16+1806*ln(5)^15-2997*ln(5)^14+2790*ln(5)^13-552*ln(5)^12-1320*ln(5 )^11-33*ln(5)^10+2328*ln(5)^9-573*ln(5)^8-3363*ln(5)^7+2478*ln(5)^6+249...
Leaf count of result is larger than twice the leaf count of optimal. 1856 vs. \(2 (28) = 56\).
Time = 0.29 (sec) , antiderivative size = 1856, normalized size of antiderivative = 66.29 \[ \text {the integral} =\text {Too large to display} \]
integrate((20736*x^5+3328*x^4+(8*x^16+72*x^15+288*x^14+672*x^13+992*x^12+8 64*x^11+96*x^10-1056*x^9-1944*x^8-2008*x^7-1344*x^6-576*x^5-144*x^4-16*x^3 )*log(5)^9+(-72*x^17-720*x^16-3296*x^15-9096*x^14-16600*x^13-20008*x^12-12 792*x^11+5624*x^10+26720*x^9+38088*x^8+34024*x^7+20528*x^6+8160*x^5+1936*x ^4+208*x^3)*log(5)^8+(288*x^18+3168*x^17+16280*x^16+51552*x^15+111048*x^14 +166928*x^13+164344*x^12+63744*x^11-109016*x^10-263376*x^9-312624*x^8-2479 04*x^7-136656*x^6-50688*x^5-11424*x^4-1184*x^3)*log(5)^7+(-672*x^19-8064*x ^18-45864*x^17-163240*x^16-402976*x^15-717024*x^14-906808*x^13-713944*x^12 -58512*x^11+796656*x^10+1389264*x^9+1429488*x^8+1024160*x^7+520928*x^6+181 152*x^5+38816*x^4+3872*x^3)*log(5)^6+356640*x^12-1207680*x^16+82560*x^6-8* x^25+256*x^3+808320*x^9+996512*x^10+233984*x^7+497088*x^8-144*x^24-1272*x^ 23-7312*x^22-30576*x^21-252432*x^19-98496*x^20-523680*x^18-884448*x^17-129 6032*x^15-1002816*x^14-369072*x^13+866544*x^11+(1008*x^20+13104*x^19+81592 *x^18+321552*x^17+891296*x^16+1818768*x^15+2752008*x^14+2948848*x^13+17658 56*x^12-636096*x^11-3134704*x^10-4421536*x^9-4045104*x^8-2651952*x^7-12540 16*x^6-410400*x^5-83664*x^4-8016*x^3)*log(5)^5+(-1008*x^21-14112*x^20-9536 8*x^19-411432*x^18-1261512*x^17-2889992*x^16-5036528*x^15-6586272*x^14-596 8528*x^13-2422544*x^12+2904672*x^11+7401248*x^10+8921456*x^9+7384608*x^8+4 472960*x^7+1978064*x^6+611136*x^5+118608*x^4+10896*x^3)*log(5)^4+(672*x^22 +10080*x^21+73416*x^20+343616*x^19+1152200*x^18+2918160*x^17+5718832*x^16+ 8684032*x^15+9906576*x^14+7517632*x^13+1446496*x^12-5840736*x^11-10817504* x^10-11506656*x^9-8728272*x^8-4921888*x^7-2045488*x^6-598176*x^5-110592*x^ 4-9728*x^3)*log(5)^3+(-288*x^23-4608*x^22-35960*x^21-181272*x^20-658768*x^ 19-1823216*x^18-3951792*x^17-6771984*x^16-9080256*x^15-9084192*x^14-565955 2*x^13+375072*x^12+6366336*x^11+9595520*x^10+9198320*x^9+6457392*x^8+34112 00*x^7+1337760*x^6+371136*x^5+65408*x^4+5504*x^3)*log(5)^2+(72*x^24+1224*x ^23+10184*x^22+54960*x^21+214896*x^20+644016*x^19+1525072*x^18+2894688*x^1 7+4403552*x^16+5263520*x^15+4629792*x^14+2287104*x^13-952528*x^12-3653904* x^11-4734416*x^10-4151456*x^9-2718720*x^8-1352576*x^7-502336*x^6-132480*x^ 5-22272*x^4-1792*x^3)*log(5))/(-1-18*x-8568*x^5-3060*x^4-153*x^2+(9*x^17+1 53*x^16+1224*x^15+6120*x^14+21420*x^13+55692*x^12+111384*x^11+175032*x^10+ 218790*x^9+218790*x^8+175032*x^7+111384*x^6+55692*x^5+21420*x^4+6120*x^3+1 224*x^2+153*x+9)*log(5)+(-9*x^10-90*x^9-405*x^8-1080*x^7-1890*x^6-2268*x^5 -1890*x^4-1080*x^3-405*x^2-90*x-9)*log(5)^8+(36*x^11+396*x^10+1980*x^9+594 0*x^8+11880*x^7+16632*x^6+16632*x^5+11880*x^4+5940*x^3+1980*x^2+396*x+36)* log(5)^7+(-84*x^12-1008*x^11-5544*x^10-18480*x^9-41580*x^8-66528*x^7-77616 *x^6-66528*x^5-41580*x^4-18480*x^3-5544*x^2-1008*x-84)*log(5)^6+(126*x^13+ 1638*x^12+9828*x^11+36036*x^10+90090*x^9+162162*x^8+216216*x^7+216216*x^6+ 162162*x^5+90090*x^4+36036*x^3+9828*x^2+1638*x+126)*log(5)^5-18564*x^12-15 3*x^16-18564*x^6-816*x^3-48620*x^9-43758*x^10-31824*x^7-43758*x^8-x^18-18* x^17-816*x^15-3060*x^14-8568*x^13-31824*x^11+(-126*x^14-1764*x^13-11466*x^ 12-45864*x^11-126126*x^10-252252*x^9-378378*x^8-432432*x^7-378378*x^6-2522 52*x^5-126126*x^4-45864*x^3-11466*x^2-1764*x-126)*log(5)^4+(84*x^15+1260*x ^14+8820*x^13+38220*x^12+114660*x^11+252252*x^10+420420*x^9+540540*x^8+540 540*x^7+420420*x^6+252252*x^5+114660*x^4+38220*x^3+8820*x^2+1260*x+84)*log (5)^3+(-36*x^16-576*x^15-4320*x^14-20160*x^13-65520*x^12-157248*x^11-28828 8*x^10-411840*x^9-463320*x^8-411840*x^7-288288*x^6-157248*x^5-65520*x^4-20 160*x^3-4320*x^2-576*x-36)*log(5)^2+(x^9+9*x^8+36*x^7+84*x^6+126*x^5+126*x ^4+84*x^3+36*x^2+9*x+1)*log(5)^9),x, algorithm=\
(x^24 + 16*x^23 + 128*x^22 + 672*x^21 + 2572*x^20 + 7552*x^19 + 17424*x^18 + 31712*x^17 + 42374*x^16 + 9408*x^15 - 8*(x^8 + 8*x^7 + 28*x^6 + 56*x^5 + 70*x^4 + 56*x^3 + 28*x^2 + 8*x + 1)*log(5)^14 - 243168*x^14 + 8*(8*x^9 + 79*x^8 + 344*x^7 + 868*x^6 + 1400*x^5 + 1498*x^4 + 1064*x^3 + 484*x^2 + 1 28*x + 15)*log(5)^13 - 1259904*x^13 - 28*(8*x^10 + 96*x^9 + 515*x^8 + 1624 *x^7 + 3332*x^6 + 4648*x^5 + 4466*x^4 + 2920*x^3 + 1244*x^2 + 312*x + 35)* log(5)^12 - 4093116*x^12 + 56*(8*x^11 + 116*x^10 + 764*x^9 + 2995*x^8 + 77 36*x^7 + 13804*x^6 + 17360*x^5 + 15394*x^4 + 9440*x^3 + 3816*x^2 + 916*x + 99)*log(5)^11 - 9753408*x^11 - 4*(140*x^12 + 2464*x^11 + 20020*x^10 + 976 08*x^9 + 315423*x^8 + 709656*x^7 + 1139628*x^6 + 1317624*x^5 + 1090278*x^4 + 630728*x^3 + 242536*x^2 + 55744*x + 5799)*log(5)^10 - 17795216*x^10 + 8 *(56*x^13 + 1218*x^12 + 12404*x^11 + 75796*x^10 + 306024*x^9 + 859625*x^8 + 1730896*x^7 + 2536940*x^6 + 2715328*x^5 + 2102464*x^4 + 1147804*x^3 + 41 9368*x^2 + 92096*x + 9197)*log(5)^9 - 25353120*x^9 + (x^16 + 8*x^15 - 196* x^14 - 6216*x^13 - 82646*x^12 - 644424*x^11 - 3265780*x^10 - 11399192*x^9 - 28427825*x^8 - 51787056*x^7 - 69653640*x^6 - 69174032*x^5 - 50138456*x^4 - 25807824*x^3 - 8943320*x^2 - 1872080*x - 178954)*log(5)^8 - 28481260*x^ 8 - 8*(x^17 + 9*x^16 + 29*x^15 - 225*x^14 - 5597*x^13 - 58689*x^12 - 37872 7*x^11 - 1645013*x^10 - 5049012*x^9 - 11286992*x^8 - 18705694*x^7 - 231549 26*x^6 - 21360186*x^5 - 14489572*x^4 - 7023380*x^3 - 2303824*x^2 - 4584...
Timed out. \[ \text {the integral} =\text {Timed out} \]
integrate((-98496*x**20+3328*x**4+808320*x**9+20736*x**5+82560*x**6-523680 *x**18-884448*x**17-1296032*x**15-1002816*x**14-369072*x**13+866544*x**11+ 356640*x**12-252432*x**19-1207680*x**16+256*x**3-144*x**24-1272*x**23-7312 *x**22-30576*x**21+(-1008*x**21-14112*x**20-95368*x**19-411432*x**18-12615 12*x**17-2889992*x**16-5036528*x**15-6586272*x**14-5968528*x**13-2422544*x **12+2904672*x**11+7401248*x**10+8921456*x**9+7384608*x**8+4472960*x**7+19 78064*x**6+611136*x**5+118608*x**4+10896*x**3)*ln(5)**4+(672*x**22+10080*x **21+73416*x**20+343616*x**19+1152200*x**18+2918160*x**17+5718832*x**16+86 84032*x**15+9906576*x**14+7517632*x**13+1446496*x**12-5840736*x**11-108175 04*x**10-11506656*x**9-8728272*x**8-4921888*x**7-2045488*x**6-598176*x**5- 110592*x**4-9728*x**3)*ln(5)**3+(-288*x**23-4608*x**22-35960*x**21-181272* x**20-658768*x**19-1823216*x**18-3951792*x**17-6771984*x**16-9080256*x**15 -9084192*x**14-5659552*x**13+375072*x**12+6366336*x**11+9595520*x**10+9198 320*x**9+6457392*x**8+3411200*x**7+1337760*x**6+371136*x**5+65408*x**4+550 4*x**3)*ln(5)**2+(72*x**24+1224*x**23+10184*x**22+54960*x**21+214896*x**20 +644016*x**19+1525072*x**18+2894688*x**17+4403552*x**16+5263520*x**15+4629 792*x**14+2287104*x**13-952528*x**12-3653904*x**11-4734416*x**10-4151456*x **9-2718720*x**8-1352576*x**7-502336*x**6-132480*x**5-22272*x**4-1792*x**3 )*ln(5)+(8*x**16+72*x**15+288*x**14+672*x**13+992*x**12+864*x**11+96*x**10 -1056*x**9-1944*x**8-2008*x**7-1344*x**6-576*x**5-144*x**4-16*x**3)*ln(5)* *9+233984*x**7+497088*x**8-8*x**25+(-72*x**17-720*x**16-3296*x**15-9096*x* *14-16600*x**13-20008*x**12-12792*x**11+5624*x**10+26720*x**9+38088*x**8+3 4024*x**7+20528*x**6+8160*x**5+1936*x**4+208*x**3)*ln(5)**8+(288*x**18+316 8*x**17+16280*x**16+51552*x**15+111048*x**14+166928*x**13+164344*x**12+637 44*x**11-109016*x**10-263376*x**9-312624*x**8-247904*x**7-136656*x**6-5068 8*x**5-11424*x**4-1184*x**3)*ln(5)**7+(-672*x**19-8064*x**18-45864*x**17-1 63240*x**16-402976*x**15-717024*x**14-906808*x**13-713944*x**12-58512*x**1 1+796656*x**10+1389264*x**9+1429488*x**8+1024160*x**7+520928*x**6+181152*x **5+38816*x**4+3872*x**3)*ln(5)**6+(1008*x**20+13104*x**19+81592*x**18+321 552*x**17+891296*x**16+1818768*x**15+2752008*x**14+2948848*x**13+1765856*x **12-636096*x**11-3134704*x**10-4421536*x**9-4045104*x**8-2651952*x**7-125 4016*x**6-410400*x**5-83664*x**4-8016*x**3)*ln(5)**5+996512*x**10)/(-1-18* x-153*x**2-3060*x**4-48620*x**9-8568*x**5+(84*x**15+1260*x**14+8820*x**13+ 38220*x**12+114660*x**11+252252*x**10+420420*x**9+540540*x**8+540540*x**7+ 420420*x**6+252252*x**5+114660*x**4+38220*x**3+8820*x**2+1260*x+84)*ln(5)* *3+(-36*x**16-576*x**15-4320*x**14-20160*x**13-65520*x**12-157248*x**11-28 8288*x**10-411840*x**9-463320*x**8-411840*x**7-288288*x**6-157248*x**5-655 20*x**4-20160*x**3-4320*x**2-576*x-36)*ln(5)**2+(x**9+9*x**8+36*x**7+84*x* *6+126*x**5+126*x**4+84*x**3+36*x**2+9*x+1)*ln(5)**9-18564*x**6+(9*x**17+1 53*x**16+1224*x**15+6120*x**14+21420*x**13+55692*x**12+111384*x**11+175032 *x**10+218790*x**9+218790*x**8+175032*x**7+111384*x**6+55692*x**5+21420*x* *4+6120*x**3+1224*x**2+153*x+9)*ln(5)+(-9*x**10-90*x**9-405*x**8-1080*x**7 -1890*x**6-2268*x**5-1890*x**4-1080*x**3-405*x**2-90*x-9)*ln(5)**8+(36*x** 11+396*x**10+1980*x**9+5940*x**8+11880*x**7+16632*x**6+16632*x**5+11880*x* *4+5940*x**3+1980*x**2+396*x+36)*ln(5)**7+(-84*x**12-1008*x**11-5544*x**10 -18480*x**9-41580*x**8-66528*x**7-77616*x**6-66528*x**5-41580*x**4-18480*x **3-5544*x**2-1008*x-84)*ln(5)**6+(126*x**13+1638*x**12+9828*x**11+36036*x **10+90090*x**9+162162*x**8+216216*x**7+216216*x**6+162162*x**5+90090*x**4 +36036*x**3+9828*x**2+1638*x+126)*ln(5)**5+(-126*x**14-1764*x**13-11466*x* *12-45864*x**11-126126*x**10-252252*x**9-378378*x**8-432432*x**7-378378*x* *6-252252*x**5-126126*x**4-45864*x**3-11466*x**2-1764*x-126)*ln(5)**4-x**1 8-18*x**17-816*x**15-3060*x**14-8568*x**13-31824*x**11-18564*x**12-153*x** 16-816*x**3-31824*x**7-43758*x**8-43758*x**10),x)
Leaf count of result is larger than twice the leaf count of optimal. 2015 vs. \(2 (28) = 56\).
Time = 0.29 (sec) , antiderivative size = 2015, normalized size of antiderivative = 71.96 \[ \text {the integral} =\text {Too large to display} \]
integrate((20736*x^5+3328*x^4+(8*x^16+72*x^15+288*x^14+672*x^13+992*x^12+8 64*x^11+96*x^10-1056*x^9-1944*x^8-2008*x^7-1344*x^6-576*x^5-144*x^4-16*x^3 )*log(5)^9+(-72*x^17-720*x^16-3296*x^15-9096*x^14-16600*x^13-20008*x^12-12 792*x^11+5624*x^10+26720*x^9+38088*x^8+34024*x^7+20528*x^6+8160*x^5+1936*x ^4+208*x^3)*log(5)^8+(288*x^18+3168*x^17+16280*x^16+51552*x^15+111048*x^14 +166928*x^13+164344*x^12+63744*x^11-109016*x^10-263376*x^9-312624*x^8-2479 04*x^7-136656*x^6-50688*x^5-11424*x^4-1184*x^3)*log(5)^7+(-672*x^19-8064*x ^18-45864*x^17-163240*x^16-402976*x^15-717024*x^14-906808*x^13-713944*x^12 -58512*x^11+796656*x^10+1389264*x^9+1429488*x^8+1024160*x^7+520928*x^6+181 152*x^5+38816*x^4+3872*x^3)*log(5)^6+356640*x^12-1207680*x^16+82560*x^6-8* x^25+256*x^3+808320*x^9+996512*x^10+233984*x^7+497088*x^8-144*x^24-1272*x^ 23-7312*x^22-30576*x^21-252432*x^19-98496*x^20-523680*x^18-884448*x^17-129 6032*x^15-1002816*x^14-369072*x^13+866544*x^11+(1008*x^20+13104*x^19+81592 *x^18+321552*x^17+891296*x^16+1818768*x^15+2752008*x^14+2948848*x^13+17658 56*x^12-636096*x^11-3134704*x^10-4421536*x^9-4045104*x^8-2651952*x^7-12540 16*x^6-410400*x^5-83664*x^4-8016*x^3)*log(5)^5+(-1008*x^21-14112*x^20-9536 8*x^19-411432*x^18-1261512*x^17-2889992*x^16-5036528*x^15-6586272*x^14-596 8528*x^13-2422544*x^12+2904672*x^11+7401248*x^10+8921456*x^9+7384608*x^8+4 472960*x^7+1978064*x^6+611136*x^5+118608*x^4+10896*x^3)*log(5)^4+(672*x^22 +10080*x^21+73416*x^20+343616*x^19+1152200*x^18+2918160*x^17+5718832*x^16+ 8684032*x^15+9906576*x^14+7517632*x^13+1446496*x^12-5840736*x^11-10817504* x^10-11506656*x^9-8728272*x^8-4921888*x^7-2045488*x^6-598176*x^5-110592*x^ 4-9728*x^3)*log(5)^3+(-288*x^23-4608*x^22-35960*x^21-181272*x^20-658768*x^ 19-1823216*x^18-3951792*x^17-6771984*x^16-9080256*x^15-9084192*x^14-565955 2*x^13+375072*x^12+6366336*x^11+9595520*x^10+9198320*x^9+6457392*x^8+34112 00*x^7+1337760*x^6+371136*x^5+65408*x^4+5504*x^3)*log(5)^2+(72*x^24+1224*x ^23+10184*x^22+54960*x^21+214896*x^20+644016*x^19+1525072*x^18+2894688*x^1 7+4403552*x^16+5263520*x^15+4629792*x^14+2287104*x^13-952528*x^12-3653904* x^11-4734416*x^10-4151456*x^9-2718720*x^8-1352576*x^7-502336*x^6-132480*x^ 5-22272*x^4-1792*x^3)*log(5))/(-1-18*x-8568*x^5-3060*x^4-153*x^2+(9*x^17+1 53*x^16+1224*x^15+6120*x^14+21420*x^13+55692*x^12+111384*x^11+175032*x^10+ 218790*x^9+218790*x^8+175032*x^7+111384*x^6+55692*x^5+21420*x^4+6120*x^3+1 224*x^2+153*x+9)*log(5)+(-9*x^10-90*x^9-405*x^8-1080*x^7-1890*x^6-2268*x^5 -1890*x^4-1080*x^3-405*x^2-90*x-9)*log(5)^8+(36*x^11+396*x^10+1980*x^9+594 0*x^8+11880*x^7+16632*x^6+16632*x^5+11880*x^4+5940*x^3+1980*x^2+396*x+36)* log(5)^7+(-84*x^12-1008*x^11-5544*x^10-18480*x^9-41580*x^8-66528*x^7-77616 *x^6-66528*x^5-41580*x^4-18480*x^3-5544*x^2-1008*x-84)*log(5)^6+(126*x^13+ 1638*x^12+9828*x^11+36036*x^10+90090*x^9+162162*x^8+216216*x^7+216216*x^6+ 162162*x^5+90090*x^4+36036*x^3+9828*x^2+1638*x+126)*log(5)^5-18564*x^12-15 3*x^16-18564*x^6-816*x^3-48620*x^9-43758*x^10-31824*x^7-43758*x^8-x^18-18* x^17-816*x^15-3060*x^14-8568*x^13-31824*x^11+(-126*x^14-1764*x^13-11466*x^ 12-45864*x^11-126126*x^10-252252*x^9-378378*x^8-432432*x^7-378378*x^6-2522 52*x^5-126126*x^4-45864*x^3-11466*x^2-1764*x-126)*log(5)^4+(84*x^15+1260*x ^14+8820*x^13+38220*x^12+114660*x^11+252252*x^10+420420*x^9+540540*x^8+540 540*x^7+420420*x^6+252252*x^5+114660*x^4+38220*x^3+8820*x^2+1260*x+84)*log (5)^3+(-36*x^16-576*x^15-4320*x^14-20160*x^13-65520*x^12-157248*x^11-28828 8*x^10-411840*x^9-463320*x^8-411840*x^7-288288*x^6-157248*x^5-65520*x^4-20 160*x^3-4320*x^2-576*x-36)*log(5)^2+(x^9+9*x^8+36*x^7+84*x^6+126*x^5+126*x ^4+84*x^3+36*x^2+9*x+1)*log(5)^9),x, algorithm=\
x^8 + 8*x^6 + 8*x^5*(log(5) - 2) + 8*(log(5)^2 - 3*log(5) + 6)*x^4 + 8*(lo g(5)^3 - 4*log(5)^2 + 13*log(5) - 18)*x^3 + 4*(2*log(5)^4 - 10*log(5)^3 + 41*log(5)^2 - 90*log(5) + 90)*x^2 + 8*(log(5)^5 - 6*log(5)^4 + 29*log(5)^3 - 83*log(5)^2 + 139*log(5) - 114)*x + (8*(log(5)^7 - 8*log(5)^6 + 49*log( 5)^5 - 196*log(5)^4 + 530*log(5)^3 - 972*log(5)^2 + 1123*log(5) - 646)*x^1 5 - 4*(14*log(5)^8 - 142*log(5)^7 + 919*log(5)^6 - 4158*log(5)^5 + 13034*l og(5)^4 - 28668*log(5)^3 + 43117*log(5)^2 - 40378*log(5) + 17742)*x^14 + 8 *(21*log(5)^9 - 266*log(5)^8 + 1897*log(5)^7 - 9541*log(5)^6 + 34300*log(5 )^5 - 88606*log(5)^4 + 163545*log(5)^3 - 206859*log(5)^2 + 160817*log(5) - 57310)*x^13 - 8*log(5)^14 - 2*(140*log(5)^10 - 2212*log(5)^9 + 17934*log( 5)^8 - 100380*log(5)^7 + 409794*log(5)^6 - 1228024*log(5)^5 + 2700899*log( 5)^4 - 4282884*log(5)^3 + 4648214*log(5)^2 - 3074124*log(5) + 922812)*x^12 + 120*log(5)^13 + 8*(35*log(5)^11 - 700*log(5)^10 + 6643*log(5)^9 - 41902 *log(5)^8 + 193613*log(5)^7 - 667702*log(5)^6 + 1722473*log(5)^5 - 3300867 *log(5)^4 + 4578836*log(5)^3 - 4337342*log(5)^2 + 2490581*log(5) - 646466) *x^11 - 980*log(5)^12 - 4*(42*log(5)^12 - 1106*log(5)^11 + 12733*log(5)^10 - 92554*log(5)^9 + 486570*log(5)^8 - 1925238*log(5)^7 + 5777029*log(5)^6 - 13124342*log(5)^5 + 22294481*log(5)^4 - 27445824*log(5)^3 + 23019303*log (5)^2 - 11667222*log(5) + 2669238)*x^10 + 5544*log(5)^11 + 8*(7*log(5)^13 - 266*log(5)^12 + 3927*log(5)^11 - 34069*log(5)^10 + 206997*log(5)^9 - ...
Leaf count of result is larger than twice the leaf count of optimal. 1904 vs. \(2 (28) = 56\).
Time = 0.34 (sec) , antiderivative size = 1904, normalized size of antiderivative = 68.00 \[ \text {the integral} =\text {Too large to display} \]
integrate((20736*x^5+3328*x^4+(8*x^16+72*x^15+288*x^14+672*x^13+992*x^12+8 64*x^11+96*x^10-1056*x^9-1944*x^8-2008*x^7-1344*x^6-576*x^5-144*x^4-16*x^3 )*log(5)^9+(-72*x^17-720*x^16-3296*x^15-9096*x^14-16600*x^13-20008*x^12-12 792*x^11+5624*x^10+26720*x^9+38088*x^8+34024*x^7+20528*x^6+8160*x^5+1936*x ^4+208*x^3)*log(5)^8+(288*x^18+3168*x^17+16280*x^16+51552*x^15+111048*x^14 +166928*x^13+164344*x^12+63744*x^11-109016*x^10-263376*x^9-312624*x^8-2479 04*x^7-136656*x^6-50688*x^5-11424*x^4-1184*x^3)*log(5)^7+(-672*x^19-8064*x ^18-45864*x^17-163240*x^16-402976*x^15-717024*x^14-906808*x^13-713944*x^12 -58512*x^11+796656*x^10+1389264*x^9+1429488*x^8+1024160*x^7+520928*x^6+181 152*x^5+38816*x^4+3872*x^3)*log(5)^6+356640*x^12-1207680*x^16+82560*x^6-8* x^25+256*x^3+808320*x^9+996512*x^10+233984*x^7+497088*x^8-144*x^24-1272*x^ 23-7312*x^22-30576*x^21-252432*x^19-98496*x^20-523680*x^18-884448*x^17-129 6032*x^15-1002816*x^14-369072*x^13+866544*x^11+(1008*x^20+13104*x^19+81592 *x^18+321552*x^17+891296*x^16+1818768*x^15+2752008*x^14+2948848*x^13+17658 56*x^12-636096*x^11-3134704*x^10-4421536*x^9-4045104*x^8-2651952*x^7-12540 16*x^6-410400*x^5-83664*x^4-8016*x^3)*log(5)^5+(-1008*x^21-14112*x^20-9536 8*x^19-411432*x^18-1261512*x^17-2889992*x^16-5036528*x^15-6586272*x^14-596 8528*x^13-2422544*x^12+2904672*x^11+7401248*x^10+8921456*x^9+7384608*x^8+4 472960*x^7+1978064*x^6+611136*x^5+118608*x^4+10896*x^3)*log(5)^4+(672*x^22 +10080*x^21+73416*x^20+343616*x^19+1152200*x^18+2918160*x^17+5718832*x^16+ 8684032*x^15+9906576*x^14+7517632*x^13+1446496*x^12-5840736*x^11-10817504* x^10-11506656*x^9-8728272*x^8-4921888*x^7-2045488*x^6-598176*x^5-110592*x^ 4-9728*x^3)*log(5)^3+(-288*x^23-4608*x^22-35960*x^21-181272*x^20-658768*x^ 19-1823216*x^18-3951792*x^17-6771984*x^16-9080256*x^15-9084192*x^14-565955 2*x^13+375072*x^12+6366336*x^11+9595520*x^10+9198320*x^9+6457392*x^8+34112 00*x^7+1337760*x^6+371136*x^5+65408*x^4+5504*x^3)*log(5)^2+(72*x^24+1224*x ^23+10184*x^22+54960*x^21+214896*x^20+644016*x^19+1525072*x^18+2894688*x^1 7+4403552*x^16+5263520*x^15+4629792*x^14+2287104*x^13-952528*x^12-3653904* x^11-4734416*x^10-4151456*x^9-2718720*x^8-1352576*x^7-502336*x^6-132480*x^ 5-22272*x^4-1792*x^3)*log(5))/(-1-18*x-8568*x^5-3060*x^4-153*x^2+(9*x^17+1 53*x^16+1224*x^15+6120*x^14+21420*x^13+55692*x^12+111384*x^11+175032*x^10+ 218790*x^9+218790*x^8+175032*x^7+111384*x^6+55692*x^5+21420*x^4+6120*x^3+1 224*x^2+153*x+9)*log(5)+(-9*x^10-90*x^9-405*x^8-1080*x^7-1890*x^6-2268*x^5 -1890*x^4-1080*x^3-405*x^2-90*x-9)*log(5)^8+(36*x^11+396*x^10+1980*x^9+594 0*x^8+11880*x^7+16632*x^6+16632*x^5+11880*x^4+5940*x^3+1980*x^2+396*x+36)* log(5)^7+(-84*x^12-1008*x^11-5544*x^10-18480*x^9-41580*x^8-66528*x^7-77616 *x^6-66528*x^5-41580*x^4-18480*x^3-5544*x^2-1008*x-84)*log(5)^6+(126*x^13+ 1638*x^12+9828*x^11+36036*x^10+90090*x^9+162162*x^8+216216*x^7+216216*x^6+ 162162*x^5+90090*x^4+36036*x^3+9828*x^2+1638*x+126)*log(5)^5-18564*x^12-15 3*x^16-18564*x^6-816*x^3-48620*x^9-43758*x^10-31824*x^7-43758*x^8-x^18-18* x^17-816*x^15-3060*x^14-8568*x^13-31824*x^11+(-126*x^14-1764*x^13-11466*x^ 12-45864*x^11-126126*x^10-252252*x^9-378378*x^8-432432*x^7-378378*x^6-2522 52*x^5-126126*x^4-45864*x^3-11466*x^2-1764*x-126)*log(5)^4+(84*x^15+1260*x ^14+8820*x^13+38220*x^12+114660*x^11+252252*x^10+420420*x^9+540540*x^8+540 540*x^7+420420*x^6+252252*x^5+114660*x^4+38220*x^3+8820*x^2+1260*x+84)*log (5)^3+(-36*x^16-576*x^15-4320*x^14-20160*x^13-65520*x^12-157248*x^11-28828 8*x^10-411840*x^9-463320*x^8-411840*x^7-288288*x^6-157248*x^5-65520*x^4-20 160*x^3-4320*x^2-576*x-36)*log(5)^2+(x^9+9*x^8+36*x^7+84*x^6+126*x^5+126*x ^4+84*x^3+36*x^2+9*x+1)*log(5)^9),x, algorithm=\
x^8 + 8*x^6 + 8*x^5*log(5) + 8*x^4*log(5)^2 + 8*x^3*log(5)^3 + 8*x^2*log(5 )^4 + 8*x*log(5)^5 - 16*x^5 - 24*x^4*log(5) - 32*x^3*log(5)^2 - 40*x^2*log (5)^3 - 48*x*log(5)^4 + 48*x^4 + 104*x^3*log(5) + 164*x^2*log(5)^2 + 232*x *log(5)^3 - 144*x^3 - 360*x^2*log(5) - 664*x*log(5)^2 + 360*x^2 + 1112*x*l og(5) - 912*x + (8*x^15*log(5)^7 - 56*x^14*log(5)^8 + 168*x^13*log(5)^9 - 280*x^12*log(5)^10 + 280*x^11*log(5)^11 - 168*x^10*log(5)^12 + 56*x^9*log( 5)^13 - 8*x^8*log(5)^14 - 64*x^15*log(5)^6 + 568*x^14*log(5)^7 - 2128*x^13 *log(5)^8 + 4424*x^12*log(5)^9 - 5600*x^11*log(5)^10 + 4424*x^10*log(5)^11 - 2128*x^9*log(5)^12 + 568*x^8*log(5)^13 - 64*x^7*log(5)^14 + 392*x^15*lo g(5)^5 - 3676*x^14*log(5)^6 + 15176*x^13*log(5)^7 - 35868*x^12*log(5)^8 + 53144*x^11*log(5)^9 - 50932*x^10*log(5)^10 + 31416*x^9*log(5)^11 - 11956*x ^8*log(5)^12 + 2528*x^7*log(5)^13 - 224*x^6*log(5)^14 - 1568*x^15*log(5)^4 + 16632*x^14*log(5)^5 - 76328*x^13*log(5)^6 + 200760*x^12*log(5)^7 - 3352 16*x^11*log(5)^8 + 370216*x^10*log(5)^9 - 272552*x^9*log(5)^10 + 131208*x^ 8*log(5)^11 - 39200*x^7*log(5)^12 + 6496*x^6*log(5)^13 - 448*x^5*log(5)^14 + 4240*x^15*log(5)^3 - 52136*x^14*log(5)^4 + 274400*x^13*log(5)^5 - 81958 8*x^12*log(5)^6 + 1548904*x^11*log(5)^7 - 1946280*x^10*log(5)^8 + 1655976* x^9*log(5)^9 - 949660*x^8*log(5)^10 + 357168*x^7*log(5)^11 - 83104*x^6*log (5)^12 + 10640*x^5*log(5)^13 - 560*x^4*log(5)^14 - 7776*x^15*log(5)^2 + 11 4672*x^14*log(5)^3 - 708848*x^13*log(5)^4 + 2456048*x^12*log(5)^5 - 534...
Time = 45.74 (sec) , antiderivative size = 13908, normalized size of antiderivative = 496.71 \[ \text {the integral} =\text {Too large to display} \]
int((log(5)^2*(5659552*x^13 - 65408*x^4 - 371136*x^5 - 1337760*x^6 - 34112 00*x^7 - 6457392*x^8 - 9198320*x^9 - 9595520*x^10 - 6366336*x^11 - 375072* x^12 - 5504*x^3 + 9084192*x^14 + 9080256*x^15 + 6771984*x^16 + 3951792*x^1 7 + 1823216*x^18 + 658768*x^19 + 181272*x^20 + 35960*x^21 + 4608*x^22 + 28 8*x^23) + log(5)^6*(58512*x^11 - 38816*x^4 - 181152*x^5 - 520928*x^6 - 102 4160*x^7 - 1429488*x^8 - 1389264*x^9 - 796656*x^10 - 3872*x^3 + 713944*x^1 2 + 906808*x^13 + 717024*x^14 + 402976*x^15 + 163240*x^16 + 45864*x^17 + 8 064*x^18 + 672*x^19) + log(5)^5*(8016*x^3 + 83664*x^4 + 410400*x^5 + 12540 16*x^6 + 2651952*x^7 + 4045104*x^8 + 4421536*x^9 + 3134704*x^10 + 636096*x ^11 - 1765856*x^12 - 2948848*x^13 - 2752008*x^14 - 1818768*x^15 - 891296*x ^16 - 321552*x^17 - 81592*x^18 - 13104*x^19 - 1008*x^20) + log(5)^9*(16*x^ 3 + 144*x^4 + 576*x^5 + 1344*x^6 + 2008*x^7 + 1944*x^8 + 1056*x^9 - 96*x^1 0 - 864*x^11 - 992*x^12 - 672*x^13 - 288*x^14 - 72*x^15 - 8*x^16) + log(5) ^4*(2422544*x^12 - 118608*x^4 - 611136*x^5 - 1978064*x^6 - 4472960*x^7 - 7 384608*x^8 - 8921456*x^9 - 7401248*x^10 - 2904672*x^11 - 10896*x^3 + 59685 28*x^13 + 6586272*x^14 + 5036528*x^15 + 2889992*x^16 + 1261512*x^17 + 4114 32*x^18 + 95368*x^19 + 14112*x^20 + 1008*x^21) - log(5)^8*(208*x^3 + 1936* x^4 + 8160*x^5 + 20528*x^6 + 34024*x^7 + 38088*x^8 + 26720*x^9 + 5624*x^10 - 12792*x^11 - 20008*x^12 - 16600*x^13 - 9096*x^14 - 3296*x^15 - 720*x^16 - 72*x^17) - 256*x^3 - 3328*x^4 - 20736*x^5 - 82560*x^6 - 233984*x^7 - 49 7088*x^8 - 808320*x^9 - 996512*x^10 - 866544*x^11 - 356640*x^12 + 369072*x ^13 + 1002816*x^14 + 1296032*x^15 + 1207680*x^16 + 884448*x^17 + 523680*x^ 18 + 252432*x^19 + 98496*x^20 + 30576*x^21 + 7312*x^22 + 1272*x^23 + 144*x ^24 + 8*x^25 - log(5)^3*(1446496*x^12 - 110592*x^4 - 598176*x^5 - 2045488* x^6 - 4921888*x^7 - 8728272*x^8 - 11506656*x^9 - 10817504*x^10 - 5840736*x ^11 - 9728*x^3 + 7517632*x^13 + 9906576*x^14 + 8684032*x^15 + 5718832*x^16 + 2918160*x^17 + 1152200*x^18 + 343616*x^19 + 73416*x^20 + 10080*x^21 + 6 72*x^22) - log(5)*(2287104*x^13 - 22272*x^4 - 132480*x^5 - 502336*x^6 - 13 52576*x^7 - 2718720*x^8 - 4151456*x^9 - 4734416*x^10 - 3653904*x^11 - 9525 28*x^12 - 1792*x^3 + 4629792*x^14 + 5263520*x^15 + 4403552*x^16 + 2894688* x^17 + 1525072*x^18 + 644016*x^19 + 214896*x^20 + 54960*x^21 + 10184*x^22 + 1224*x^23 + 72*x^24) + log(5)^7*(1184*x^3 + 11424*x^4 + 50688*x^5 + 1366 56*x^6 + 247904*x^7 + 312624*x^8 + 263376*x^9 + 109016*x^10 - 63744*x^11 - 164344*x^12 - 166928*x^13 - 111048*x^14 - 51552*x^15 - 16280*x^16 - 3168* x^17 - 288*x^18))/(18*x + log(5)^4*(1764*x + 11466*x^2 + 45864*x^3 + 12612 6*x^4 + 252252*x^5 + 378378*x^6 + 432432*x^7 + 378378*x^8 + 252252*x^9 + 1 26126*x^10 + 45864*x^11 + 11466*x^12 + 1764*x^13 + 126*x^14 + 126) + log(5 )^8*(90*x + 405*x^2 + 1080*x^3 + 1890*x^4 + 2268*x^5 + 1890*x^6 + 1080*x^7 + 405*x^8 + 90*x^9 + 9*x^10 + 9) - log(5)^3*(1260*x + 8820*x^2 + 38220*x^ 3 + 114660*x^4 + 252252*x^5 + 420420*x^6 + 540540*x^7 + 540540*x^8 + 42042 0*x^9 + 252252*x^10 + 114660*x^11 + 38220*x^12 + 8820*x^13 + 1260*x^14 + 8 4*x^15 + 84) - log(5)*(153*x + 1224*x^2 + 6120*x^3 + 21420*x^4 + 55692*x^5 + 111384*x^6 + 175032*x^7 + 218790*x^8 + 218790*x^9 + 175032*x^10 + 11138 4*x^11 + 55692*x^12 + 21420*x^13 + 6120*x^14 + 1224*x^15 + 153*x^16 + 9*x^ 17 + 9) - log(5)^7*(396*x + 1980*x^2 + 5940*x^3 + 11880*x^4 + 16632*x^5 + 16632*x^6 + 11880*x^7 + 5940*x^8 + 1980*x^9 + 396*x^10 + 36*x^11 + 36) + l og(5)^2*(576*x + 4320*x^2 + 20160*x^3 + 65520*x^4 + 157248*x^5 + 288288*x^ 6 + 411840*x^7 + 463320*x^8 + 411840*x^9 + 288288*x^10 + 157248*x^11 + 655 20*x^12 + 20160*x^13 + 4320*x^14 + 576*x^15 + 36*x^16 + 36) - log(5)^9*(9* x + 36*x^2 + 84*x^3 + 126*x^4 + 126*x^5 + 84*x^6 + 36*x^7 + 9*x^8 + x^9 + 1) + log(5)^6*(1008*x + 5544*x^2 + 18480*x^3 + 41580*x^4 + 66528*x^5 + 776 16*x^6 + 66528*x^7 + 41580*x^8 + 18480*x^9 + 5544*x^10 + 1008*x^11 + 84*x^ 12 + 84) + 153*x^2 + 816*x^3 + 3060*x^4 + 8568*x^5 + 18564*x^6 + 31824*x^7 + 43758*x^8 + 48620*x^9 + 43758*x^10 + 31824*x^11 + 18564*x^12 + 8568*x^1 3 + 3060*x^14 + 816*x^15 + 153*x^16 + 18*x^17 + x^18 - log(5)^5*(1638*x + 9828*x^2 + 36036*x^3 + 90090*x^4 + 162162*x^5 + 216216*x^6 + 216216*x^7 + 162162*x^8 + 90090*x^9 + 36036*x^10 + 9828*x^11 + 1638*x^12 + 126*x^13 + 1 26) + 1),x)
x*(394160*log(5) - (40*log(5) - 80)*(4320*log(5)^2 - 6120*log(5) - 1260*lo g(5)^3 + 126*log(5)^4 + 3060) + (9*log(5) - 18)*(95280*log(5) + (40*log(5) - 80)*(1224*log(5) - 576*log(5)^2 + 84*log(5)^3 - 816) + (9*log(5) - 18)* (15216*log(5) + (9*log(5) - 18)*(1344*log(5) + (9*log(5) - 18)*(40*log(5) - 80) - 328*log(5)^2 - 1248) - 7656*log(5)^2 + 1176*log(5)^3 - (40*log(5) - 80)*(36*log(5)^2 - 153*log(5) + 153) - 9216) - (36*log(5)^2 - 153*log(5) + 153)*(1344*log(5) + (9*log(5) - 18)*(40*log(5) - 80) - 328*log(5)^2 - 1 248) - 72752*log(5)^2 + 22624*log(5)^3 - 2408*log(5)^4 - 42960) - (36*log( 5)^2 - 153*log(5) + 153)*(15216*log(5) + (9*log(5) - 18)*(1344*log(5) + (9 *log(5) - 18)*(40*log(5) - 80) - 328*log(5)^2 - 1248) - 7656*log(5)^2 + 11 76*log(5)^3 - (40*log(5) - 80)*(36*log(5)^2 - 153*log(5) + 153) - 9216) - 402448*log(5)^2 + 188440*log(5)^3 - 40152*log(5)^4 + 3080*log(5)^5 + (1344 *log(5) + (9*log(5) - 18)*(40*log(5) - 80) - 328*log(5)^2 - 1248)*(1224*lo g(5) - 576*log(5)^2 + 84*log(5)^3 - 816) - 142176) + x^3*(5072*log(5) + (( 9*log(5) - 18)*(1344*log(5) + (9*log(5) - 18)*(40*log(5) - 80) - 328*log(5 )^2 - 1248))/3 - 2552*log(5)^2 + 392*log(5)^3 - ((40*log(5) - 80)*(36*log( 5)^2 - 153*log(5) + 153))/3 - 3072) + x^2*(47640*log(5) + ((40*log(5) - 80 )*(1224*log(5) - 576*log(5)^2 + 84*log(5)^3 - 816))/2 + ((9*log(5) - 18)*( 15216*log(5) + (9*log(5) - 18)*(1344*log(5) + (9*log(5) - 18)*(40*log(5) - 80) - 328*log(5)^2 - 1248) - 7656*log(5)^2 + 1176*log(5)^3 - (40*log(5...