3.73.61 \(\int \frac {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}-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}+1224 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}-4608 x^{22}-288 x^{23}) \log ^2(5)+(-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 ^3(5)+(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 ^4(5)+(-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}+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}-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 ^6(5)+(-1184 x^3-11424 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}+51552 x^{15}+16280 x^{16}+3168 x^{17}+288 x^{18}) \log ^7(5)+(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 ^8(5)+(-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 ^9(5)}{-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^{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+111384 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}) \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}-65520 x^{12}-20160 x^{13}-4320 x^{14}-576 x^{15}-36 x^{16}) \log ^2(5)+(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 ^3(5)+(-126-1764 x-11466 x^2-45864 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^{14}) \log ^4(5)+(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 ^6(5)+(36+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}) \log ^7(5)+(-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 ^8(5)+(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 ^9(5)} \, dx\) [7261]

Optimal. Leaf size=28 \[ \left (-2+\left (x+\frac {x^2}{\left (x+x^2\right ) (1+x-\log (5))}\right )^4\right )^2 \]

[Out]

((x^2/(1+x-ln(5))/(x^2+x)+x)^4-2)^2

________________________________________________________________________________________

Rubi [B] Leaf count is larger than twice the leaf count of optimal. \(1192\) vs. \(2(28)=56\).
time = 24.99, antiderivative size = 1192, normalized size of antiderivative = 42.57, number of steps used = 2, number of rules used = 1, integrand size = 1697, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.001, Rules used = {2099} \begin {gather*} 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)} \end {gather*}

Antiderivative was successfully verified.

[In]

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 - 1002816*x^14 - 1296032*x^15 - 1207680*x^16 - 884448*x^17 - 523680*x^18 - 25
2432*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 - 132
480*x^5 - 502336*x^6 - 1352576*x^7 - 2718720*x^8 - 4151456*x^9 - 4734416*x^10 - 3653904*x^11 - 952528*x^12 + 2
287104*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 + 1224*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 - 90841
92*x^14 - 9080256*x^15 - 6771984*x^16 - 3951792*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 + (10
896*x^3 + 118608*x^4 + 611136*x^5 + 1978064*x^6 + 4472960*x^7 + 7384608*x^8 + 8921456*x^9 + 7401248*x^10 + 290
4672*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 - 2651
952*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]^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 - 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 - 11424*x^4 - 50688*x^5 - 136656*x^6 - 247904*x^7 - 312624*x^8 - 263376*x^9 - 109016*x^10 + 63744*x^1
1 + 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 + 8160*x^5 + 20528*x^6 + 34024*x^7 + 38088*x^8 + 26720*x^9 + 5624*x^10 - 12792*x^11 - 20008*x^1
2 - 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 - 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)*L
og[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^11 - 18564*x^12 - 8568*x^13 - 3060*x^14 - 816*x^15 - 153*x^16 - 18*x^17 - x^18 + (9 + 1
53*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 + 17503
2*x^10 + 111384*x^11 + 55692*x^12 + 21420*x^13 + 6120*x^14 + 1224*x^15 + 153*x^16 + 9*x^17)*Log[5] + (-36 - 57
6*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 - 2882
88*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 + 88
20*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 - 378378*x^8 - 252252*x^9 - 126126*x^10 - 45864*x^11 -
11466*x^12 - 1764*x^13 - 126*x^14)*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 + 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)*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]

[Out]

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*Log[5]^9) + 8*x^4*(6 - 3*Log[5] + Log[5]^2) - 8*x^3*(2 - Log[5])*(9 - 2*Lo
g[5] + Log[5]^2) - (8*(1 - Log[5])^7*(1 - Log[5]^2 + Log[5]^3))/((1 + x - Log[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 - 3
6*Log[5] + 49*Log[5]^3 - 7*Log[5]^4 - 28*Log[5]^5 - 7*Log[5]^6))/((1 + x)^5*Log[5]^11) + (4*(1 - Log[5])^6*(9
- 2*Log[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 + 672*Log[5]^3 - 455*Log[5]^4 - 448*Log[5]^5 + 252*Log[5]^6 + 224*Log[
5]^7 + 33*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 - 3
30*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]^14) + (2*(1 - Log[5])^4*(165 - 180*Log[5] - 282*Log[5]^2 + 444
*Log[5]^3 + 182*Log[5]^4 - 504*Log[5]^5 + 392*Log[5]^7 - 121*Log[5]^8 - 252*Log[5]^9 + 294*Log[5]^10 - 140*Log
[5]^11 + 35*Log[5]^12))/((1 + x - Log[5])^4*Log[5]^12) + (8*(429 - 1716*Log[5] + 1848*Log[5]^2 + 1386*Log[5]^3
- 3948*Log[5]^4 + 924*Log[5]^5 + 3066*Log[5]^6 - 1765*Log[5]^7 - 1333*Log[5]^8 + 1084*Log[5]^9 + 448*Log[5]^1
0 - 344*Log[5]^11 - 183*Log[5]^12 - 16*Log[5]^13 + Log[5]^14))/((1 + x)*Log[5]^15) - (8*(1 - Log[5])^3*(99 - 1
65*Log[5] - 120*Log[5]^2 + 360*Log[5]^3 + Log[5]^4 - 364*Log[5]^5 + 91*Log[5]^6 + 245*Log[5]^7 - 93*Log[5]^8 -
147*Log[5]^9 + 72*Log[5]^10 + 124*Log[5]^11 - 175*Log[5]^12 + 105*Log[5]^13 - 35*Log[5]^14 + 7*Log[5]^15))/((
1 + x - Log[5])^3*Log[5]^13) + (4*(1 - Log[5])^2*(429 - 990*Log[5] - 99*Log[5]^2 + 1884*Log[5]^3 - 837*Log[5]^
4 - 1598*Log[5]^5 + 1120*Log[5]^6 + 868*Log[5]^7 - 745*Log[5]^8 - 430*Log[5]^9 + 327*Log[5]^10 + 300*Log[5]^11
- 94*Log[5]^12 - 520*Log[5]^13 + 694*Log[5]^14 - 448*Log[5]^15 + 175*Log[5]^16 - 42*Log[5]^17 + 7*Log[5]^18))
/((1 + x - Log[5])^2*Log[5]^14) - (8*(1 - Log[5])*(429 - 1287*Log[5] + 561*Log[5]^2 + 1947*Log[5]^3 - 2001*Log
[5]^4 - 1077*Log[5]^5 + 1989*Log[5]^6 + 224*Log[5]^7 - 1109*Log[5]^8 - 25*Log[5]^9 + 423*Log[5]^10 + 79*Log[5]
^11 - 104*Log[5]^12 - 120*Log[5]^13 - 119*Log[5]^14 + 527*Log[5]^15 - 596*Log[5]^16 + 376*Log[5]^17 - 154*Log[
5]^18 + 42*Log[5]^19 - 7*Log[5]^20 + Log[5]^21))/((1 + x - Log[5])*Log[5]^15)

Rule 2099

Int[(P_)^(p_)*(Q_)^(q_.), x_Symbol] :> With[{PP = Factor[P]}, Int[ExpandIntegrand[PP^p*Q^q, x], x] /;  !SumQ[N
onfreeFactors[PP, x]]] /; FreeQ[q, x] && PolyQ[P, x] && PolyQ[Q, x] && IntegerQ[p] && NeQ[P, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} \end {aligned} \end {gather*}

________________________________________________________________________________________

Mathematica [B] Leaf count is larger than twice the leaf count of optimal. \(1517\) vs. \(2(28)=56\).
time = 2.15, size = 1517, normalized size = 54.18 \begin {gather*} \text {too large to display} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(256*x^3 + 3328*x^4 + 20736*x^5 + 82560*x^6 + 233984*x^7 + 497088*x^8 + 808320*x^9 + 996512*x^10 + 8
66544*x^11 + 356640*x^12 - 369072*x^13 - 1002816*x^14 - 1296032*x^15 - 1207680*x^16 - 884448*x^17 - 523680*x^1
8 - 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 + 2
14896*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 + 1337
760*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 - 4608*x^22 - 288*x^23)*Log[5]^2 + (-9728*x^3 - 110592*x^4 - 598176*x^5 - 2045488*x^6 - 4921888*x^7 - 872
8272*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 - 41
1432*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 - 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]^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 - 58512*x^11 - 71
3944*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 - 109016*x^10 + 637
44*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 + 8160*x^5 + 20528*x^6 + 34024*x^7 + 38088*x^8 + 26720*x^9 + 5624*x^10 - 12792*x^11 - 200
08*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 - 1
344*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 - 4862
0*x^9 - 43758*x^10 - 31824*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 + 111384*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)*Log[5] + (-3
6 - 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 - 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 + 25225
2*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^14)*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 + 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)*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]

[Out]

-((-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*Log[5]^2 + 728*Log[5]^3 - 70*Log[5]^4) + 8*x^19*(-944 + 1928*Log[5] - 1526
*Log[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 + 10312*Log[5]^5 - 1232*Log[5]^6 + 64*Log[5]^7) + (-1 + Log[5])^8*(3699 -
7256*Log[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 - 608*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 - 88
54*Log[5]^3 + 3846*Log[5]^4 - 573*Log[5]^5 - 132*Log[5]^6 + 63*Log[5]^7 - 9*Log[5]^8 + Log[5]^9) + 4*x^14*(105
462 - 301270*Log[5] + 398331*Log[5]^2 - 328404*Log[5]^3 + 189520*Log[5]^4 - 80210*Log[5]^5 + 25121*Log[5]^6 -
5658*Log[5]^7 + 851*Log[5]^8 - 86*Log[5]^9 + 7*Log[5]^10) + 4*x^2*(-1 + Log[5])^6*(110970 - 328650*Log[5] + 45
0573*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 + Log[5])^5*(-36990 + 128045*Log[5] - 203733*Log[5]^2 + 198711*
Log[5]^3 - 132696*Log[5]^4 + 63894*Log[5]^5 - 22754*Log[5]^6 + 6026*Log[5]^7 - 1158*Log[5]^8 + 155*Log[5]^9 -
15*Log[5]^10 + Log[5]^11) - 8*x^13*(-261718 + 900465*Log[5] - 1422745*Log[5]^2 + 1379403*Log[5]^3 - 918372*Log
[5]^4 + 442512*Log[5]^5 - 158123*Log[5]^6 + 42039*Log[5]^7 - 8099*Log[5]^8 + 1085*Log[5]^9 - 105*Log[5]^10 + 7
*Log[5]^11) + 2*x^12*(3401548 - 13446252*Log[5] + 24334426*Log[5]^2 - 26934604*Log[5]^3 + 20452269*Log[5]^4 -
11273696*Log[5]^5 + 4644458*Log[5]^6 - 1447324*Log[5]^7 + 338823*Log[5]^8 - 57988*Log[5]^9 + 7126*Log[5]^10 -
644*Log[5]^11 + 35*Log[5]^12) + 2*x^4*(-1 + Log[5])^4*(3366122 - 13335204*Log[5] + 24197494*Log[5]^2 - 2685411
6*Log[5]^3 + 20433751*Log[5]^4 - 11276608*Log[5]^5 + 4646992*Log[5]^6 - 1447824*Log[5]^7 + 338856*Log[5]^8 - 5
7988*Log[5]^9 + 7126*Log[5]^10 - 644*Log[5]^11 + 35*Log[5]^12) + 8*x^5*(-1 + Log[5])^3*(-2019750 + 9011167*Log
[5] - 18384638*Log[5]^2 + 22905754*Log[5]^3 - 19575965*Log[5]^4 + 12175335*Log[5]^5 - 5691112*Log[5]^6 + 20323
24*Log[5]^7 - 555856*Log[5]^8 + 114863*Log[5]^9 - 17542*Log[5]^10 + 1974*Log[5]^11 - 161*Log[5]^12 + 7*Log[5]^
13) - 8*x^11*(-2032170 + 9056673*Log[5] - 18453990*Log[5]^2 + 22962474*Log[5]^3 - 19602607*Log[5]^4 + 12182377
*Log[5]^5 - 5692022*Log[5]^6 + 2032351*Log[5]^7 - 555853*Log[5]^8 + 114863*Log[5]^9 - 17542*Log[5]^10 + 1974*L
og[5]^11 - 161*Log[5]^12 + 7*Log[5]^13) + 4*x^6*(-1 + Log[5])^2*(7406486 - 36746338*Log[5] + 83317229*Log[5]^2
- 115250768*Log[5]^3 + 109346787*Log[5]^4 - 75637262*Log[5]^5 + 39481183*Log[5]^6 - 15850576*Log[5]^7 + 49307
16*Log[5]^8 - 1182426*Log[5]^9 + 215061*Log[5]^10 - 29260*Log[5]^11 + 2975*Log[5]^12 - 210*Log[5]^13 + 7*Log[5
]^14) + 4*x^10*(7429782 - 36841070*Log[5] + 83480067*Log[5]^2 - 115404604*Log[5]^3 + 109433533*Log[5]^4 - 7566
6822*Log[5]^5 + 39487013*Log[5]^6 - 15851162*Log[5]^7 + 4930737*Log[5]^8 - 1182426*Log[5]^9 + 215061*Log[5]^10
- 29260*Log[5]^11 + 2975*Log[5]^12 - 210*Log[5]^13 + 7*Log[5]^14) - 8*x^9*(-5298410 + 28928199*Log[5] - 72174
151*Log[5]^2 + 109788313*Log[5]^3 - 114508915*Log[5]^4 + 87144309*Log[5]^5 - 50165665*Log[5]^6 + 22306259*Log[
5]^7 - 7740311*Log[5]^8 + 2096211*Log[5]^9 - 438429*Log[5]^10 + 69751*Log[5]^11 - 8385*Log[5]^12 + 749*Log[5]^
13 - 43*Log[5]^14 + Log[5]^15) + x^8*(47644690 - 283990136*Log[5] + 773732396*Log[5]^2 - 1284735800*Log[5]^3 +
1461881646*Log[5]^4 - 1213746616*Log[5]^5 + 763071156*Log[5]^6 - 371436136*Log[5]^7 + 141693036*Log[5]^8 - 42
498416*Log[5]^9 + 9960504*Log[5]^10 - 1799536*Log[5]^11 + 247696*Log[5]^12 - 25808*Log[5]^13 + 1920*Log[5]^14
- 80*Log[5]^15 + Log[5]^16) + 8*x^7*(5291506 - 34188849*Log[5] + 101012664*Log[5]^2 - 181841238*Log[5]^3 + 224
194664*Log[5]^4 - 201597042*Log[5]^5 + 137290120*Log[5]^6 - 72467582*Log[5]^7 + 30046041*Log[5]^8 - 9836495*Lo
g[5]^9 + 2534640*Log[5]^10 - 508180*Log[5]^11 + 78136*Log[5]^12 - 9134*Log[5]^13 + 792*Log[5]^14 - 44*Log[5]^1
5 + Log[5]^16))/((1 + x)^8*(1 + x - Log[5])^8))

________________________________________________________________________________________

Maple [B] Leaf count of result is larger than twice the leaf count of optimal. \(1402\) vs. \(2(28)=56\).
time = 4.59, size = 1403, normalized size = 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	\(\text {Expression too large to display}\)	\(3198\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((-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+79
6656*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+131
04*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^11-313
4704*x^10-4421536*x^9-4045104*x^8-2651952*x^7-1254016*x^6-410400*x^5-83664*x^4-8016*x^3)*ln(5)^5+(-1008*x^21-1
4112*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)*ln
(5)^4+(-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+133776
0*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+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+(-
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)*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^10-263376*x^9-312624*x^8-247904*x^7-136656*x^6-50688*x^5-11424*x^4-1184*x^3)*
ln(5)^7+(672*x^22+10080*x^21+73416*x^20+343616*x^19+1152200*x^18+2918160*x^17+5718832*x^16+8684032*x^15+990657
6*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^6-5
98176*x^5-110592*x^4-9728*x^3)*ln(5)^3-8*x^25-144*x^24-1272*x^23-7312*x^22-30576*x^21-98496*x^20-252432*x^19-5
23680*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+4
97088*x^8+996512*x^10+808320*x^9+82560*x^6+20736*x^5+3328*x^4+256*x^3)/(-1-18*x+(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)*ln(5)^7+(-84*x^12-1008*x^11-5544*x^1
0-18480*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+(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^11-288288*x^10-411840*x^9-4
63320*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+1
11384*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-x^18-18
*x^17-31824*x^11-18564*x^12-8568*x^13-3060*x^14-153*x^16-816*x^15-31824*x^7-43758*x^8-43758*x^10-48620*x^9-185
64*x^6-8568*x^5-3060*x^4-816*x^3-153*x^2),x,method=_RETURNVERBOSE)

[Out]

-912*x-40*x^2*ln(5)^3-32*x^3*ln(5)^2+8*x^3*ln(5)^3+8*x^5*ln(5)-48*x*ln(5)^4+164*x^2*ln(5)^2+1112*x*ln(5)+104*x
^3*ln(5)+8*x^4*ln(5)^2-664*x*ln(5)^2-24*x^4*ln(5)-360*x^2*ln(5)+x^8+8*x^6-16*x^5+48*x^4-144*x^3+360*x^2+232*ln
(5)^3*x+8*ln(5)^4*x^2-(-ln(5)^8+8*ln(5)^7-28*ln(5)^6+56*ln(5)^5-70*ln(5)^4+56*ln(5)^3-28*ln(5)^2+8*ln(5)-1)/ln
(5)^8/(1+x-ln(5))^8-4/3*(-21*ln(5)^12+168*ln(5)^11-594*ln(5)^10+1176*ln(5)^9-1302*ln(5)^8+510*ln(5)^7+609*ln(5
)^6-924*ln(5)^5+294*ln(5)^4+342*ln(5)^3-399*ln(5)^2+168*ln(5)-27)/ln(5)^10/(1+x-ln(5))^6-8/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)/(x+1)-8/5*(-35*ln(5)^14+280*ln(5)^13-1015*ln(5)^1
2+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))^5-4*(-ln(5)^12-96*ln(5)^11-454*ln(5)^10-240*ln(5)^9+130
5*ln(5)^8+560*ln(5)^7-2653*ln(5)^6+112*ln(5)^5+3192*ln(5)^4-1680*ln(5)^3-1386*ln(5)^2+1584*ln(5)-429)/ln(5)^14
/(x+1)^2-2*(-33*ln(5)^8-224*ln(5)^7-252*ln(5)^6+448*ln(5)^5+455*ln(5)^4-672*ln(5)^3-168*ln(5)^2+480*ln(5)-165)
/ln(5)^12/(x+1)^4-8/5*(35*ln(5)^6+140*ln(5)^5+35*ln(5)^4-245*ln(5)^3+180*ln(5)-75)/ln(5)^11/(x+1)^5-8/7*(-7*ln
(5)^10+56*ln(5)^9-196*ln(5)^8+385*ln(5)^7-441*ln(5)^6+245*ln(5)^5+49*ln(5)^4-189*ln(5)^3+140*ln(5)^2-49*ln(5)+
7)/ln(5)^9/(1+x-ln(5))^7-8/3*(15*ln(5)^10+204*ln(5)^9+489*ln(5)^8-252*ln(5)^7-1239*ln(5)^6+609*ln(5)^5+1554*ln
(5)^4-1260*ln(5)^3-630*ln(5)^2+990*ln(5)-297)/ln(5)^13/(x+1)^3-8*(-ln(5)^22+8*ln(5)^21-49*ln(5)^20+196*ln(5)^1
9-530*ln(5)^18+972*ln(5)^17-1123*ln(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)^5-3948*ln(5)^4+1386*ln(5)^3+1848*ln(5)^2-17
16*ln(5)+429)/ln(5)^15/(1+x-ln(5))-8/7*(7*ln(5)^2+7*ln(5)-7)/ln(5)^9/(x+1)^7+8*ln(5)^5*x-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*l
n(5)^9-573*ln(5)^8-3363*ln(5)^7+2478*ln(5)^6+2499*ln(5)^5-3822*ln(5)^4+378*ln(5)^3+2016*ln(5)^2-1386*ln(5)+297
)/ln(5)^13/(1+x-ln(5))^3-4*(-7*ln(5)^20+56*ln(5)^19-266*ln(5)^18+840*ln(5)^17-1765*ln(5)^16+2356*ln(5)^15-1640
*ln(5)^14+32*ln(5)^13+367*ln(5)^12+784*ln(5)^11-442*ln(5)^10-1928*ln(5)^9+1361*ln(5)^8+2970*ln(5)^7-3479*ln(5)
^6-1960*ln(5)^5+4704*ln(5)^4-1092*ln(5)^3-2310*ln(5)^2+1848*ln(5)-429)/ln(5)^14/(1+x-ln(5))^2-4/3*(-21*ln(5)^4
-48*ln(5)^3+21*ln(5)^2+48*ln(5)-27)/ln(5)^10/(x+1)^6-2*(-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+1/ln(5)^8/(x+1)^8

________________________________________________________________________________________

Maxima [B] Leaf count of result is larger than twice the leaf count of optimal. 2015 vs. \(2 (28) = 56\).
time = 0.41, size = 2015, normalized size = 71.96 \begin {gather*} \text {Too large to display} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-144*x^24-1272*x^23-7312*x^22-30576*x^21-252432*x^19+233984*x^7+3328*x^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^12-5
840736*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^14-5659552*x^13+375072*x^12+6366336*x^11+9595520*x^10+9198320*x^9+6457392*x^8+3411200*x^7+133776
0*x^6+371136*x^5+65408*x^4+5504*x^3)*log(5)^2+996512*x^10+20736*x^5+(72*x^24+1224*x^23+10184*x^22+54960*x^21+2
14896*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)*log
(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^5-14
4*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^12-12792*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)*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^8-247904*x^7-136656*x^6-5068
8*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+181152*x^5+38816*x^4+38
72*x^3)*log(5)^6+(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)*log(5)^5+356640*x^12-1207680*x^16+82560*x^6+497088*x^8-98496*x^20+(-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)*log(5)^4+256*x^3-8*x^25
-523680*x^18-884448*x^17-1296032*x^15-1002816*x^14-369072*x^13+866544*x^11+808320*x^9)/(-1-18*x-31824*x^7-3060
*x^4-43758*x^10-153*x^2-8568*x^5-18564*x^12-153*x^16-18564*x^6-43758*x^8+(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)*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+5940*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)^6-816*x^3-x^18-18*x^17-816*x^15-3060*x^14-8568*x^13-31824*x^11-48620*x^9
+(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+3603
6*x^3+9828*x^2+1638*x+126)*log(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)*log(5)^4+(84*x^15+1260*x^14+882
0*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+38
220*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^11-288288*x^1
0-411840*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)*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="maxima")

[Out]

x^8 + 8*x^6 + 8*x^5*(log(5) - 2) + 8*(log(5)^2 - 3*log(5) + 6)*x^4 + 8*(log(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^15 - 4*(14*log(5)^8 - 142*log(5)^7 + 919*log(5)^6 - 4158*log(5)^5 + 130
34*log(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 + 1
897*log(5)^7 - 9541*log(5)^6 + 34300*log(5)^5 - 88606*log(5)^4 + 163545*log(5)^3 - 206859*log(5)^2 + 160817*lo
g(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 + 40979
4*log(5)^6 - 1228024*log(5)^5 + 2700899*log(5)^4 - 4282884*log(5)^3 + 4648214*log(5)^2 - 3074124*log(5) + 9228
12)*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*l
og(5)^11 - 34069*log(5)^10 + 206997*log(5)^9 - 942998*log(5)^8 + 3282843*log(5)^7 - 8758453*log(5)^6 + 1781848
1*log(5)^5 - 27189579*log(5)^4 + 30056609*log(5)^3 - 22590159*log(5)^2 + 10241923*log(5) - 2095746)*x^9 - 2319
6*log(5)^10 - (8*log(5)^14 - 568*log(5)^13 + 11956*log(5)^12 - 131208*log(5)^11 + 949660*log(5)^10 - 5044024*l
og(5)^9 + 20443506*log(5)^8 - 63892104*log(5)^7 + 154020340*log(5)^6 - 284202936*log(5)^5 + 393698270*log(5)^4
- 394642184*log(5)^3 + 268489348*log(5)^2 - 110080776*log(5) + 20381229)*x^8 + 73576*log(5)^9 - 16*(4*log(5)^
14 - 158*log(5)^13 + 2450*log(5)^12 - 22323*log(5)^11 + 141938*log(5)^10 - 677561*log(5)^9 + 2490309*log(5)^8
- 7094486*log(5)^7 + 15644254*log(5)^6 - 26445814*log(5)^5 + 33546047*log(5)^4 - 30743931*log(5)^3 + 19095502*
log(5)^2 - 7144361*log(5) + 1208130)*x^7 - 178954*log(5)^8 - 8*(28*log(5)^14 - 812*log(5)^13 + 10388*log(5)^12
- 83202*log(5)^11 + 479213*log(5)^10 - 2095478*log(5)^9 + 7085442*log(5)^8 - 18617732*log(5)^7 + 37918800*log
(5)^6 - 59197452*log(5)^5 + 69255787*log(5)^4 - 58438586*log(5)^3 + 33379267*log(5)^2 - 11482974*log(5) + 1787
311)*x^6 + 334592*log(5)^7 - 8*(56*log(5)^14 - 1330*log(5)^13 + 14896*log(5)^12 - 108486*log(5)^11 + 577486*lo
g(5)^10 - 2345539*log(5)^9 + 7378168*log(5)^8 - 18048212*log(5)^7 + 34214604*log(5)^6 - 49656694*log(5)^5 + 53
906330*log(5)^4 - 42134026*log(5)^3 + 22270498*log(5)^2 - 7090161*log(5) + 1022410)*x^5 - 478360*log(5)^6 - 8*
(70*log(5)^14 - 1442*log(5)^13 + 14651*log(5)^12 - 99162*log(5)^11 + 494774*log(5)^10 - 1886507*log(5)^9 + 556
9571*log(5)^8 - 12778332*log(5)^7 + 22690286*log(5)^6 - 30784102*log(5)^5 + 31171885*log(5)^4 - 22687446*log(5
)^3 + 11157214*log(5)^2 - 3305521*log(5) + 444061)*x^4 + 516376*log(5)^5 - 56*(8*log(5)^14 - 148*log(5)^13 + 1
396*log(5)^12 - 8913*log(5)^11 + 42120*log(5)^10 - 152021*log(5)^9 + 424248*log(5)^8 - 918518*log(5)^7 + 15357
32*log(5)^6 - 1956876*log(5)^5 + 1856698*log(5)^4 - 1264125*log(5)^3 + 581152*log(5)^2 - 160999*log(5) + 20246
)*x^3 - 412048*log(5)^4 - 4*(56*log(5)^14 - 952*log(5)^13 + 8470*log(5)^12 - 51562*log(5)^11 + 232617*log(5)^1
0 - 800058*log(5)^9 + 2122904*log(5)^8 - 4359244*log(5)^7 + 6893124*log(5)^6 - 8282904*log(5)^5 + 7393092*log(
5)^4 - 4727842*log(5)^3 + 2040339*log(5)^2 - 530782*log(5) + 62742)*x^2 + 234904*log(5)^3 - 8*(8*log(5)^14 - 1
27*log(5)^13 + 1078*log(5)^12 - 6307*log(5)^11 + 27333*log(5)^10 - 90075*log(5)^9 + 228360*log(5)^8 - 446644*l
og(5)^7 + 670468*log(5)^6 - 762419*log(5)^5 + 642432*log(5)^4 - 387273*log(5)^3 + 157471*log(5)^2 - 38611*log(
5) + 4306)*x - 90292*log(5)^2 + 20936*log(5) - 2210)/(x^16 - 8*x^15*(log(5) - 2) + 4*(7*log(5)^2 - 30*log(5) +
30)*x^14 - 56*(log(5)^3 - 7*log(5)^2 + 15*log(5) - 10)*x^13 + 14*(5*log(5)^4 - 52*log(5)^3 + 182*log(5)^2 - 2
60*log(5) + 130)*x^12 - 56*(log(5)^5 - 15*log(5)^4 + 78*log(5)^3 - 182*log(5)^2 + 195*log(5) - 78)*x^11 + 28*(
log(5)^6 - 22*log(5)^5 + 165*log(5)^4 - 572*log(5)^3 + 1001*log(5)^2 - 858*log(5) + 286)*x^10 - 8*(log(5)^7 -
35*log(5)^6 + 385*log(5)^5 - 1925*log(5)^4 + 5005*log(5)^3 - 7007*log(5)^2 + 5005*log(5) - 1430)*x^9 + (log(5)
^8 - 72*log(5)^7 + 1260*log(5)^6 - 9240*log(5)^5 + 34650*log(5)^4 - 72072*log(5)^3 + 84084*log(5)^2 - 51480*lo
g(5) + 12870)*x^8 + 8*(log(5)^8 - 36*log(5)^7 + 420*log(5)^6 - 2310*log(5)^5 + 6930*log(5)^4 - 12012*log(5)^3
+ 12012*log(5)^2 - 6435*log(5) + 1430)*x^7 + log(5)^8 + 28*(log(5)^8 - 24*log(5)^7 + 210*log(5)^6 - 924*log(5)
^5 + 2310*log(5)^4 - 3432*log(5)^3 + 3003*log(5)^2 - 1430*log(5) + 286)*x^6 - 8*log(5)^7 + 56*(log(5)^8 - 18*l
og(5)^7 + 126*log(5)^6 - 462*log(5)^5 + 990*log...

________________________________________________________________________________________

Fricas [B] Leaf count of result is larger than twice the leaf count of optimal. 1856 vs. \(2 (28) = 56\).
time = 0.46, size = 1856, normalized size = 66.29 \begin {gather*} \text {Too large to display} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-144*x^24-1272*x^23-7312*x^22-30576*x^21-252432*x^19+233984*x^7+3328*x^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^12-5
840736*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^14-5659552*x^13+375072*x^12+6366336*x^11+9595520*x^10+9198320*x^9+6457392*x^8+3411200*x^7+133776
0*x^6+371136*x^5+65408*x^4+5504*x^3)*log(5)^2+996512*x^10+20736*x^5+(72*x^24+1224*x^23+10184*x^22+54960*x^21+2
14896*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)*log
(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^5-14
4*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^12-12792*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)*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^8-247904*x^7-136656*x^6-5068
8*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+181152*x^5+38816*x^4+38
72*x^3)*log(5)^6+(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)*log(5)^5+356640*x^12-1207680*x^16+82560*x^6+497088*x^8-98496*x^20+(-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)*log(5)^4+256*x^3-8*x^25
-523680*x^18-884448*x^17-1296032*x^15-1002816*x^14-369072*x^13+866544*x^11+808320*x^9)/(-1-18*x-31824*x^7-3060
*x^4-43758*x^10-153*x^2-8568*x^5-18564*x^12-153*x^16-18564*x^6-43758*x^8+(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)*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+5940*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)^6-816*x^3-x^18-18*x^17-816*x^15-3060*x^14-8568*x^13-31824*x^11-48620*x^9
+(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+3603
6*x^3+9828*x^2+1638*x+126)*log(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)*log(5)^4+(84*x^15+1260*x^14+882
0*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+38
220*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^11-288288*x^1
0-411840*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)*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="fricas")

[Out]

(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 + 128*x + 15)*log(5)^13 - 1259904*x^1
3 - 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 + 7736*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
+ 97608*x^9 + 315423*x^8 + 709656*x^7 + 1139628*x^6 + 1317624*x^5 + 1090278*x^4 + 630728*x^3 + 242536*x^2 + 5
5744*x + 5799)*log(5)^10 - 17795216*x^10 + 8*(56*x^13 + 1218*x^12 + 12404*x^11 + 75796*x^10 + 306024*x^9 + 859
625*x^8 + 1730896*x^7 + 2536940*x^6 + 2715328*x^5 + 2102464*x^4 + 1147804*x^3 + 419368*x^2 + 92096*x + 9197)*l
og(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 - 113
99192*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 - 378727*x^11 - 1645013*x^10 - 5049012*x^9 - 11286992*x^8 - 18705694*x^7 - 23154926*x^6 - 21360186*x^5 -
14489572*x^4 - 7023380*x^3 - 2303824*x^2 - 458490*x - 41824)*log(5)^7 - 25297888*x^7 + 4*(7*x^18 + 70*x^17 + 3
27*x^16 + 808*x^15 - 2235*x^14 - 55650*x^13 - 484547*x^12 - 2652132*x^11 - 10023936*x^10 - 27322048*x^9 - 5509
5642*x^8 - 83373736*x^7 - 95149102*x^6 - 81556364*x^5 - 51734948*x^4 - 23576280*x^3 - 7303774*x^2 - 1378108*x
- 119590)*log(5)^6 - 17702032*x^6 - 8*(7*x^19 + 77*x^18 + 406*x^17 + 1337*x^16 + 2639*x^15 - 4347*x^14 - 10019
8*x^13 - 734650*x^12 - 3461672*x^11 - 11506880*x^10 - 28045698*x^9 - 51222734*x^8 - 70917174*x^7 - 74652486*x^
6 - 59420266*x^5 - 35200444*x^4 - 15052674*x^3 - 4393998*x^2 - 784042*x - 64547)*log(5)^5 - 9654048*x^5 + 2*(3
5*x^20 + 420*x^19 + 2450*x^18 + 9100*x^17 + 23541*x^16 + 37800*x^15 - 57176*x^14 - 1045632*x^13 - 6509550*x^12
- 26675080*x^11 - 78498684*x^10 - 171710632*x^9 - 284518836*x^8 - 360515368*x^7 - 349864980*x^6 - 258312216*x
^5 - 142692828*x^4 - 57160712*x^3 - 15693300*x^2 - 2643032*x - 206024)*log(5)^4 - 4022264*x^4 - 8*(7*x^21 + 91
*x^20 + 581*x^19 + 2387*x^18 + 6972*x^17 + 14917*x^16 + 19406*x^15 - 37042*x^14 - 486140*x^13 - 2575952*x^12 -
9219472*x^11 - 24074708*x^10 - 47303748*x^9 - 71107294*x^8 - 82416770*x^7 - 73674226*x^6 - 50406542*x^5 - 259
37546*x^4 - 9722664*x^3 - 2507876*x^2 - 398242*x - 29363)*log(5)^3 - 1237600*x^3 + 4*(7*x^22 + 98*x^21 + 679*x
^20 + 3052*x^19 + 9856*x^18 + 23912*x^17 + 43453*x^16 + 43840*x^15 - 131828*x^14 - 1224528*x^13 - 5514840*x^12
- 17240696*x^11 - 39941572*x^10 - 70468496*x^9 - 96058250*x^8 - 101800632*x^7 - 83795050*x^6 - 53110620*x^5 -
25450218*x^4 - 8925000*x^3 - 2162450*x^2 - 323716*x - 22573)*log(5)^2 - 265200*x^2 - 8*(x^23 + 15*x^22 + 112*
x^21 + 546*x^20 + 1928*x^19 + 5176*x^18 + 10766*x^17 + 16815*x^16 + 11380*x^15 - 68300*x^14 - 464120*x^13 - 17
74068*x^12 - 4840188*x^11 - 9945068*x^10 - 15755754*x^9 - 19482052*x^8 - 18887134*x^7 - 14323210*x^6 - 8414950
*x^5 - 3757438*x^4 - 1233470*x^3 - 280890*x^2 - 39662*x - 2617)*log(5) - 35360*x - 2210)/(x^16 + 16*x^15 + 120
*x^14 + 560*x^13 + 1820*x^12 + 4368*x^11 + 8008*x^10 + 11440*x^9 + (x^8 + 8*x^7 + 28*x^6 + 56*x^5 + 70*x^4 + 5
6*x^3 + 28*x^2 + 8*x + 1)*log(5)^8 + 12870*x^8 - 8*(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)^7 + 11440*x^7 + 28*(x^10 + 10*x^9 + 45*x^8 + 120*x^7 + 210*x^6 + 252*x^5 + 210*x^4
+ 120*x^3 + 45*x^2 + 10*x + 1)*log(5)^6 + 8008*x^6 - 56*(x^11 + 11*x^10 + 55*x^9 + 165*x^8 + 330*x^7 + 462*x^
6 + 462*x^5 + 330*x^4 + 165*x^3 + 55*x^2 + 11*x + 1)*log(5)^5 + 4368*x^5 + 70*(x^12 + 12*x^11 + 66*x^10 + 220*
x^9 + 495*x^8 + 792*x^7 + 924*x^6 + 792*x^5 + 495*x^4 + 220*x^3 + 66*x^2 + 12*x + 1)*log(5)^4 + 1820*x^4 - 56*
(x^13 + 13*x^12 + 78*x^11 + 286*x^10 + 715*x^9 + 1287*x^8 + 1716*x^7 + 1716*x^6 + 1287*x^5 + 715*x^4 + 286*x^3
+ 78*x^2 + 13*x + 1)*log(5)^3 + 560*x^3 + 28*(x^14 + 14*x^13 + 91*x^12 + 364*x^11 + 1001*x^10 + 2002*x^9 + 30
03*x^8 + 3432*x^7 + 3003*x^6 + 2002*x^5 + 1001*x^4 + 364*x^3 + 91*x^2 + 14*x + 1)*log(5)^2 + 120*x^2 - 8*(x^15
+ 15*x^14 + 105*x^13 + 455*x^12 + 1365*x^11 + 3003*x^10 + 5005*x^9 + 6435*x^8 + 6435*x^7 + 5005*x^6 + 3003*x^
5 + 1365*x^4 + 455*x^3 + 105*x^2 + 15*x + 1)*log(5) + 16*x + 1)

________________________________________________________________________________________

Sympy [F(-1)] Timed out
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-8*x**25+3328*x**4+233984*x**7+82560*x**6+497088*x**8+808320*x**9+996512*x**10+20736*x**5-523680*x*
*18-884448*x**17-1207680*x**16-1296032*x**15-1002816*x**14-369072*x**13+356640*x**12+866544*x**11-144*x**24-12
72*x**23-7312*x**22-30576*x**21-98496*x**20+256*x**3-252432*x**19+(-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+102
4160*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+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)*ln(5)**5+(-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+2
904672*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)*ln(5)**4+(-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)*ln(5)**2+(72*x**24+1224*x**23+10184*x**22+54
960*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**8-1352576*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**9-1
944*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**14-16
600*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+2
08*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**10-263376*x**9-312624*x**8-247904*x**7-136656*x**6-50688*x**5-11424*x**4-1184*x**3)*ln(5)**7+(6
72*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)*ln(5)**3)/(-1-18*x-3060*x**4-31824*x**7-18564*x**6-43758*x**8-153*x**
2-48620*x**9-43758*x**10-8568*x**5-x**18-18*x**17-153*x**16-816*x**15-3060*x**14-8568*x**13-18564*x**12-31824*
x**11-816*x**3+(-36*x**16-576*x**15-4320*x**14-20160*x**13-65520*x**12-157248*x**11-288288*x**10-411840*x**9-4
63320*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+21
420*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+214
20*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+1
1880*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**1
1+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+(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),x)

[Out]

Timed out

________________________________________________________________________________________

Giac [B] Leaf count of result is larger than twice the leaf count of optimal. 1904 vs. \(2 (28) = 56\).
time = 0.45, size = 1904, normalized size = 68.00 \begin {gather*} \text {Too large to display} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-144*x^24-1272*x^23-7312*x^22-30576*x^21-252432*x^19+233984*x^7+3328*x^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^12-5
840736*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^14-5659552*x^13+375072*x^12+6366336*x^11+9595520*x^10+9198320*x^9+6457392*x^8+3411200*x^7+133776
0*x^6+371136*x^5+65408*x^4+5504*x^3)*log(5)^2+996512*x^10+20736*x^5+(72*x^24+1224*x^23+10184*x^22+54960*x^21+2
14896*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)*log
(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^5-14
4*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^12-12792*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)*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^8-247904*x^7-136656*x^6-5068
8*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+181152*x^5+38816*x^4+38
72*x^3)*log(5)^6+(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)*log(5)^5+356640*x^12-1207680*x^16+82560*x^6+497088*x^8-98496*x^20+(-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)*log(5)^4+256*x^3-8*x^25
-523680*x^18-884448*x^17-1296032*x^15-1002816*x^14-369072*x^13+866544*x^11+808320*x^9)/(-1-18*x-31824*x^7-3060
*x^4-43758*x^10-153*x^2-8568*x^5-18564*x^12-153*x^16-18564*x^6-43758*x^8+(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)*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+5940*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)^6-816*x^3-x^18-18*x^17-816*x^15-3060*x^14-8568*x^13-31824*x^11-48620*x^9
+(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+3603
6*x^3+9828*x^2+1638*x+126)*log(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)*log(5)^4+(84*x^15+1260*x^14+882
0*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+38
220*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^11-288288*x^1
0-411840*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)*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="giac")

[Out]

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*log(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*log(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 - 335216*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 - 819588*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 - 8
3104*x^6*log(5)^12 + 10640*x^5*log(5)^13 - 560*x^4*log(5)^14 - 7776*x^15*log(5)^2 + 114672*x^14*log(5)^3 - 708
848*x^13*log(5)^4 + 2456048*x^12*log(5)^5 - 5341616*x^11*log(5)^6 + 7700952*x^10*log(5)^7 - 7543984*x^9*log(5)
^8 + 5044024*x^8*log(5)^9 - 2271008*x^7*log(5)^10 + 665616*x^6*log(5)^11 - 119168*x^5*log(5)^12 + 11536*x^4*lo
g(5)^13 - 448*x^3*log(5)^14 + 8984*x^15*log(5) - 172468*x^14*log(5)^2 + 1308360*x^13*log(5)^3 - 5401798*x^12*l
og(5)^4 + 13779784*x^11*log(5)^5 - 23108116*x^10*log(5)^6 + 26262744*x^9*log(5)^7 - 20443506*x^8*log(5)^8 + 10
840976*x^7*log(5)^9 - 3833704*x^6*log(5)^10 + 867888*x^5*log(5)^11 - 117208*x^4*log(5)^12 + 8288*x^3*log(5)^13
- 224*x^2*log(5)^14 - 5168*x^15 + 161512*x^14*log(5) - 1654872*x^13*log(5)^2 + 8565768*x^12*log(5)^3 - 264069
36*x^11*log(5)^4 + 52497368*x^10*log(5)^5 - 70067624*x^9*log(5)^6 + 63892104*x^8*log(5)^7 - 39844944*x^7*log(5
)^8 + 16763824*x^6*log(5)^9 - 4619888*x^5*log(5)^10 + 793296*x^4*log(5)^11 - 78176*x^3*log(5)^12 + 3808*x^2*lo
g(5)^13 - 64*x*log(5)^14 - 70968*x^14 + 1286536*x^13*log(5) - 9296428*x^12*log(5)^2 + 36630688*x^11*log(5)^3 -
89177924*x^10*log(5)^4 + 142547848*x^9*log(5)^5 - 154020340*x^8*log(5)^6 + 113511776*x^7*log(5)^7 - 56683536*
x^6*log(5)^8 + 18764312*x^5*log(5)^9 - 3958192*x^4*log(5)^10 + 499128*x^3*log(5)^11 - 33880*x^2*log(5)^12 + 10
16*x*log(5)^13 - 8*log(5)^14 - 458480*x^13 + 6148248*x^12*log(5) - 34698736*x^11*log(5)^2 + 109783296*x^10*log
(5)^3 - 217516632*x^9*log(5)^4 + 284202936*x^8*log(5)^5 - 250308064*x^7*log(5)^6 + 148941856*x^6*log(5)^7 - 59
025344*x^5*log(5)^8 + 15092056*x^4*log(5)^9 - 2358720*x^3*log(5)^10 + 206248*x^2*log(5)^11 - 8624*x*log(5)^12
+ 120*log(5)^13 - 1845624*x^12 + 19924648*x^11*log(5) - 92077212*x^10*log(5)^2 + 240452872*x^9*log(5)^3 - 3936
98270*x^8*log(5)^4 + 423133024*x^7*log(5)^5 - 303350400*x^6*log(5)^6 + 144385696*x^5*log(5)^7 - 44556568*x^4*l
og(5)^8 + 8513176*x^3*log(5)^9 - 930468*x^2*log(5)^10 + 50456*x*log(5)^11 - 980*log(5)^12 - 5171728*x^11 + 466
68888*x^10*log(5) - 180721272*x^9*log(5)^2 + 394642184*x^8*log(5)^3 - 536736752*x^7*log(5)^4 + 473579616*x^6*l
og(5)^5 - 273716832*x^5*log(5)^6 + 102226656*x^4*log(5)^7 - 23757888*x^3*log(5)^8 + 3200232*x^2*log(5)^9 - 218
664*x*log(5)^10 + 5544*log(5)^11 - 10676952*x^10 + 81935384*x^9*log(5) - 268489348*x^8*log(5)^2 + 491902896*x^
7*log(5)^3 - 554046296*x^6*log(5)^4 + 397253552*x^5*log(5)^5 - 181522288*x^4*log(5)^6 + 51437008*x^3*log(5)^7
- 8491616*x^2*log(5)^8 + 720600*x*log(5)^9 - 23196*log(5)^10 - 16765968*x^9 + 110080776*x^8*log(5) - 305528032
*x^7*log(5)^2 + 467508688*x^6*log(5)^3 - 431250640*x^5*log(5)^4 + 246272816*x^4*log(5)^5 - 86000992*x^3*log(5)
^6 + 17436976*x^2*log(5)^7 - 1826880*x*log(5)^8 + 73576*log(5)^9 - 20381229*x^8 + 114309776*x^7*log(5) - 26703
4136*x^6*log(5)^2 + 337072208*x^5*log(5)^3 - 249375080*x^4*log(5)^4 + 109585056*x^3*log(5)^5 - 27572496*x^2*lo
g(5)^6 + 3573152*x*log(5)^7 - 178954*log(5)^8 - 19330080*x^7 + 91863792*x^6*log(5) - 178163984*x^5*log(5)^2 +
181499568*x^4*log(5)^3 - 103975088*x^3*log(5)^4 + 33131616*x^2*log(5)^5 - 5363744*x*log(5)^6 + 334592*log(5)^7
- 14298488*x^6 + 56721288*x^5*log(5) - 89257712*x^4*log(5)^2 + 70791000*x^3*log(5)^3 - 29572368*x^2*log(5)^4
+ 6099352*x*log(5)^5 - 478360*log(5)^6 - 8179280*x^5 + 26444168*x^4*log(5) - 32544512*x^3*log(5)^2 + 18911368*
x^2*log(5)^3 - 5139456*x*log(5)^4 + 516376*log(5)^5 - 3552488*x^4 + 9015944*x^3*log(5) - 8161356*x^2*log(5)^2
+ 3098184*x*log(5)^3 - 412048*log(5)^4 - 1133776*x^3 + 2123128*x^2*log(5) - 1259768*x*log(5)^2 + 234904*log(5)
^3 - 250968*x^2 + 308888*x*log(5) - 90292*log(5)^2 - 34448*x + 20936*log(5) - 2210)/(x^2 - x*log(5) + 2*x - lo
g(5) + 1)^8

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Mupad [B]
time = 29.20, size = 2500, normalized size = 89.29 \begin {gather*} \text {Too large to display} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((log(5)^2*(5659552*x^13 - 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 - 5504*x^3 + 9084192*x^14 + 9080256*x^15 + 6771984*x^16 + 3951792*x
^17 + 1823216*x^18 + 658768*x^19 + 181272*x^20 + 35960*x^21 + 4608*x^22 + 288*x^23) + log(5)^6*(58512*x^11 - 3
8816*x^4 - 181152*x^5 - 520928*x^6 - 1024160*x^7 - 1429488*x^8 - 1389264*x^9 - 796656*x^10 - 3872*x^3 + 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)^5*
(8016*x^3 + 83664*x^4 + 410400*x^5 + 1254016*x^6 + 2651952*x^7 + 4045104*x^8 + 4421536*x^9 + 3134704*x^10 + 63
6096*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^10 - 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 - 7384608*x^8 - 8921456*x^9 - 7401248*x^10 - 2904672*x^11 - 10896*x
^3 + 5968528*x^13 + 6586272*x^14 + 5036528*x^15 + 2889992*x^16 + 1261512*x^17 + 411432*x^18 + 95368*x^19 + 141
12*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 - 497088*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 + 984
96*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 - 59817
6*x^5 - 2045488*x^6 - 4921888*x^7 - 8728272*x^8 - 11506656*x^9 - 10817504*x^10 - 5840736*x^11 - 9728*x^3 + 751
7632*x^13 + 9906576*x^14 + 8684032*x^15 + 5718832*x^16 + 2918160*x^17 + 1152200*x^18 + 343616*x^19 + 73416*x^2
0 + 10080*x^21 + 672*x^22) - log(5)*(2287104*x^13 - 22272*x^4 - 132480*x^5 - 502336*x^6 - 1352576*x^7 - 271872
0*x^8 - 4151456*x^9 - 4734416*x^10 - 3653904*x^11 - 952528*x^12 - 1792*x^3 + 4629792*x^14 + 5263520*x^15 + 440
3552*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 + 136656*x^6 + 247904*x^7 + 312624*x^8 + 263376*x^9 + 1090
16*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^1
8))/(18*x + log(5)^4*(1764*x + 11466*x^2 + 45864*x^3 + 126126*x^4 + 252252*x^5 + 378378*x^6 + 432432*x^7 + 378
378*x^8 + 252252*x^9 + 126126*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*(12
60*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 + 25
2252*x^10 + 114660*x^11 + 38220*x^12 + 8820*x^13 + 1260*x^14 + 84*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 + 111384*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) + log(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 + 65520*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 + 77616*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^13 + 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 + 126) + 1),x)

[Out]

x*(394160*log(5) - (40*log(5) - 80)*(4320*log(5)^2 - 6120*log(5) - 1260*log(5)^3 + 126*log(5)^4 + 3060) + (9*l
og(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) - 765
6*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*lo
g(5) + 153)*(1344*log(5) + (9*log(5) - 18)*(40*log(5) - 80) - 328*log(5)^2 - 1248) - 72752*log(5)^2 + 22624*lo
g(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 + 1176*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*log(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*lo
g(5) - 18)*(15216*log(5) + (9*log(5) - 18)*(1344*log(5) + (9*log(5) - 18)*(40*log(5) - 80) - 328*log(5)^2 - 12
48) - 7656*log(5)^2 + 1176*log(5)^3 - (40*log(5) - 80)*(36*log(5)^2 - 153*log(5) + 153) - 9216))/2 - ((36*log(
5)^2 - 153*log(5) + 153)*(1344*log(5) + (9*log(5) - 18)*(40*log(5) - 80) - 328*log(5)^2 - 1248))/2 - 36376*log
(5)^2 + 11312*log(5)^3 - 1204*log(5)^4 - 21480) + x^4*(336*log(5) + ((9*log(5) - 18)*(40*log(5) - 80))/4 - 82*
log(5)^2 - 312) + x^5*(8*log(5) - 16) + 8*x^6 + x^8 - ((2*(4497292800*log(5) - 1499097600*log(125) + 152792640
00*log(5)*log(125) - 11459448000*log(5)*log(125)^2 - 73171338240*log(5)^2*log(125) + 3819816000*log(5)*log(125
)^3 + 221074613760*log(5)^3*log(125) - 477477000*log(5)*log(125)^4 - 478475437440*log(5)^4*log(125) + 79867647
5520*log(5)^5*log(125) - 1077807158208*log(5)^6*log(125) + 1211034016896*log(5)^7*log(125) - 1152746569216*log
(5)^8*log(125) + 938640675280*log(5)^9*log(125) - 656748456016*log(5)^10*log(125) + 394547783424*log(5)^11*log
(125) - 202198732448*log(5)^12*log(125) + 87291289168*log(5)^13*log(125) - 31073014816*log(5)^14*log(125) + 87
80302608*log(5)^15*log(125) - 1840953968*log(5)^16*log(125) + 254158908*log(5)^17*log(125) - 18054460*log(5)^1
8*log(125) + 223688*log(5)^19*log(125) + 8600*log(5)^20*log(125) + 524*log(5)^21*log(125) + 36*log(5)^22*log(1
25) - 55956700800*log(5)^2 + 332767955520*log(5)^3 - 1259000542800*log(5)^4 + 3398575700520*log(5)^5 - 6949956
764520*log(5)^6 + 11149118132724*log(5)^7 - 14330831790132*log(5)^8 + 14948487919200*log(5)^9 - 12741286874448
*log(5)^10 + 8894845964676*log(5)^11 - 5076902973816*log(5)^12 + 2354695019754*log(5)^13 - 877402282458*log(5)
^14 + 257775776319*log(5)^15 - 57910748992*log(5)^16 + 9440483074*log(5)^17 - 1010675288*log(5)^18 + 52840499*
log(5)^19 + 6641485*log(5)^20 - 9056278*log(5)^21 + 8370214*log(5)^22 - 5855468*log(5)^23 + 3131695*log(5)^24
- 1287580*log(5)^25 + 405930*log(5)^26 - 97020*log(5)^27 + 17150*log(5)^28 - 2100*log(5)^29 + 140*log(5)^30 +
1124323200*log(125)^2 - 374774400*log(125)^3 + 46846800*log(125)^4 + 54316342080*log(5)^2*log(125)^2 - 1791806
0160*log(5)^2*log(125)^3 - 160076236320*log(5)^3*log(125)^2 + 2216334120*log(5)^2*log(125)^4 + 51448837440*log
(5)^3*log(125)^3 + 331698407040*log(5)^4*log(125)^2 - 6192366180*log(5)^3*log(125)^4 - 101607105600*log(5)^4*l
og(125)^3 - 518969238480*log(5)^5*log(125)^2 + 11592721140*log(5)^4*log(125)^4 + 147265327440*log(5)^5*log(125
)^3 + 642506165136*log(5)^6*log(125)^2 - 15311982840*log(5)^5*log(125)^4 - 163365168912*log(5)^6*log(125)^3 -
648790893432*log(5)^7*log(125)^2 + 14624285544*log(5)^6*log(125)^4 + 142630967424*log(5)^7*log(125)^3 + 543306
844344*log(5)^8*log(125)^2 - 10172879508*log(5)^7*log(125)^4 - 99419696992*log(5)^8*log(125)^3 - 379585059744*
log(5)^9*log(125)^2 + 5115319352*log(5)^8*log(125)^4 + 55212869536*log(5)^9*log(125)^3 + 220907919840*log(5)^1
0*log(125)^2 - 1815168938*log(5)^9*log(125)^4 - 23926124784*log(5)^10*log(125)^3 - 106118307696*log(5)^11*log(
125)^2 + 433105922*log(5)^10*log(125)^4 + 7766334464*log(5)^11*log(125)^3 + 41195089416*log(5)^12*log(125)^2 -
63207339*log(5)^11*log(125)^4 - 1768634080*log(5)^12*log(125)^3 - 12409313028*log(5)^13*log(125)^2 + 4526299*
log(5)^12*log(125)^4 + 253270444*log(5)^13*log(125)^3 + 2707216404*log(5)^14*log(125)^2 - 55136*log(5)^13*log(
125)^4 - 18088428*log(5)^14*log(125)^3 - 380570442*log(5)^15*log(125)^2 - 2096*log(5)^14*log(125)^4 + 221592*l
og(5)^15*log(125)^3 + 27107274*log(5)^16*log(125)^2 - 131*log(5)^15*log(125)^4 + 8456*log(5)^16*log(125)^3 - 3
33960*log(5)^17*log(125)^2 - 9*log(5)^16*log(125)^4 + 524*log(5)^17*log(125)^3 - 12792*log(5)^18*log(125)^2 +
36*log(5)^18*log(125)^3 - 786*log(5)^19*log(125...

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