Integrand size = 2007, antiderivative size = 29 \[ \text {the integral} =-x+\left (x-\frac {(3-\log (5))^2}{(3-x) \log ^2(4)}\right )^8 \] Output:
(x-1/4*(3-ln(5))^2/ln(2)^2/(3-x))^8-x
Leaf count is larger than twice the leaf count of optimal. \(479\) vs. \(2(29)=58\).
Time = 0.51 (sec) , antiderivative size = 479, normalized size of antiderivative = 16.52 \[ \text {the integral} =\frac {x^8 \log ^{16}(4)-x \log ^{10}(4) \left (\log ^6(4)-1944 \log ^4(4) (-3+\log (5))^2-3024 \log ^2(4) (-3+\log (5))^4-504 (-3+\log (5))^6\right )+24 x^5 \log ^{14}(4) (-3+\log (5))^2+8 x^6 \log ^{14}(4) (-3+\log (5))^2+24 x^3 \log ^{12}(4) \left (9 \log ^2(4)+7 (-3+\log (5))^2\right ) (-3+\log (5))^2+4 x^4 \log ^{12}(4) \left (18 \log ^2(4)+7 (-3+\log (5))^2\right ) (-3+\log (5))^2+4 x^2 \log ^{10}(4) \left (162 \log ^4(4)+189 \log ^2(4) (-3+\log (5))^2+14 (-3+\log (5))^4\right ) (-3+\log (5))^2+\frac {24 \log ^8(4) \left (729 \log ^6(4)+1701 \log ^4(4) (-3+\log (5))^2+630 \log ^2(4) (-3+\log (5))^4+35 (-3+\log (5))^6\right ) (-3+\log (5))^2}{-3+x}+\frac {28 \log ^6(4) \left (729 \log ^6(4)+810 \log ^4(4) (-3+\log (5))^2+135 \log ^2(4) (-3+\log (5))^4+2 (-3+\log (5))^6\right ) (-3+\log (5))^4}{(-3+x)^2}+\frac {504 \log ^6(4) \left (27 \log ^4(4)+15 \log ^2(4) (-3+\log (5))^2+(-3+\log (5))^4\right ) (-3+\log (5))^6}{(-3+x)^3}+\frac {14 \log ^4(4) \left (405 \log ^4(4)+108 \log ^2(4) (-3+\log (5))^2+2 (-3+\log (5))^4\right ) (-3+\log (5))^8}{(-3+x)^4}+\frac {168 \log ^4(4) \left (9 \log ^2(4)+(-3+\log (5))^2\right ) (-3+\log (5))^{10}}{(-3+x)^5}+\frac {4 \log ^2(4) \left (63 \log ^2(4)+2 (-3+\log (5))^2\right ) (-3+\log (5))^{12}}{(-3+x)^6}+\frac {24 \log ^2(4) (-3+\log (5))^{14}}{(-3+x)^7}+\frac {(-3+\log (5))^{16}}{(-3+x)^8}}{\log ^{16}(4)} \] Input:
Integrate[(-344373768 + (344373768 + 573956280*x - 229582512*x^2)*Log[4]^2 + (-803538792*x + 267846264*x^3 - 59521392*x^4)*Log[4]^4 + (803538792*x^2 - 624974616*x^3 + 89282088*x^4 + 29760696*x^5 - 6613488*x^6)*Log[4]^6 + ( -446410440*x^3 + 595213920*x^4 - 297606960*x^5 + 66134880*x^6 - 5511240*x^ 7)*Log[4]^8 + (148803480*x^4 - 267846264*x^5 + 198404640*x^6 - 77157360*x^ 7 + 16533720*x^8 - 1837080*x^9 + 81648*x^10)*Log[4]^10 + (-29760696*x^5 + 66134880*x^6 - 62828136*x^7 + 33067440*x^8 - 10410120*x^9 + 1959552*x^10 - 204120*x^11 + 9072*x^12)*Log[4]^12 + (3306744*x^6 - 8660520*x^7 + 9920232 *x^8 - 6491016*x^9 + 2653560*x^10 - 694008*x^11 + 113400*x^12 - 10584*x^13 + 432*x^14)*Log[4]^14 + (19683 - 59049*x + 78732*x^2 - 61236*x^3 + 30618* x^4 - 10206*x^5 + 2268*x^6 - 157788*x^7 + 472419*x^8 - 629857*x^9 + 489888 *x^10 - 244944*x^11 + 81648*x^12 - 18144*x^13 + 2592*x^14 - 216*x^15 + 8*x ^16)*Log[4]^16 + (1836660096 + (-1607077584 - 2678462640*x + 1071385056*x^ 2)*Log[4]^2 + (3214155168*x - 1071385056*x^3 + 238085568*x^4)*Log[4]^4 + ( -2678462640*x^2 + 2083248720*x^3 - 297606960*x^4 - 99202320*x^5 + 22044960 *x^6)*Log[4]^6 + (1190427840*x^3 - 1587237120*x^4 + 793618560*x^5 - 176359 680*x^6 + 14696640*x^7)*Log[4]^8 + (-297606960*x^4 + 535692528*x^5 - 39680 9280*x^6 + 154314720*x^7 - 33067440*x^8 + 3674160*x^9 - 163296*x^10)*Log[4 ]^10 + (39680928*x^5 - 88179840*x^6 + 83770848*x^7 - 44089920*x^8 + 138801 60*x^9 - 2612736*x^10 + 272160*x^11 - 12096*x^12)*Log[4]^12 + (-2204496*x^ 6 + 5773680*x^7 - 6613488*x^8 + 4327344*x^9 - 1769040*x^10 + 462672*x^11 - 75600*x^12 + 7056*x^13 - 288*x^14)*Log[4]^14)*Log[5] + (-4591650240 + (34 82001432 + 5803335720*x - 2321334288*x^2)*Log[4]^2 + (-5892617808*x + 1964 205936*x^3 - 436490208*x^4)*Log[4]^4 + (4017693960*x^2 - 3124873080*x^3 + 446410440*x^4 + 148803480*x^5 - 33067440*x^6)*Log[4]^6 + (-1388832480*x^3 + 1851776640*x^4 - 925888320*x^5 + 205752960*x^6 - 17146080*x^7)*Log[4]^8 + (248005800*x^4 - 446410440*x^5 + 330674400*x^6 - 128595600*x^7 + 2755620 0*x^8 - 3061800*x^9 + 136080*x^10)*Log[4]^10 + (-19840464*x^5 + 44089920*x ^6 - 41885424*x^7 + 22044960*x^8 - 6940080*x^9 + 1306368*x^10 - 136080*x^1 1 + 6048*x^12)*Log[4]^12 + (367416*x^6 - 962280*x^7 + 1102248*x^8 - 721224 *x^9 + 294840*x^10 - 77112*x^11 + 12600*x^12 - 1176*x^13 + 48*x^14)*Log[4] ^14)*Log[5]^2 + (7142567040 + (-4642668576 - 7737780960*x + 3095112384*x^2 )*Log[4]^2 + (6547353120*x - 2182451040*x^3 + 484989120*x^4)*Log[4]^4 + (- 3571283520*x^2 + 2777664960*x^3 - 396809280*x^4 - 132269760*x^5 + 29393280 *x^6)*Log[4]^6 + (925888320*x^3 - 1234517760*x^4 + 617258880*x^5 - 1371686 40*x^6 + 11430720*x^7)*Log[4]^8 + (-110224800*x^4 + 198404640*x^5 - 146966 400*x^6 + 57153600*x^7 - 12247200*x^8 + 1360800*x^9 - 60480*x^10)*Log[4]^1 0 + (4408992*x^5 - 9797760*x^6 + 9307872*x^7 - 4898880*x^8 + 1542240*x^9 - 290304*x^10 + 30240*x^11 - 1344*x^12)*Log[4]^12)*Log[5]^3 + (-7737780960 + (4255779528 + 7092965880*x - 2837186352*x^2)*Log[4]^2 + (-4910514840*x + 1636838280*x^3 - 363741840*x^4)*Log[4]^4 + (2083248720*x^2 - 1620304560*x ^3 + 231472080*x^4 + 77157360*x^5 - 17146080*x^6)*Log[4]^6 + (-385786800*x ^3 + 514382400*x^4 - 257191200*x^5 + 57153600*x^6 - 4762800*x^7)*Log[4]^8 + (27556200*x^4 - 49601160*x^5 + 36741600*x^6 - 14288400*x^7 + 3061800*x^8 - 340200*x^9 + 15120*x^10)*Log[4]^10 + (-367416*x^5 + 816480*x^6 - 775656 *x^7 + 408240*x^8 - 128520*x^9 + 24192*x^10 - 2520*x^11 + 112*x^12)*Log[4] ^12)*Log[5]^4 + (6190224768 + (-2837186352 - 4728643920*x + 1891457568*x^2 )*Log[4]^2 + (2618941248*x - 872980416*x^3 + 193995648*x^4)*Log[4]^4 + (-8 33299488*x^2 + 648121824*x^3 - 92588832*x^4 - 30862944*x^5 + 6858432*x^6)* Log[4]^6 + (102876480*x^3 - 137168640*x^4 + 68584320*x^5 - 15240960*x^6 + 1270080*x^7)*Log[4]^8 + (-3674160*x^4 + 6613488*x^5 - 4898880*x^6 + 190512 0*x^7 - 408240*x^8 + 45360*x^9 - 2016*x^10)*Log[4]^10)*Log[5]^5 + (-378291 5136 + (1418593176 + 2364321960*x - 945728784*x^2)*Log[4]^2 + (-1018477152 *x + 339492384*x^3 - 75442752*x^4)*Log[4]^4 + (231472080*x^2 - 180033840*x ^3 + 25719120*x^4 + 8573040*x^5 - 1905120*x^6)*Log[4]^6 + (-17146080*x^3 + 22861440*x^4 - 11430720*x^5 + 2540160*x^6 - 211680*x^7)*Log[4]^8 + (20412 0*x^4 - 367416*x^5 + 272160*x^6 - 105840*x^7 + 22680*x^8 - 2520*x^9 + 112* x^10)*Log[4]^10)*Log[5]^6 + (1801388160 + (-540416448 - 900694080*x + 3602 77632*x^2)*Log[4]^2 + (290993472*x - 96997824*x^3 + 21555072*x^4)*Log[4]^4 + (-44089920*x^2 + 34292160*x^3 - 4898880*x^4 - 1632960*x^5 + 362880*x^6) *Log[4]^6 + (1632960*x^3 - 2177280*x^4 + 1088640*x^5 - 241920*x^6 + 20160* x^7)*Log[4]^8)*Log[5]^7 + (-675520560 + (157621464 + 262702440*x - 1050809 76*x^2)*Log[4]^2 + (-60623640*x + 20207880*x^3 - 4490640*x^4)*Log[4]^4 + ( 5511240*x^2 - 4286520*x^3 + 612360*x^4 + 204120*x^5 - 45360*x^6)*Log[4]^6 + (-68040*x^3 + 90720*x^4 - 45360*x^5 + 10080*x^6 - 840*x^7)*Log[4]^8)*Log [5]^8 + (200154240 + (-35026992 - 58378320*x + 23351328*x^2)*Log[4]^2 + (8 981280*x - 2993760*x^3 + 665280*x^4)*Log[4]^4 + (-408240*x^2 + 317520*x^3 - 45360*x^4 - 15120*x^5 + 3360*x^6)*Log[4]^6)*Log[5]^9 + (-46702656 + (583 7832 + 9729720*x - 3891888*x^2)*Log[4]^2 + (-898128*x + 299376*x^3 - 66528 *x^4)*Log[4]^4 + (13608*x^2 - 10584*x^3 + 1512*x^4 + 504*x^5 - 112*x^6)*Lo g[4]^6)*Log[5]^10 + (8491392 + (-707616 - 1179360*x + 471744*x^2)*Log[4]^2 + (54432*x - 18144*x^3 + 4032*x^4)*Log[4]^4)*Log[5]^11 + (-1179360 + (589 68 + 98280*x - 39312*x^2)*Log[4]^2 + (-1512*x + 504*x^3 - 112*x^4)*Log[4]^ 4)*Log[5]^12 + (120960 + (-3024 - 5040*x + 2016*x^2)*Log[4]^2)*Log[5]^13 + (-8640 + (72 + 120*x - 48*x^2)*Log[4]^2)*Log[5]^14 + 384*Log[5]^15 - 8*Lo g[5]^16)/((-19683 + 59049*x - 78732*x^2 + 61236*x^3 - 30618*x^4 + 10206*x^ 5 - 2268*x^6 + 324*x^7 - 27*x^8 + x^9)*Log[4]^16),x]
Output:
(x^8*Log[4]^16 - x*Log[4]^10*(Log[4]^6 - 1944*Log[4]^4*(-3 + Log[5])^2 - 3 024*Log[4]^2*(-3 + Log[5])^4 - 504*(-3 + Log[5])^6) + 24*x^5*Log[4]^14*(-3 + Log[5])^2 + 8*x^6*Log[4]^14*(-3 + Log[5])^2 + 24*x^3*Log[4]^12*(9*Log[4 ]^2 + 7*(-3 + Log[5])^2)*(-3 + Log[5])^2 + 4*x^4*Log[4]^12*(18*Log[4]^2 + 7*(-3 + Log[5])^2)*(-3 + Log[5])^2 + 4*x^2*Log[4]^10*(162*Log[4]^4 + 189*L og[4]^2*(-3 + Log[5])^2 + 14*(-3 + Log[5])^4)*(-3 + Log[5])^2 + (24*Log[4] ^8*(729*Log[4]^6 + 1701*Log[4]^4*(-3 + Log[5])^2 + 630*Log[4]^2*(-3 + Log[ 5])^4 + 35*(-3 + Log[5])^6)*(-3 + Log[5])^2)/(-3 + x) + (28*Log[4]^6*(729* Log[4]^6 + 810*Log[4]^4*(-3 + Log[5])^2 + 135*Log[4]^2*(-3 + Log[5])^4 + 2 *(-3 + Log[5])^6)*(-3 + Log[5])^4)/(-3 + x)^2 + (504*Log[4]^6*(27*Log[4]^4 + 15*Log[4]^2*(-3 + Log[5])^2 + (-3 + Log[5])^4)*(-3 + Log[5])^6)/(-3 + x )^3 + (14*Log[4]^4*(405*Log[4]^4 + 108*Log[4]^2*(-3 + Log[5])^2 + 2*(-3 + Log[5])^4)*(-3 + Log[5])^8)/(-3 + x)^4 + (168*Log[4]^4*(9*Log[4]^2 + (-3 + Log[5])^2)*(-3 + Log[5])^10)/(-3 + x)^5 + (4*Log[4]^2*(63*Log[4]^2 + 2*(- 3 + Log[5])^2)*(-3 + Log[5])^12)/(-3 + x)^6 + (24*Log[4]^2*(-3 + Log[5])^1 4)/(-3 + x)^7 + (-3 + Log[5])^16/(-3 + x)^8)/Log[4]^16
Leaf count is larger than twice the leaf count of optimal. \(557\) vs. \(2(29)=58\).
Time = 3.88 (sec) , antiderivative size = 557, normalized size of antiderivative = 19.21, number of steps used = 5, number of rules used = 5, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.002, Rules used = {27, 25, 2007, 2389, 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 {\log ^2(4) \left (-229582512 x^2+573956280 x+344373768\right )-8 \log ^{16}(5)+384 \log ^{15}(5)+\left (\left (-48 x^2+120 x+72\right ) \log ^2(4)-8640\right ) \log ^{14}(5)+\left (\log ^2(4) \left (2016 x^2-5040 x-3024\right )+120960\right ) \log ^{13}(5)+\left (\log ^2(4) \left (-39312 x^2+98280 x+58968\right )+\left (-112 x^4+504 x^3-1512 x\right ) \log ^4(4)-1179360\right ) \log ^{12}(5)+\left (\log ^2(4) \left (471744 x^2-1179360 x-707616\right )+\left (4032 x^4-18144 x^3+54432 x\right ) \log ^4(4)+8491392\right ) \log ^{11}(5)+\left (\log ^2(4) \left (-3891888 x^2+9729720 x+5837832\right )+\left (-112 x^6+504 x^5+1512 x^4-10584 x^3+13608 x^2\right ) \log ^6(4)+\left (-66528 x^4+299376 x^3-898128 x\right ) \log ^4(4)-46702656\right ) \log ^{10}(5)+\left (\log ^2(4) \left (23351328 x^2-58378320 x-35026992\right )+\left (3360 x^6-15120 x^5-45360 x^4+317520 x^3-408240 x^2\right ) \log ^6(4)+\left (665280 x^4-2993760 x^3+8981280 x\right ) \log ^4(4)+200154240\right ) \log ^9(5)+\left (\log ^2(4) \left (-105080976 x^2+262702440 x+157621464\right )+\left (-840 x^7+10080 x^6-45360 x^5+90720 x^4-68040 x^3\right ) \log ^8(4)+\left (-45360 x^6+204120 x^5+612360 x^4-4286520 x^3+5511240 x^2\right ) \log ^6(4)+\left (-4490640 x^4+20207880 x^3-60623640 x\right ) \log ^4(4)-675520560\right ) \log ^8(5)+\left (\log ^2(4) \left (360277632 x^2-900694080 x-540416448\right )+\left (20160 x^7-241920 x^6+1088640 x^5-2177280 x^4+1632960 x^3\right ) \log ^8(4)+\left (362880 x^6-1632960 x^5-4898880 x^4+34292160 x^3-44089920 x^2\right ) \log ^6(4)+\left (21555072 x^4-96997824 x^3+290993472 x\right ) \log ^4(4)+1801388160\right ) \log ^7(5)+\left (\log ^2(4) \left (-945728784 x^2+2364321960 x+1418593176\right )+\left (112 x^{10}-2520 x^9+22680 x^8-105840 x^7+272160 x^6-367416 x^5+204120 x^4\right ) \log ^{10}(4)+\left (-211680 x^7+2540160 x^6-11430720 x^5+22861440 x^4-17146080 x^3\right ) \log ^8(4)+\left (-1905120 x^6+8573040 x^5+25719120 x^4-180033840 x^3+231472080 x^2\right ) \log ^6(4)+\left (-75442752 x^4+339492384 x^3-1018477152 x\right ) \log ^4(4)-3782915136\right ) \log ^6(5)+\left (\log ^2(4) \left (1891457568 x^2-4728643920 x-2837186352\right )+\left (-2016 x^{10}+45360 x^9-408240 x^8+1905120 x^7-4898880 x^6+6613488 x^5-3674160 x^4\right ) \log ^{10}(4)+\left (1270080 x^7-15240960 x^6+68584320 x^5-137168640 x^4+102876480 x^3\right ) \log ^8(4)+\left (6858432 x^6-30862944 x^5-92588832 x^4+648121824 x^3-833299488 x^2\right ) \log ^6(4)+\left (193995648 x^4-872980416 x^3+2618941248 x\right ) \log ^4(4)+6190224768\right ) \log ^5(5)+\left (\log ^2(4) \left (-2837186352 x^2+7092965880 x+4255779528\right )+\left (112 x^{12}-2520 x^{11}+24192 x^{10}-128520 x^9+408240 x^8-775656 x^7+816480 x^6-367416 x^5\right ) \log ^{12}(4)+\left (15120 x^{10}-340200 x^9+3061800 x^8-14288400 x^7+36741600 x^6-49601160 x^5+27556200 x^4\right ) \log ^{10}(4)+\left (-4762800 x^7+57153600 x^6-257191200 x^5+514382400 x^4-385786800 x^3\right ) \log ^8(4)+\left (-17146080 x^6+77157360 x^5+231472080 x^4-1620304560 x^3+2083248720 x^2\right ) \log ^6(4)+\left (-363741840 x^4+1636838280 x^3-4910514840 x\right ) \log ^4(4)-7737780960\right ) \log ^4(5)+\left (\log ^2(4) \left (3095112384 x^2-7737780960 x-4642668576\right )+\left (-1344 x^{12}+30240 x^{11}-290304 x^{10}+1542240 x^9-4898880 x^8+9307872 x^7-9797760 x^6+4408992 x^5\right ) \log ^{12}(4)+\left (-60480 x^{10}+1360800 x^9-12247200 x^8+57153600 x^7-146966400 x^6+198404640 x^5-110224800 x^4\right ) \log ^{10}(4)+\left (11430720 x^7-137168640 x^6+617258880 x^5-1234517760 x^4+925888320 x^3\right ) \log ^8(4)+\left (29393280 x^6-132269760 x^5-396809280 x^4+2777664960 x^3-3571283520 x^2\right ) \log ^6(4)+\left (484989120 x^4-2182451040 x^3+6547353120 x\right ) \log ^4(4)+7142567040\right ) \log ^3(5)+\left (\log ^2(4) \left (-2321334288 x^2+5803335720 x+3482001432\right )+\left (48 x^{14}-1176 x^{13}+12600 x^{12}-77112 x^{11}+294840 x^{10}-721224 x^9+1102248 x^8-962280 x^7+367416 x^6\right ) \log ^{14}(4)+\left (6048 x^{12}-136080 x^{11}+1306368 x^{10}-6940080 x^9+22044960 x^8-41885424 x^7+44089920 x^6-19840464 x^5\right ) \log ^{12}(4)+\left (136080 x^{10}-3061800 x^9+27556200 x^8-128595600 x^7+330674400 x^6-446410440 x^5+248005800 x^4\right ) \log ^{10}(4)+\left (-17146080 x^7+205752960 x^6-925888320 x^5+1851776640 x^4-1388832480 x^3\right ) \log ^8(4)+\left (-33067440 x^6+148803480 x^5+446410440 x^4-3124873080 x^3+4017693960 x^2\right ) \log ^6(4)+\left (-436490208 x^4+1964205936 x^3-5892617808 x\right ) \log ^4(4)-4591650240\right ) \log ^2(5)+\left (\log ^2(4) \left (1071385056 x^2-2678462640 x-1607077584\right )+\left (-288 x^{14}+7056 x^{13}-75600 x^{12}+462672 x^{11}-1769040 x^{10}+4327344 x^9-6613488 x^8+5773680 x^7-2204496 x^6\right ) \log ^{14}(4)+\left (-12096 x^{12}+272160 x^{11}-2612736 x^{10}+13880160 x^9-44089920 x^8+83770848 x^7-88179840 x^6+39680928 x^5\right ) \log ^{12}(4)+\left (-163296 x^{10}+3674160 x^9-33067440 x^8+154314720 x^7-396809280 x^6+535692528 x^5-297606960 x^4\right ) \log ^{10}(4)+\left (14696640 x^7-176359680 x^6+793618560 x^5-1587237120 x^4+1190427840 x^3\right ) \log ^8(4)+\left (22044960 x^6-99202320 x^5-297606960 x^4+2083248720 x^3-2678462640 x^2\right ) \log ^6(4)+\left (238085568 x^4-1071385056 x^3+3214155168 x\right ) \log ^4(4)+1836660096\right ) \log (5)+\left (8 x^{16}-216 x^{15}+2592 x^{14}-18144 x^{13}+81648 x^{12}-244944 x^{11}+489888 x^{10}-629857 x^9+472419 x^8-157788 x^7+2268 x^6-10206 x^5+30618 x^4-61236 x^3+78732 x^2-59049 x+19683\right ) \log ^{16}(4)+\left (432 x^{14}-10584 x^{13}+113400 x^{12}-694008 x^{11}+2653560 x^{10}-6491016 x^9+9920232 x^8-8660520 x^7+3306744 x^6\right ) \log ^{14}(4)+\left (9072 x^{12}-204120 x^{11}+1959552 x^{10}-10410120 x^9+33067440 x^8-62828136 x^7+66134880 x^6-29760696 x^5\right ) \log ^{12}(4)+\left (81648 x^{10}-1837080 x^9+16533720 x^8-77157360 x^7+198404640 x^6-267846264 x^5+148803480 x^4\right ) \log ^{10}(4)+\left (-5511240 x^7+66134880 x^6-297606960 x^5+595213920 x^4-446410440 x^3\right ) \log ^8(4)+\left (-6613488 x^6+29760696 x^5+89282088 x^4-624974616 x^3+803538792 x^2\right ) \log ^6(4)+\left (-59521392 x^4+267846264 x^3-803538792 x\right ) \log ^4(4)-344373768}{\left (x^9-27 x^8+324 x^7-2268 x^6+10206 x^5-30618 x^4+61236 x^3-78732 x^2+59049 x-19683\right ) \log ^{16}(4)} \, dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle \frac {\int -\frac {114791256 \log ^2(4) \left (-2 x^2+5 x+3\right )-8 \left (43046721-48 \log ^{15}(5)+\log ^{16}(5)\right )-24 \left (360-\left (-2 x^2+5 x+3\right ) \log ^2(4)\right ) \log ^{14}(5)+1008 \left (120-\left (-2 x^2+5 x+3\right ) \log ^2(4)\right ) \log ^{13}(5)-56 \left (-351 \log ^2(4) \left (-2 x^2+5 x+3\right )+\left (2 x^4-9 x^3+27 x\right ) \log ^4(4)+21060\right ) \log ^{12}(5)+2016 \left (-117 \log ^2(4) \left (-2 x^2+5 x+3\right )+\left (2 x^4-9 x^3+27 x\right ) \log ^4(4)+4212\right ) \log ^{11}(5)-56 \left (-34749 \log ^2(4) \left (-2 x^2+5 x+3\right )-\left (-2 x^6+9 x^5+27 x^4-189 x^3+243 x^2\right ) \log ^6(4)+594 \left (2 x^4-9 x^3+27 x\right ) \log ^4(4)+833976\right ) \log ^{10}(5)+48 \left (-243243 \log ^2(4) \left (-2 x^2+5 x+3\right )-35 \left (-2 x^6+9 x^5+27 x^4-189 x^3+243 x^2\right ) \log ^6(4)+6930 \left (2 x^4-9 x^3+27 x\right ) \log ^4(4)+4169880\right ) \log ^9(5)-24 \left (-2189187 \log ^2(4) \left (-2 x^2+5 x+3\right )+35 \left (x^7-12 x^6+54 x^5-108 x^4+81 x^3\right ) \log ^8(4)-945 \left (-2 x^6+9 x^5+27 x^4-189 x^3+243 x^2\right ) \log ^6(4)+93555 \left (2 x^4-9 x^3+27 x\right ) \log ^4(4)+28146690\right ) \log ^8(5)+576 \left (-312741 \log ^2(4) \left (-2 x^2+5 x+3\right )+35 \left (x^7-12 x^6+54 x^5-108 x^4+81 x^3\right ) \log ^8(4)-315 \left (-2 x^6+9 x^5+27 x^4-189 x^3+243 x^2\right ) \log ^6(4)+18711 \left (2 x^4-9 x^3+27 x\right ) \log ^4(4)+3127410\right ) \log ^7(5)-56 \left (-8444007 \log ^2(4) \left (-2 x^2+5 x+3\right )-\left (2 x^{10}-45 x^9+405 x^8-1890 x^7+4860 x^6-6561 x^5+3645 x^4\right ) \log ^{10}(4)+3780 \left (x^7-12 x^6+54 x^5-108 x^4+81 x^3\right ) \log ^8(4)-17010 \left (-2 x^6+9 x^5+27 x^4-189 x^3+243 x^2\right ) \log ^6(4)+673596 \left (2 x^4-9 x^3+27 x\right ) \log ^4(4)+67552056\right ) \log ^6(5)+1008 \left (-938223 \log ^2(4) \left (-2 x^2+5 x+3\right )-\left (2 x^{10}-45 x^9+405 x^8-1890 x^7+4860 x^6-6561 x^5+3645 x^4\right ) \log ^{10}(4)+1260 \left (x^7-12 x^6+54 x^5-108 x^4+81 x^3\right ) \log ^8(4)-3402 \left (-2 x^6+9 x^5+27 x^4-189 x^3+243 x^2\right ) \log ^6(4)+96228 \left (2 x^4-9 x^3+27 x\right ) \log ^4(4)+6141096\right ) \log ^5(5)-56 \left (-25332021 \log ^2(4) \left (-2 x^2+5 x+3\right )+\left (-2 x^{12}+45 x^{11}-432 x^{10}+2295 x^9-7290 x^8+13851 x^7-14580 x^6+6561 x^5\right ) \log ^{12}(4)-135 \left (2 x^{10}-45 x^9+405 x^8-1890 x^7+4860 x^6-6561 x^5+3645 x^4\right ) \log ^{10}(4)+85050 \left (x^7-12 x^6+54 x^5-108 x^4+81 x^3\right ) \log ^8(4)-153090 \left (-2 x^6+9 x^5+27 x^4-189 x^3+243 x^2\right ) \log ^6(4)+3247695 \left (2 x^4-9 x^3+27 x\right ) \log ^4(4)+138174660\right ) \log ^4(5)+672 \left (-2302911 \log ^2(4) \left (-2 x^2+5 x+3\right )+\left (-2 x^{12}+45 x^{11}-432 x^{10}+2295 x^9-7290 x^8+13851 x^7-14580 x^6+6561 x^5\right ) \log ^{12}(4)-45 \left (2 x^{10}-45 x^9+405 x^8-1890 x^7+4860 x^6-6561 x^5+3645 x^4\right ) \log ^{10}(4)+17010 \left (x^7-12 x^6+54 x^5-108 x^4+81 x^3\right ) \log ^8(4)-21870 \left (-2 x^6+9 x^5+27 x^4-189 x^3+243 x^2\right ) \log ^6(4)+360855 \left (2 x^4-9 x^3+27 x\right ) \log ^4(4)+10628820\right ) \log ^3(5)-24 \left (-48361131 \log ^2(4) \left (-2 x^2+5 x+3\right )-\left (2 x^{14}-49 x^{13}+525 x^{12}-3213 x^{11}+12285 x^{10}-30051 x^9+45927 x^8-40095 x^7+15309 x^6\right ) \log ^{14}(4)+126 \left (-2 x^{12}+45 x^{11}-432 x^{10}+2295 x^9-7290 x^8+13851 x^7-14580 x^6+6561 x^5\right ) \log ^{12}(4)-2835 \left (2 x^{10}-45 x^9+405 x^8-1890 x^7+4860 x^6-6561 x^5+3645 x^4\right ) \log ^{10}(4)+714420 \left (x^7-12 x^6+54 x^5-108 x^4+81 x^3\right ) \log ^8(4)-688905 \left (-2 x^6+9 x^5+27 x^4-189 x^3+243 x^2\right ) \log ^6(4)+9093546 \left (2 x^4-9 x^3+27 x\right ) \log ^4(4)+191318760\right ) \log ^2(5)+144 \left (-3720087 \log ^2(4) \left (-2 x^2+5 x+3\right )-\left (2 x^{14}-49 x^{13}+525 x^{12}-3213 x^{11}+12285 x^{10}-30051 x^9+45927 x^8-40095 x^7+15309 x^6\right ) \log ^{14}(4)+42 \left (-2 x^{12}+45 x^{11}-432 x^{10}+2295 x^9-7290 x^8+13851 x^7-14580 x^6+6561 x^5\right ) \log ^{12}(4)-567 \left (2 x^{10}-45 x^9+405 x^8-1890 x^7+4860 x^6-6561 x^5+3645 x^4\right ) \log ^{10}(4)+102060 \left (x^7-12 x^6+54 x^5-108 x^4+81 x^3\right ) \log ^8(4)-76545 \left (-2 x^6+9 x^5+27 x^4-189 x^3+243 x^2\right ) \log ^6(4)+826686 \left (2 x^4-9 x^3+27 x\right ) \log ^4(4)+12754584\right ) \log (5)+\left (8 x^{16}-216 x^{15}+2592 x^{14}-18144 x^{13}+81648 x^{12}-244944 x^{11}+489888 x^{10}-629857 x^9+472419 x^8-157788 x^7+2268 x^6-10206 x^5+30618 x^4-61236 x^3+78732 x^2-59049 x+19683\right ) \log ^{16}(4)+216 \left (2 x^{14}-49 x^{13}+525 x^{12}-3213 x^{11}+12285 x^{10}-30051 x^9+45927 x^8-40095 x^7+15309 x^6\right ) \log ^{14}(4)-4536 \left (-2 x^{12}+45 x^{11}-432 x^{10}+2295 x^9-7290 x^8+13851 x^7-14580 x^6+6561 x^5\right ) \log ^{12}(4)+40824 \left (2 x^{10}-45 x^9+405 x^8-1890 x^7+4860 x^6-6561 x^5+3645 x^4\right ) \log ^{10}(4)-5511240 \left (x^7-12 x^6+54 x^5-108 x^4+81 x^3\right ) \log ^8(4)+3306744 \left (-2 x^6+9 x^5+27 x^4-189 x^3+243 x^2\right ) \log ^6(4)-29760696 \left (2 x^4-9 x^3+27 x\right ) \log ^4(4)}{-x^9+27 x^8-324 x^7+2268 x^6-10206 x^5+30618 x^4-61236 x^3+78732 x^2-59049 x+19683}dx}{\log ^{16}(4)}\) |
| \(\Big \downarrow \) 25 |
| \(\displaystyle -\frac {\int \frac {114791256 \log ^2(4) \left (-2 x^2+5 x+3\right )-8 \left (43046721-48 \log ^{15}(5)+\log ^{16}(5)\right )-24 \left (360-\left (-2 x^2+5 x+3\right ) \log ^2(4)\right ) \log ^{14}(5)+1008 \left (120-\left (-2 x^2+5 x+3\right ) \log ^2(4)\right ) \log ^{13}(5)-56 \left (-351 \log ^2(4) \left (-2 x^2+5 x+3\right )+\left (2 x^4-9 x^3+27 x\right ) \log ^4(4)+21060\right ) \log ^{12}(5)+2016 \left (-117 \log ^2(4) \left (-2 x^2+5 x+3\right )+\left (2 x^4-9 x^3+27 x\right ) \log ^4(4)+4212\right ) \log ^{11}(5)-56 \left (-34749 \log ^2(4) \left (-2 x^2+5 x+3\right )-\left (-2 x^6+9 x^5+27 x^4-189 x^3+243 x^2\right ) \log ^6(4)+594 \left (2 x^4-9 x^3+27 x\right ) \log ^4(4)+833976\right ) \log ^{10}(5)+48 \left (-243243 \log ^2(4) \left (-2 x^2+5 x+3\right )-35 \left (-2 x^6+9 x^5+27 x^4-189 x^3+243 x^2\right ) \log ^6(4)+6930 \left (2 x^4-9 x^3+27 x\right ) \log ^4(4)+4169880\right ) \log ^9(5)-24 \left (-2189187 \log ^2(4) \left (-2 x^2+5 x+3\right )+35 \left (x^7-12 x^6+54 x^5-108 x^4+81 x^3\right ) \log ^8(4)-945 \left (-2 x^6+9 x^5+27 x^4-189 x^3+243 x^2\right ) \log ^6(4)+93555 \left (2 x^4-9 x^3+27 x\right ) \log ^4(4)+28146690\right ) \log ^8(5)+576 \left (-312741 \log ^2(4) \left (-2 x^2+5 x+3\right )+35 \left (x^7-12 x^6+54 x^5-108 x^4+81 x^3\right ) \log ^8(4)-315 \left (-2 x^6+9 x^5+27 x^4-189 x^3+243 x^2\right ) \log ^6(4)+18711 \left (2 x^4-9 x^3+27 x\right ) \log ^4(4)+3127410\right ) \log ^7(5)-56 \left (-8444007 \log ^2(4) \left (-2 x^2+5 x+3\right )-\left (2 x^{10}-45 x^9+405 x^8-1890 x^7+4860 x^6-6561 x^5+3645 x^4\right ) \log ^{10}(4)+3780 \left (x^7-12 x^6+54 x^5-108 x^4+81 x^3\right ) \log ^8(4)-17010 \left (-2 x^6+9 x^5+27 x^4-189 x^3+243 x^2\right ) \log ^6(4)+673596 \left (2 x^4-9 x^3+27 x\right ) \log ^4(4)+67552056\right ) \log ^6(5)+1008 \left (-938223 \log ^2(4) \left (-2 x^2+5 x+3\right )-\left (2 x^{10}-45 x^9+405 x^8-1890 x^7+4860 x^6-6561 x^5+3645 x^4\right ) \log ^{10}(4)+1260 \left (x^7-12 x^6+54 x^5-108 x^4+81 x^3\right ) \log ^8(4)-3402 \left (-2 x^6+9 x^5+27 x^4-189 x^3+243 x^2\right ) \log ^6(4)+96228 \left (2 x^4-9 x^3+27 x\right ) \log ^4(4)+6141096\right ) \log ^5(5)-56 \left (-25332021 \log ^2(4) \left (-2 x^2+5 x+3\right )+\left (-2 x^{12}+45 x^{11}-432 x^{10}+2295 x^9-7290 x^8+13851 x^7-14580 x^6+6561 x^5\right ) \log ^{12}(4)-135 \left (2 x^{10}-45 x^9+405 x^8-1890 x^7+4860 x^6-6561 x^5+3645 x^4\right ) \log ^{10}(4)+85050 \left (x^7-12 x^6+54 x^5-108 x^4+81 x^3\right ) \log ^8(4)-153090 \left (-2 x^6+9 x^5+27 x^4-189 x^3+243 x^2\right ) \log ^6(4)+3247695 \left (2 x^4-9 x^3+27 x\right ) \log ^4(4)+138174660\right ) \log ^4(5)+672 \left (-2302911 \log ^2(4) \left (-2 x^2+5 x+3\right )+\left (-2 x^{12}+45 x^{11}-432 x^{10}+2295 x^9-7290 x^8+13851 x^7-14580 x^6+6561 x^5\right ) \log ^{12}(4)-45 \left (2 x^{10}-45 x^9+405 x^8-1890 x^7+4860 x^6-6561 x^5+3645 x^4\right ) \log ^{10}(4)+17010 \left (x^7-12 x^6+54 x^5-108 x^4+81 x^3\right ) \log ^8(4)-21870 \left (-2 x^6+9 x^5+27 x^4-189 x^3+243 x^2\right ) \log ^6(4)+360855 \left (2 x^4-9 x^3+27 x\right ) \log ^4(4)+10628820\right ) \log ^3(5)-24 \left (-48361131 \log ^2(4) \left (-2 x^2+5 x+3\right )-\left (2 x^{14}-49 x^{13}+525 x^{12}-3213 x^{11}+12285 x^{10}-30051 x^9+45927 x^8-40095 x^7+15309 x^6\right ) \log ^{14}(4)+126 \left (-2 x^{12}+45 x^{11}-432 x^{10}+2295 x^9-7290 x^8+13851 x^7-14580 x^6+6561 x^5\right ) \log ^{12}(4)-2835 \left (2 x^{10}-45 x^9+405 x^8-1890 x^7+4860 x^6-6561 x^5+3645 x^4\right ) \log ^{10}(4)+714420 \left (x^7-12 x^6+54 x^5-108 x^4+81 x^3\right ) \log ^8(4)-688905 \left (-2 x^6+9 x^5+27 x^4-189 x^3+243 x^2\right ) \log ^6(4)+9093546 \left (2 x^4-9 x^3+27 x\right ) \log ^4(4)+191318760\right ) \log ^2(5)+144 \left (-3720087 \log ^2(4) \left (-2 x^2+5 x+3\right )-\left (2 x^{14}-49 x^{13}+525 x^{12}-3213 x^{11}+12285 x^{10}-30051 x^9+45927 x^8-40095 x^7+15309 x^6\right ) \log ^{14}(4)+42 \left (-2 x^{12}+45 x^{11}-432 x^{10}+2295 x^9-7290 x^8+13851 x^7-14580 x^6+6561 x^5\right ) \log ^{12}(4)-567 \left (2 x^{10}-45 x^9+405 x^8-1890 x^7+4860 x^6-6561 x^5+3645 x^4\right ) \log ^{10}(4)+102060 \left (x^7-12 x^6+54 x^5-108 x^4+81 x^3\right ) \log ^8(4)-76545 \left (-2 x^6+9 x^5+27 x^4-189 x^3+243 x^2\right ) \log ^6(4)+826686 \left (2 x^4-9 x^3+27 x\right ) \log ^4(4)+12754584\right ) \log (5)+\left (8 x^{16}-216 x^{15}+2592 x^{14}-18144 x^{13}+81648 x^{12}-244944 x^{11}+489888 x^{10}-629857 x^9+472419 x^8-157788 x^7+2268 x^6-10206 x^5+30618 x^4-61236 x^3+78732 x^2-59049 x+19683\right ) \log ^{16}(4)+216 \left (2 x^{14}-49 x^{13}+525 x^{12}-3213 x^{11}+12285 x^{10}-30051 x^9+45927 x^8-40095 x^7+15309 x^6\right ) \log ^{14}(4)-4536 \left (-2 x^{12}+45 x^{11}-432 x^{10}+2295 x^9-7290 x^8+13851 x^7-14580 x^6+6561 x^5\right ) \log ^{12}(4)+40824 \left (2 x^{10}-45 x^9+405 x^8-1890 x^7+4860 x^6-6561 x^5+3645 x^4\right ) \log ^{10}(4)-5511240 \left (x^7-12 x^6+54 x^5-108 x^4+81 x^3\right ) \log ^8(4)+3306744 \left (-2 x^6+9 x^5+27 x^4-189 x^3+243 x^2\right ) \log ^6(4)-29760696 \left (2 x^4-9 x^3+27 x\right ) \log ^4(4)}{-x^9+27 x^8-324 x^7+2268 x^6-10206 x^5+30618 x^4-61236 x^3+78732 x^2-59049 x+19683}dx}{\log ^{16}(4)}\) |
| \(\Big \downarrow \) 2007 |
| \(\displaystyle -\frac {\int \frac {114791256 \log ^2(4) \left (-2 x^2+5 x+3\right )-8 \left (43046721-48 \log ^{15}(5)+\log ^{16}(5)\right )-24 \left (360-\left (-2 x^2+5 x+3\right ) \log ^2(4)\right ) \log ^{14}(5)+1008 \left (120-\left (-2 x^2+5 x+3\right ) \log ^2(4)\right ) \log ^{13}(5)-56 \left (-351 \log ^2(4) \left (-2 x^2+5 x+3\right )+\left (2 x^4-9 x^3+27 x\right ) \log ^4(4)+21060\right ) \log ^{12}(5)+2016 \left (-117 \log ^2(4) \left (-2 x^2+5 x+3\right )+\left (2 x^4-9 x^3+27 x\right ) \log ^4(4)+4212\right ) \log ^{11}(5)-56 \left (-34749 \log ^2(4) \left (-2 x^2+5 x+3\right )-\left (-2 x^6+9 x^5+27 x^4-189 x^3+243 x^2\right ) \log ^6(4)+594 \left (2 x^4-9 x^3+27 x\right ) \log ^4(4)+833976\right ) \log ^{10}(5)+48 \left (-243243 \log ^2(4) \left (-2 x^2+5 x+3\right )-35 \left (-2 x^6+9 x^5+27 x^4-189 x^3+243 x^2\right ) \log ^6(4)+6930 \left (2 x^4-9 x^3+27 x\right ) \log ^4(4)+4169880\right ) \log ^9(5)-24 \left (-2189187 \log ^2(4) \left (-2 x^2+5 x+3\right )+35 \left (x^7-12 x^6+54 x^5-108 x^4+81 x^3\right ) \log ^8(4)-945 \left (-2 x^6+9 x^5+27 x^4-189 x^3+243 x^2\right ) \log ^6(4)+93555 \left (2 x^4-9 x^3+27 x\right ) \log ^4(4)+28146690\right ) \log ^8(5)+576 \left (-312741 \log ^2(4) \left (-2 x^2+5 x+3\right )+35 \left (x^7-12 x^6+54 x^5-108 x^4+81 x^3\right ) \log ^8(4)-315 \left (-2 x^6+9 x^5+27 x^4-189 x^3+243 x^2\right ) \log ^6(4)+18711 \left (2 x^4-9 x^3+27 x\right ) \log ^4(4)+3127410\right ) \log ^7(5)-56 \left (-8444007 \log ^2(4) \left (-2 x^2+5 x+3\right )-\left (2 x^{10}-45 x^9+405 x^8-1890 x^7+4860 x^6-6561 x^5+3645 x^4\right ) \log ^{10}(4)+3780 \left (x^7-12 x^6+54 x^5-108 x^4+81 x^3\right ) \log ^8(4)-17010 \left (-2 x^6+9 x^5+27 x^4-189 x^3+243 x^2\right ) \log ^6(4)+673596 \left (2 x^4-9 x^3+27 x\right ) \log ^4(4)+67552056\right ) \log ^6(5)+1008 \left (-938223 \log ^2(4) \left (-2 x^2+5 x+3\right )-\left (2 x^{10}-45 x^9+405 x^8-1890 x^7+4860 x^6-6561 x^5+3645 x^4\right ) \log ^{10}(4)+1260 \left (x^7-12 x^6+54 x^5-108 x^4+81 x^3\right ) \log ^8(4)-3402 \left (-2 x^6+9 x^5+27 x^4-189 x^3+243 x^2\right ) \log ^6(4)+96228 \left (2 x^4-9 x^3+27 x\right ) \log ^4(4)+6141096\right ) \log ^5(5)-56 \left (-25332021 \log ^2(4) \left (-2 x^2+5 x+3\right )+\left (-2 x^{12}+45 x^{11}-432 x^{10}+2295 x^9-7290 x^8+13851 x^7-14580 x^6+6561 x^5\right ) \log ^{12}(4)-135 \left (2 x^{10}-45 x^9+405 x^8-1890 x^7+4860 x^6-6561 x^5+3645 x^4\right ) \log ^{10}(4)+85050 \left (x^7-12 x^6+54 x^5-108 x^4+81 x^3\right ) \log ^8(4)-153090 \left (-2 x^6+9 x^5+27 x^4-189 x^3+243 x^2\right ) \log ^6(4)+3247695 \left (2 x^4-9 x^3+27 x\right ) \log ^4(4)+138174660\right ) \log ^4(5)+672 \left (-2302911 \log ^2(4) \left (-2 x^2+5 x+3\right )+\left (-2 x^{12}+45 x^{11}-432 x^{10}+2295 x^9-7290 x^8+13851 x^7-14580 x^6+6561 x^5\right ) \log ^{12}(4)-45 \left (2 x^{10}-45 x^9+405 x^8-1890 x^7+4860 x^6-6561 x^5+3645 x^4\right ) \log ^{10}(4)+17010 \left (x^7-12 x^6+54 x^5-108 x^4+81 x^3\right ) \log ^8(4)-21870 \left (-2 x^6+9 x^5+27 x^4-189 x^3+243 x^2\right ) \log ^6(4)+360855 \left (2 x^4-9 x^3+27 x\right ) \log ^4(4)+10628820\right ) \log ^3(5)-24 \left (-48361131 \log ^2(4) \left (-2 x^2+5 x+3\right )-\left (2 x^{14}-49 x^{13}+525 x^{12}-3213 x^{11}+12285 x^{10}-30051 x^9+45927 x^8-40095 x^7+15309 x^6\right ) \log ^{14}(4)+126 \left (-2 x^{12}+45 x^{11}-432 x^{10}+2295 x^9-7290 x^8+13851 x^7-14580 x^6+6561 x^5\right ) \log ^{12}(4)-2835 \left (2 x^{10}-45 x^9+405 x^8-1890 x^7+4860 x^6-6561 x^5+3645 x^4\right ) \log ^{10}(4)+714420 \left (x^7-12 x^6+54 x^5-108 x^4+81 x^3\right ) \log ^8(4)-688905 \left (-2 x^6+9 x^5+27 x^4-189 x^3+243 x^2\right ) \log ^6(4)+9093546 \left (2 x^4-9 x^3+27 x\right ) \log ^4(4)+191318760\right ) \log ^2(5)+144 \left (-3720087 \log ^2(4) \left (-2 x^2+5 x+3\right )-\left (2 x^{14}-49 x^{13}+525 x^{12}-3213 x^{11}+12285 x^{10}-30051 x^9+45927 x^8-40095 x^7+15309 x^6\right ) \log ^{14}(4)+42 \left (-2 x^{12}+45 x^{11}-432 x^{10}+2295 x^9-7290 x^8+13851 x^7-14580 x^6+6561 x^5\right ) \log ^{12}(4)-567 \left (2 x^{10}-45 x^9+405 x^8-1890 x^7+4860 x^6-6561 x^5+3645 x^4\right ) \log ^{10}(4)+102060 \left (x^7-12 x^6+54 x^5-108 x^4+81 x^3\right ) \log ^8(4)-76545 \left (-2 x^6+9 x^5+27 x^4-189 x^3+243 x^2\right ) \log ^6(4)+826686 \left (2 x^4-9 x^3+27 x\right ) \log ^4(4)+12754584\right ) \log (5)+\left (8 x^{16}-216 x^{15}+2592 x^{14}-18144 x^{13}+81648 x^{12}-244944 x^{11}+489888 x^{10}-629857 x^9+472419 x^8-157788 x^7+2268 x^6-10206 x^5+30618 x^4-61236 x^3+78732 x^2-59049 x+19683\right ) \log ^{16}(4)+216 \left (2 x^{14}-49 x^{13}+525 x^{12}-3213 x^{11}+12285 x^{10}-30051 x^9+45927 x^8-40095 x^7+15309 x^6\right ) \log ^{14}(4)-4536 \left (-2 x^{12}+45 x^{11}-432 x^{10}+2295 x^9-7290 x^8+13851 x^7-14580 x^6+6561 x^5\right ) \log ^{12}(4)+40824 \left (2 x^{10}-45 x^9+405 x^8-1890 x^7+4860 x^6-6561 x^5+3645 x^4\right ) \log ^{10}(4)-5511240 \left (x^7-12 x^6+54 x^5-108 x^4+81 x^3\right ) \log ^8(4)+3306744 \left (-2 x^6+9 x^5+27 x^4-189 x^3+243 x^2\right ) \log ^6(4)-29760696 \left (2 x^4-9 x^3+27 x\right ) \log ^4(4)}{(3-x)^9}dx}{\log ^{16}(4)}\) |
| \(\Big \downarrow \) 2389 |
| \(\displaystyle -\frac {\int \left (-8 \log ^{16}(4) x^7-48 \log ^{14}(4) (-3+\log (5))^2 x^5-120 \log ^{14}(4) (-3+\log (5))^2 x^4+16 \log ^{12}(4) \left (-18 \log ^2(4)-7 (3-\log (5))^2\right ) (3-\log (5))^2 x^3+72 \log ^{12}(4) \left (-9 \log ^2(4)-7 (3-\log (5))^2\right ) (3-\log (5))^2 x^2+8 \log ^{10}(4) \left (-162 \log ^4(4)-189 \log ^2(4) (3-\log (5))^2-14 (3-\log (5))^4\right ) (3-\log (5))^2 x+\frac {8 (-3+\log (5))^{16}}{(x-3)^9}+\frac {168 \log ^2(4) (-3+\log (5))^{14}}{(x-3)^8}+\frac {24 \log ^2(4) \left (-63 \log ^2(4)-2 (3-\log (5))^2\right ) (3-\log (5))^{12}}{(3-x)^7}+\frac {840 \log ^4(4) \left (9 \log ^2(4)+(-3+\log (5))^2\right ) (3-\log (5))^{10}}{(3-x)^6}+\frac {56 \log ^4(4) \left (-405 \log ^4(4)-108 \log ^2(4) (3-\log (5))^2-2 (3-\log (5))^4\right ) (3-\log (5))^8}{(3-x)^5}+\frac {1512 \log ^6(4) \left (27 \log ^4(4)+15 \log ^2(4) (3-\log (5))^2+(-3+\log (5))^4\right ) (3-\log (5))^6}{(3-x)^4}+\frac {56 \log ^6(4) \left (-729 \log ^6(4)-810 \log ^4(4) (3-\log (5))^2-135 \log ^2(4) (3-\log (5))^4-2 (3-\log (5))^6\right ) (3-\log (5))^4}{(3-x)^3}+\frac {24 \log ^8(4) \left (729 \log ^6(4)+1701 \log ^4(4) (3-\log (5))^2+630 \log ^2(4) (3-\log (5))^4+35 (3-\log (5))^6\right ) (3-\log (5))^2}{(3-x)^2}+\log ^{10}(4) \left (\log ^6(4)-1944 \log ^4(4) (3-\log (5))^2-3024 \log ^2(4) (3-\log (5))^4-504 (3-\log (5))^6\right )\right )dx}{\log ^{16}(4)}\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle -\frac {x^8 \left (-\log ^{16}(4)\right )-8 x^6 \log ^{14}(4) (3-\log (5))^2-24 x^5 \log ^{14}(4) (3-\log (5))^2-4 x^4 \log ^{12}(4) \left (18 \log ^2(4)+7 (3-\log (5))^2\right ) (3-\log (5))^2-24 x^3 \log ^{12}(4) \left (9 \log ^2(4)+7 (3-\log (5))^2\right ) (3-\log (5))^2-4 x^2 \log ^{10}(4) \left (162 \log ^4(4)+189 \log ^2(4) (3-\log (5))^2+14 (3-\log (5))^4\right ) (3-\log (5))^2+\frac {24 \log ^2(4) (3-\log (5))^{14}}{(3-x)^7}-\frac {4 \log ^2(4) \left (63 \log ^2(4)+2 (3-\log (5))^2\right ) (3-\log (5))^{12}}{(3-x)^6}+\frac {168 \log ^4(4) \left (9 \log ^2(4)+(\log (5)-3)^2\right ) (3-\log (5))^{10}}{(3-x)^5}-\frac {14 \log ^4(4) \left (405 \log ^4(4)+108 \log ^2(4) (3-\log (5))^2+2 (3-\log (5))^4\right ) (3-\log (5))^8}{(3-x)^4}+\frac {504 \log ^6(4) \left (27 \log ^4(4)+15 \log ^2(4) (3-\log (5))^2+(\log (5)-3)^4\right ) (3-\log (5))^6}{(3-x)^3}-\frac {28 \log ^6(4) \left (729 \log ^6(4)+810 \log ^4(4) (3-\log (5))^2+135 \log ^2(4) (3-\log (5))^4+2 (3-\log (5))^6\right ) (3-\log (5))^4}{(3-x)^2}+x \log ^{10}(4) \left (\log ^6(4)-1944 \log ^4(4) (3-\log (5))^2-3024 \log ^2(4) (3-\log (5))^4-504 (3-\log (5))^6\right )+\frac {24 \log ^8(4) \left (729 \log ^6(4)+1701 \log ^4(4) (3-\log (5))^2+630 \log ^2(4) (3-\log (5))^4+35 (3-\log (5))^6\right ) (3-\log (5))^2}{3-x}-\frac {(3-\log (5))^{16}}{(3-x)^8}}{\log ^{16}(4)}\) |
Input:
Int[(-344373768 + (344373768 + 573956280*x - 229582512*x^2)*Log[4]^2 + (-8 03538792*x + 267846264*x^3 - 59521392*x^4)*Log[4]^4 + (803538792*x^2 - 624 974616*x^3 + 89282088*x^4 + 29760696*x^5 - 6613488*x^6)*Log[4]^6 + (-44641 0440*x^3 + 595213920*x^4 - 297606960*x^5 + 66134880*x^6 - 5511240*x^7)*Log [4]^8 + (148803480*x^4 - 267846264*x^5 + 198404640*x^6 - 77157360*x^7 + 16 533720*x^8 - 1837080*x^9 + 81648*x^10)*Log[4]^10 + (-29760696*x^5 + 661348 80*x^6 - 62828136*x^7 + 33067440*x^8 - 10410120*x^9 + 1959552*x^10 - 20412 0*x^11 + 9072*x^12)*Log[4]^12 + (3306744*x^6 - 8660520*x^7 + 9920232*x^8 - 6491016*x^9 + 2653560*x^10 - 694008*x^11 + 113400*x^12 - 10584*x^13 + 432 *x^14)*Log[4]^14 + (19683 - 59049*x + 78732*x^2 - 61236*x^3 + 30618*x^4 - 10206*x^5 + 2268*x^6 - 157788*x^7 + 472419*x^8 - 629857*x^9 + 489888*x^10 - 244944*x^11 + 81648*x^12 - 18144*x^13 + 2592*x^14 - 216*x^15 + 8*x^16)*L og[4]^16 + (1836660096 + (-1607077584 - 2678462640*x + 1071385056*x^2)*Log [4]^2 + (3214155168*x - 1071385056*x^3 + 238085568*x^4)*Log[4]^4 + (-26784 62640*x^2 + 2083248720*x^3 - 297606960*x^4 - 99202320*x^5 + 22044960*x^6)* Log[4]^6 + (1190427840*x^3 - 1587237120*x^4 + 793618560*x^5 - 176359680*x^ 6 + 14696640*x^7)*Log[4]^8 + (-297606960*x^4 + 535692528*x^5 - 396809280*x ^6 + 154314720*x^7 - 33067440*x^8 + 3674160*x^9 - 163296*x^10)*Log[4]^10 + (39680928*x^5 - 88179840*x^6 + 83770848*x^7 - 44089920*x^8 + 13880160*x^9 - 2612736*x^10 + 272160*x^11 - 12096*x^12)*Log[4]^12 + (-2204496*x^6 + 57 73680*x^7 - 6613488*x^8 + 4327344*x^9 - 1769040*x^10 + 462672*x^11 - 75600 *x^12 + 7056*x^13 - 288*x^14)*Log[4]^14)*Log[5] + (-4591650240 + (34820014 32 + 5803335720*x - 2321334288*x^2)*Log[4]^2 + (-5892617808*x + 1964205936 *x^3 - 436490208*x^4)*Log[4]^4 + (4017693960*x^2 - 3124873080*x^3 + 446410 440*x^4 + 148803480*x^5 - 33067440*x^6)*Log[4]^6 + (-1388832480*x^3 + 1851 776640*x^4 - 925888320*x^5 + 205752960*x^6 - 17146080*x^7)*Log[4]^8 + (248 005800*x^4 - 446410440*x^5 + 330674400*x^6 - 128595600*x^7 + 27556200*x^8 - 3061800*x^9 + 136080*x^10)*Log[4]^10 + (-19840464*x^5 + 44089920*x^6 - 4 1885424*x^7 + 22044960*x^8 - 6940080*x^9 + 1306368*x^10 - 136080*x^11 + 60 48*x^12)*Log[4]^12 + (367416*x^6 - 962280*x^7 + 1102248*x^8 - 721224*x^9 + 294840*x^10 - 77112*x^11 + 12600*x^12 - 1176*x^13 + 48*x^14)*Log[4]^14)*L og[5]^2 + (7142567040 + (-4642668576 - 7737780960*x + 3095112384*x^2)*Log[ 4]^2 + (6547353120*x - 2182451040*x^3 + 484989120*x^4)*Log[4]^4 + (-357128 3520*x^2 + 2777664960*x^3 - 396809280*x^4 - 132269760*x^5 + 29393280*x^6)* Log[4]^6 + (925888320*x^3 - 1234517760*x^4 + 617258880*x^5 - 137168640*x^6 + 11430720*x^7)*Log[4]^8 + (-110224800*x^4 + 198404640*x^5 - 146966400*x^ 6 + 57153600*x^7 - 12247200*x^8 + 1360800*x^9 - 60480*x^10)*Log[4]^10 + (4 408992*x^5 - 9797760*x^6 + 9307872*x^7 - 4898880*x^8 + 1542240*x^9 - 29030 4*x^10 + 30240*x^11 - 1344*x^12)*Log[4]^12)*Log[5]^3 + (-7737780960 + (425 5779528 + 7092965880*x - 2837186352*x^2)*Log[4]^2 + (-4910514840*x + 16368 38280*x^3 - 363741840*x^4)*Log[4]^4 + (2083248720*x^2 - 1620304560*x^3 + 2 31472080*x^4 + 77157360*x^5 - 17146080*x^6)*Log[4]^6 + (-385786800*x^3 + 5 14382400*x^4 - 257191200*x^5 + 57153600*x^6 - 4762800*x^7)*Log[4]^8 + (275 56200*x^4 - 49601160*x^5 + 36741600*x^6 - 14288400*x^7 + 3061800*x^8 - 340 200*x^9 + 15120*x^10)*Log[4]^10 + (-367416*x^5 + 816480*x^6 - 775656*x^7 + 408240*x^8 - 128520*x^9 + 24192*x^10 - 2520*x^11 + 112*x^12)*Log[4]^12)*L og[5]^4 + (6190224768 + (-2837186352 - 4728643920*x + 1891457568*x^2)*Log[ 4]^2 + (2618941248*x - 872980416*x^3 + 193995648*x^4)*Log[4]^4 + (-8332994 88*x^2 + 648121824*x^3 - 92588832*x^4 - 30862944*x^5 + 6858432*x^6)*Log[4] ^6 + (102876480*x^3 - 137168640*x^4 + 68584320*x^5 - 15240960*x^6 + 127008 0*x^7)*Log[4]^8 + (-3674160*x^4 + 6613488*x^5 - 4898880*x^6 + 1905120*x^7 - 408240*x^8 + 45360*x^9 - 2016*x^10)*Log[4]^10)*Log[5]^5 + (-3782915136 + (1418593176 + 2364321960*x - 945728784*x^2)*Log[4]^2 + (-1018477152*x + 3 39492384*x^3 - 75442752*x^4)*Log[4]^4 + (231472080*x^2 - 180033840*x^3 + 2 5719120*x^4 + 8573040*x^5 - 1905120*x^6)*Log[4]^6 + (-17146080*x^3 + 22861 440*x^4 - 11430720*x^5 + 2540160*x^6 - 211680*x^7)*Log[4]^8 + (204120*x^4 - 367416*x^5 + 272160*x^6 - 105840*x^7 + 22680*x^8 - 2520*x^9 + 112*x^10)* Log[4]^10)*Log[5]^6 + (1801388160 + (-540416448 - 900694080*x + 360277632* x^2)*Log[4]^2 + (290993472*x - 96997824*x^3 + 21555072*x^4)*Log[4]^4 + (-4 4089920*x^2 + 34292160*x^3 - 4898880*x^4 - 1632960*x^5 + 362880*x^6)*Log[4 ]^6 + (1632960*x^3 - 2177280*x^4 + 1088640*x^5 - 241920*x^6 + 20160*x^7)*L og[4]^8)*Log[5]^7 + (-675520560 + (157621464 + 262702440*x - 105080976*x^2 )*Log[4]^2 + (-60623640*x + 20207880*x^3 - 4490640*x^4)*Log[4]^4 + (551124 0*x^2 - 4286520*x^3 + 612360*x^4 + 204120*x^5 - 45360*x^6)*Log[4]^6 + (-68 040*x^3 + 90720*x^4 - 45360*x^5 + 10080*x^6 - 840*x^7)*Log[4]^8)*Log[5]^8 + (200154240 + (-35026992 - 58378320*x + 23351328*x^2)*Log[4]^2 + (8981280 *x - 2993760*x^3 + 665280*x^4)*Log[4]^4 + (-408240*x^2 + 317520*x^3 - 4536 0*x^4 - 15120*x^5 + 3360*x^6)*Log[4]^6)*Log[5]^9 + (-46702656 + (5837832 + 9729720*x - 3891888*x^2)*Log[4]^2 + (-898128*x + 299376*x^3 - 66528*x^4)* Log[4]^4 + (13608*x^2 - 10584*x^3 + 1512*x^4 + 504*x^5 - 112*x^6)*Log[4]^6 )*Log[5]^10 + (8491392 + (-707616 - 1179360*x + 471744*x^2)*Log[4]^2 + (54 432*x - 18144*x^3 + 4032*x^4)*Log[4]^4)*Log[5]^11 + (-1179360 + (58968 + 9 8280*x - 39312*x^2)*Log[4]^2 + (-1512*x + 504*x^3 - 112*x^4)*Log[4]^4)*Log [5]^12 + (120960 + (-3024 - 5040*x + 2016*x^2)*Log[4]^2)*Log[5]^13 + (-864 0 + (72 + 120*x - 48*x^2)*Log[4]^2)*Log[5]^14 + 384*Log[5]^15 - 8*Log[5]^1 6)/((-19683 + 59049*x - 78732*x^2 + 61236*x^3 - 30618*x^4 + 10206*x^5 - 22 68*x^6 + 324*x^7 - 27*x^8 + x^9)*Log[4]^16),x]
Output:
-((-(x^8*Log[4]^16) + x*Log[4]^10*(Log[4]^6 - 1944*Log[4]^4*(3 - Log[5])^2 - 3024*Log[4]^2*(3 - Log[5])^4 - 504*(3 - Log[5])^6) - 24*x^5*Log[4]^14*( 3 - Log[5])^2 - 8*x^6*Log[4]^14*(3 - Log[5])^2 - 24*x^3*Log[4]^12*(9*Log[4 ]^2 + 7*(3 - Log[5])^2)*(3 - Log[5])^2 - 4*x^4*Log[4]^12*(18*Log[4]^2 + 7* (3 - Log[5])^2)*(3 - Log[5])^2 - 4*x^2*Log[4]^10*(162*Log[4]^4 + 189*Log[4 ]^2*(3 - Log[5])^2 + 14*(3 - Log[5])^4)*(3 - Log[5])^2 + (24*Log[4]^8*(729 *Log[4]^6 + 1701*Log[4]^4*(3 - Log[5])^2 + 630*Log[4]^2*(3 - Log[5])^4 + 3 5*(3 - Log[5])^6)*(3 - Log[5])^2)/(3 - x) - (28*Log[4]^6*(729*Log[4]^6 + 8 10*Log[4]^4*(3 - Log[5])^2 + 135*Log[4]^2*(3 - Log[5])^4 + 2*(3 - Log[5])^ 6)*(3 - Log[5])^4)/(3 - x)^2 + (504*Log[4]^6*(27*Log[4]^4 + 15*Log[4]^2*(3 - Log[5])^2 + (-3 + Log[5])^4)*(3 - Log[5])^6)/(3 - x)^3 - (14*Log[4]^4*( 405*Log[4]^4 + 108*Log[4]^2*(3 - Log[5])^2 + 2*(3 - Log[5])^4)*(3 - Log[5] )^8)/(3 - x)^4 + (168*Log[4]^4*(9*Log[4]^2 + (-3 + Log[5])^2)*(3 - Log[5]) ^10)/(3 - x)^5 - (4*Log[4]^2*(63*Log[4]^2 + 2*(3 - Log[5])^2)*(3 - Log[5]) ^12)/(3 - x)^6 + (24*Log[4]^2*(3 - Log[5])^14)/(3 - x)^7 - (3 - Log[5])^16 /(3 - x)^8)/Log[4]^16)
Int[(a_)*(Fx_), x_Symbol] :> Simp[a Int[Fx, x], x] /; FreeQ[a, x] && !Ma tchQ[Fx, (b_)*(Gx_) /; FreeQ[b, x]]
Int[(u_.)*(Px_)^(p_), x_Symbol] :> With[{a = Rt[Coeff[Px, x, 0], Expon[Px, x]], b = Rt[Coeff[Px, x, Expon[Px, x]], Expon[Px, x]]}, Int[u*(a + b*x)^(Ex pon[Px, x]*p), x] /; EqQ[Px, (a + b*x)^Expon[Px, x]]] /; IntegerQ[p] && Pol yQ[Px, x] && GtQ[Expon[Px, x], 1] && NeQ[Coeff[Px, x, 0], 0]
Int[(Pq_)*((a_) + (b_.)*(x_)^(n_.))^(p_.), x_Symbol] :> Int[ExpandIntegrand [Pq*(a + b*x^n)^p, x], x] /; FreeQ[{a, b, n}, x] && PolyQ[Pq, x] && (IGtQ[p , 0] || EqQ[n, 1])
Leaf count of result is larger than twice the leaf count of optimal. \(2133\) vs. \(2(29)=58\).
Time = 7.40 (sec) , antiderivative size = 2134, normalized size of antiderivative = 73.59
| method | result | size |
| default | \(\text {Expression too large to display}\) | \(2134\) |
| norman | \(\text {Expression too large to display}\) | \(3204\) |
| risch | \(\text {Expression too large to display}\) | \(3559\) |
| gosper | \(\text {Expression too large to display}\) | \(4453\) |
| parallelrisch | \(\text {Expression too large to display}\) | \(4453\) |
Input:
int(1/65536*(-344373768+65536*(8*x^16-216*x^15+2592*x^14-18144*x^13+81648* x^12-244944*x^11+489888*x^10-629857*x^9+472419*x^8-157788*x^7+2268*x^6-102 06*x^5+30618*x^4-61236*x^3+78732*x^2-59049*x+19683)*ln(2)^16+16384*(432*x^ 14-10584*x^13+113400*x^12-694008*x^11+2653560*x^10-6491016*x^9+9920232*x^8 -8660520*x^7+3306744*x^6)*ln(2)^14+4096*(9072*x^12-204120*x^11+1959552*x^1 0-10410120*x^9+33067440*x^8-62828136*x^7+66134880*x^6-29760696*x^5)*ln(2)^ 12+1024*(81648*x^10-1837080*x^9+16533720*x^8-77157360*x^7+198404640*x^6-26 7846264*x^5+148803480*x^4)*ln(2)^10+256*(-5511240*x^7+66134880*x^6-2976069 60*x^5+595213920*x^4-446410440*x^3)*ln(2)^8+64*(-6613488*x^6+29760696*x^5+ 89282088*x^4-624974616*x^3+803538792*x^2)*ln(2)^6+16*(-59521392*x^4+267846 264*x^3-803538792*x)*ln(2)^4+4*(-229582512*x^2+573956280*x+344373768)*ln(2 )^2+(4*(-48*x^2+120*x+72)*ln(2)^2-8640)*ln(5)^14+(4*(2016*x^2-5040*x-3024) *ln(2)^2+120960)*ln(5)^13+(16*(-112*x^4+504*x^3-1512*x)*ln(2)^4+4*(-39312* x^2+98280*x+58968)*ln(2)^2-1179360)*ln(5)^12+(16*(4032*x^4-18144*x^3+54432 *x)*ln(2)^4+4*(471744*x^2-1179360*x-707616)*ln(2)^2+8491392)*ln(5)^11+(64* (-112*x^6+504*x^5+1512*x^4-10584*x^3+13608*x^2)*ln(2)^6+16*(-66528*x^4+299 376*x^3-898128*x)*ln(2)^4+4*(-3891888*x^2+9729720*x+5837832)*ln(2)^2-46702 656)*ln(5)^10+(16384*(48*x^14-1176*x^13+12600*x^12-77112*x^11+294840*x^10- 721224*x^9+1102248*x^8-962280*x^7+367416*x^6)*ln(2)^14+4096*(6048*x^12-136 080*x^11+1306368*x^10-6940080*x^9+22044960*x^8-41885424*x^7+44089920*x^6-1 9840464*x^5)*ln(2)^12+1024*(136080*x^10-3061800*x^9+27556200*x^8-128595600 *x^7+330674400*x^6-446410440*x^5+248005800*x^4)*ln(2)^10+256*(-17146080*x^ 7+205752960*x^6-925888320*x^5+1851776640*x^4-1388832480*x^3)*ln(2)^8+64*(- 33067440*x^6+148803480*x^5+446410440*x^4-3124873080*x^3+4017693960*x^2)*ln (2)^6+16*(-436490208*x^4+1964205936*x^3-5892617808*x)*ln(2)^4+4*(-23213342 88*x^2+5803335720*x+3482001432)*ln(2)^2-4591650240)*ln(5)^2+(256*(20160*x^ 7-241920*x^6+1088640*x^5-2177280*x^4+1632960*x^3)*ln(2)^8+64*(362880*x^6-1 632960*x^5-4898880*x^4+34292160*x^3-44089920*x^2)*ln(2)^6+16*(21555072*x^4 -96997824*x^3+290993472*x)*ln(2)^4+4*(360277632*x^2-900694080*x-540416448) *ln(2)^2+1801388160)*ln(5)^7+(64*(3360*x^6-15120*x^5-45360*x^4+317520*x^3- 408240*x^2)*ln(2)^6+16*(665280*x^4-2993760*x^3+8981280*x)*ln(2)^4+4*(23351 328*x^2-58378320*x-35026992)*ln(2)^2+200154240)*ln(5)^9+(256*(-840*x^7+100 80*x^6-45360*x^5+90720*x^4-68040*x^3)*ln(2)^8+64*(-45360*x^6+204120*x^5+61 2360*x^4-4286520*x^3+5511240*x^2)*ln(2)^6+16*(-4490640*x^4+20207880*x^3-60 623640*x)*ln(2)^4+4*(-105080976*x^2+262702440*x+157621464)*ln(2)^2-6755205 60)*ln(5)^8+(1024*(112*x^10-2520*x^9+22680*x^8-105840*x^7+272160*x^6-36741 6*x^5+204120*x^4)*ln(2)^10+256*(-211680*x^7+2540160*x^6-11430720*x^5+22861 440*x^4-17146080*x^3)*ln(2)^8+64*(-1905120*x^6+8573040*x^5+25719120*x^4-18 0033840*x^3+231472080*x^2)*ln(2)^6+16*(-75442752*x^4+339492384*x^3-1018477 152*x)*ln(2)^4+4*(-945728784*x^2+2364321960*x+1418593176)*ln(2)^2-37829151 36)*ln(5)^6+(1024*(-2016*x^10+45360*x^9-408240*x^8+1905120*x^7-4898880*x^6 +6613488*x^5-3674160*x^4)*ln(2)^10+256*(1270080*x^7-15240960*x^6+68584320* x^5-137168640*x^4+102876480*x^3)*ln(2)^8+64*(6858432*x^6-30862944*x^5-9258 8832*x^4+648121824*x^3-833299488*x^2)*ln(2)^6+16*(193995648*x^4-872980416* x^3+2618941248*x)*ln(2)^4+4*(1891457568*x^2-4728643920*x-2837186352)*ln(2) ^2+6190224768)*ln(5)^5-8*ln(5)^16+384*ln(5)^15+(16384*(-288*x^14+7056*x^13 -75600*x^12+462672*x^11-1769040*x^10+4327344*x^9-6613488*x^8+5773680*x^7-2 204496*x^6)*ln(2)^14+4096*(-12096*x^12+272160*x^11-2612736*x^10+13880160*x ^9-44089920*x^8+83770848*x^7-88179840*x^6+39680928*x^5)*ln(2)^12+1024*(-16 3296*x^10+3674160*x^9-33067440*x^8+154314720*x^7-396809280*x^6+535692528*x ^5-297606960*x^4)*ln(2)^10+256*(14696640*x^7-176359680*x^6+793618560*x^5-1 587237120*x^4+1190427840*x^3)*ln(2)^8+64*(22044960*x^6-99202320*x^5-297606 960*x^4+2083248720*x^3-2678462640*x^2)*ln(2)^6+16*(238085568*x^4-107138505 6*x^3+3214155168*x)*ln(2)^4+4*(1071385056*x^2-2678462640*x-1607077584)*ln( 2)^2+1836660096)*ln(5)+(4096*(112*x^12-2520*x^11+24192*x^10-128520*x^9+408 240*x^8-775656*x^7+816480*x^6-367416*x^5)*ln(2)^12+1024*(15120*x^10-340200 *x^9+3061800*x^8-14288400*x^7+36741600*x^6-49601160*x^5+27556200*x^4)*ln(2 )^10+256*(-4762800*x^7+57153600*x^6-257191200*x^5+514382400*x^4-385786800* x^3)*ln(2)^8+64*(-17146080*x^6+77157360*x^5+231472080*x^4-1620304560*x^3+2 083248720*x^2)*ln(2)^6+16*(-363741840*x^4+1636838280*x^3-4910514840*x)*ln( 2)^4+4*(-2837186352*x^2+7092965880*x+4255779528)*ln(2)^2-7737780960)*ln(5) ^4+(4096*(-1344*x^12+30240*x^11-290304*x^10+1542240*x^9-4898880*x^8+930787 2*x^7-9797760*x^6+4408992*x^5)*ln(2)^12+1024*(-60480*x^10+1360800*x^9-1224 7200*x^8+57153600*x^7-146966400*x^6+198404640*x^5-110224800*x^4)*ln(2)^10+ 256*(11430720*x^7-137168640*x^6+617258880*x^5-1234517760*x^4+925888320*x^3 )*ln(2)^8+64*(29393280*x^6-132269760*x^5-396809280*x^4+2777664960*x^3-3571 283520*x^2)*ln(2)^6+16*(484989120*x^4-2182451040*x^3+6547353120*x)*ln(2)^4 +4*(3095112384*x^2-7737780960*x-4642668576)*ln(2)^2+7142567040)*ln(5)^3)/( x^9-27*x^8+324*x^7-2268*x^6+10206*x^5-30618*x^4+61236*x^3-78732*x^2+59049* x-19683)/ln(2)^16,x,method=_RETURNVERBOSE)
Output:
1/65536/ln(2)^16*(376233984*ln(2)^10*x+95551488*ln(2)^14*x^2+9289728*ln(2) ^12*x^4+286654464*ln(2)^14*x+55738368*ln(2)^12*x^3+250822656*ln(2)^12*x^2+ 1003290624*ln(2)^12*x-2359296*ln(2)^14*ln(5)*x^5+114688*ln(2)^12*ln(5)^4*x ^4+393216*ln(2)^14*ln(5)^2*x^5-786432*ln(2)^14*ln(5)*x^6-7077888*ln(2)^14* ln(5)*x^4+688128*ln(2)^12*ln(5)^4*x^3+10616832*ln(2)^14*ln(5)^2*x^2-212336 64*ln(2)^14*ln(5)*x^3+3096576*ln(2)^12*ln(5)^4*x^2-8257536*ln(2)^12*ln(5)^ 3*x^3+57344*ln(2)^10*ln(5)^6*x^2+131072*ln(2)^14*ln(5)^2*x^6+6144*ln(2)^8* (46656*ln(2)^6*ln(5)^2+27216*ln(2)^4*ln(5)^4+2520*ln(2)^2*ln(5)^6+35*ln(5) ^8-279936*ln(2)^6*ln(5)-326592*ln(2)^4*ln(5)^3-45360*ln(2)^2*ln(5)^5-840*l n(5)^7+419904*ln(2)^6+1469664*ln(2)^4*ln(5)^2+340200*ln(2)^2*ln(5)^4+8820* ln(5)^6-2939328*ln(2)^4*ln(5)-1360800*ln(2)^2*ln(5)^3-52920*ln(5)^5+220449 6*ln(2)^4+3061800*ln(2)^2*ln(5)^2+198450*ln(5)^4-3674160*ln(2)^2*ln(5)-476 280*ln(5)^3+1837080*ln(2)^2+714420*ln(5)^2-612360*ln(5)+229635)/(-3+x)+448 *ln(2)^4*(531441+63772920*ln(2)^2*ln(5)^2+21257640*ln(2)^4+3897234*ln(5)^2 -2125764*ln(5)+12754584*ln(2)^2+40095*ln(5)^8+3247695*ln(5)^4-77760*ln(2)^ 4*ln(5)^7-6480*ln(2)^2*ln(5)^9+816480*ln(2)^4*ln(5)^6+87480*ln(2)^2*ln(5)^ 8-4898880*ln(2)^4*ln(5)^5-699840*ln(2)^2*ln(5)^7+3240*ln(2)^4*ln(5)^8+216* ln(2)^2*ln(5)^10-5940*ln(5)^9+ln(5)^12-36*ln(5)^11+594*ln(5)^10-4330260*ln (5)^3+673596*ln(5)^6-42515280*ln(2)^2*ln(5)-56687040*ln(2)^4*ln(5)-5668704 0*ln(2)^2*ln(5)^3+66134880*ln(2)^4*ln(5)^2+33067440*ln(2)^2*ln(5)^4-440...
Leaf count of result is larger than twice the leaf count of optimal. 2270 vs. \(2 (28) = 56\).
Time = 0.15 (sec) , antiderivative size = 2270, normalized size of antiderivative = 78.28 \[ \text {the integral} =\text {Too large to display} \] Input:
integrate(1/65536*(-344373768+65536*(8*x^16-216*x^15+2592*x^14-18144*x^13+ 81648*x^12-244944*x^11+489888*x^10-629857*x^9+472419*x^8-157788*x^7+2268*x ^6-10206*x^5+30618*x^4-61236*x^3+78732*x^2-59049*x+19683)*log(2)^16+16384* (432*x^14-10584*x^13+113400*x^12-694008*x^11+2653560*x^10-6491016*x^9+9920 232*x^8-8660520*x^7+3306744*x^6)*log(2)^14+4096*(9072*x^12-204120*x^11+195 9552*x^10-10410120*x^9+33067440*x^8-62828136*x^7+66134880*x^6-29760696*x^5 )*log(2)^12+1024*(81648*x^10-1837080*x^9+16533720*x^8-77157360*x^7+1984046 40*x^6-267846264*x^5+148803480*x^4)*log(2)^10+256*(-5511240*x^7+66134880*x ^6-297606960*x^5+595213920*x^4-446410440*x^3)*log(2)^8+64*(-6613488*x^6+29 760696*x^5+89282088*x^4-624974616*x^3+803538792*x^2)*log(2)^6+16*(-5952139 2*x^4+267846264*x^3-803538792*x)*log(2)^4+4*(-229582512*x^2+573956280*x+34 4373768)*log(2)^2+(256*(-840*x^7+10080*x^6-45360*x^5+90720*x^4-68040*x^3)* log(2)^8+64*(-45360*x^6+204120*x^5+612360*x^4-4286520*x^3+5511240*x^2)*log (2)^6+16*(-4490640*x^4+20207880*x^3-60623640*x)*log(2)^4+4*(-105080976*x^2 +262702440*x+157621464)*log(2)^2-675520560)*log(5)^8+(1024*(112*x^10-2520* x^9+22680*x^8-105840*x^7+272160*x^6-367416*x^5+204120*x^4)*log(2)^10+256*( -211680*x^7+2540160*x^6-11430720*x^5+22861440*x^4-17146080*x^3)*log(2)^8+6 4*(-1905120*x^6+8573040*x^5+25719120*x^4-180033840*x^3+231472080*x^2)*log( 2)^6+16*(-75442752*x^4+339492384*x^3-1018477152*x)*log(2)^4+4*(-945728784* x^2+2364321960*x+1418593176)*log(2)^2-3782915136)*log(5)^6+(1024*(-2016*x^ 10+45360*x^9-408240*x^8+1905120*x^7-4898880*x^6+6613488*x^5-3674160*x^4)*l og(2)^10+256*(1270080*x^7-15240960*x^6+68584320*x^5-137168640*x^4+10287648 0*x^3)*log(2)^8+64*(6858432*x^6-30862944*x^5-92588832*x^4+648121824*x^3-83 3299488*x^2)*log(2)^6+16*(193995648*x^4-872980416*x^3+2618941248*x)*log(2) ^4+4*(1891457568*x^2-4728643920*x-2837186352)*log(2)^2+6190224768)*log(5)^ 5+(4*(-48*x^2+120*x+72)*log(2)^2-8640)*log(5)^14+(4*(2016*x^2-5040*x-3024) *log(2)^2+120960)*log(5)^13+(16*(-112*x^4+504*x^3-1512*x)*log(2)^4+4*(-393 12*x^2+98280*x+58968)*log(2)^2-1179360)*log(5)^12+(16*(4032*x^4-18144*x^3+ 54432*x)*log(2)^4+4*(471744*x^2-1179360*x-707616)*log(2)^2+8491392)*log(5) ^11+(64*(-112*x^6+504*x^5+1512*x^4-10584*x^3+13608*x^2)*log(2)^6+16*(-6652 8*x^4+299376*x^3-898128*x)*log(2)^4+4*(-3891888*x^2+9729720*x+5837832)*log (2)^2-46702656)*log(5)^10+(4096*(-1344*x^12+30240*x^11-290304*x^10+1542240 *x^9-4898880*x^8+9307872*x^7-9797760*x^6+4408992*x^5)*log(2)^12+1024*(-604 80*x^10+1360800*x^9-12247200*x^8+57153600*x^7-146966400*x^6+198404640*x^5- 110224800*x^4)*log(2)^10+256*(11430720*x^7-137168640*x^6+617258880*x^5-123 4517760*x^4+925888320*x^3)*log(2)^8+64*(29393280*x^6-132269760*x^5-3968092 80*x^4+2777664960*x^3-3571283520*x^2)*log(2)^6+16*(484989120*x^4-218245104 0*x^3+6547353120*x)*log(2)^4+4*(3095112384*x^2-7737780960*x-4642668576)*lo g(2)^2+7142567040)*log(5)^3+(16384*(48*x^14-1176*x^13+12600*x^12-77112*x^1 1+294840*x^10-721224*x^9+1102248*x^8-962280*x^7+367416*x^6)*log(2)^14+4096 *(6048*x^12-136080*x^11+1306368*x^10-6940080*x^9+22044960*x^8-41885424*x^7 +44089920*x^6-19840464*x^5)*log(2)^12+1024*(136080*x^10-3061800*x^9+275562 00*x^8-128595600*x^7+330674400*x^6-446410440*x^5+248005800*x^4)*log(2)^10+ 256*(-17146080*x^7+205752960*x^6-925888320*x^5+1851776640*x^4-1388832480*x ^3)*log(2)^8+64*(-33067440*x^6+148803480*x^5+446410440*x^4-3124873080*x^3+ 4017693960*x^2)*log(2)^6+16*(-436490208*x^4+1964205936*x^3-5892617808*x)*l og(2)^4+4*(-2321334288*x^2+5803335720*x+3482001432)*log(2)^2-4591650240)*l og(5)^2+(256*(20160*x^7-241920*x^6+1088640*x^5-2177280*x^4+1632960*x^3)*lo g(2)^8+64*(362880*x^6-1632960*x^5-4898880*x^4+34292160*x^3-44089920*x^2)*l og(2)^6+16*(21555072*x^4-96997824*x^3+290993472*x)*log(2)^4+4*(360277632*x ^2-900694080*x-540416448)*log(2)^2+1801388160)*log(5)^7+(64*(3360*x^6-1512 0*x^5-45360*x^4+317520*x^3-408240*x^2)*log(2)^6+16*(665280*x^4-2993760*x^3 +8981280*x)*log(2)^4+4*(23351328*x^2-58378320*x-35026992)*log(2)^2+2001542 40)*log(5)^9+(16384*(-288*x^14+7056*x^13-75600*x^12+462672*x^11-1769040*x^ 10+4327344*x^9-6613488*x^8+5773680*x^7-2204496*x^6)*log(2)^14+4096*(-12096 *x^12+272160*x^11-2612736*x^10+13880160*x^9-44089920*x^8+83770848*x^7-8817 9840*x^6+39680928*x^5)*log(2)^12+1024*(-163296*x^10+3674160*x^9-33067440*x ^8+154314720*x^7-396809280*x^6+535692528*x^5-297606960*x^4)*log(2)^10+256* (14696640*x^7-176359680*x^6+793618560*x^5-1587237120*x^4+1190427840*x^3)*l og(2)^8+64*(22044960*x^6-99202320*x^5-297606960*x^4+2083248720*x^3-2678462 640*x^2)*log(2)^6+16*(238085568*x^4-1071385056*x^3+3214155168*x)*log(2)^4+ 4*(1071385056*x^2-2678462640*x-1607077584)*log(2)^2+1836660096)*log(5)+(40 96*(112*x^12-2520*x^11+24192*x^10-128520*x^9+408240*x^8-775656*x^7+816480* x^6-367416*x^5)*log(2)^12+1024*(15120*x^10-340200*x^9+3061800*x^8-14288400 *x^7+36741600*x^6-49601160*x^5+27556200*x^4)*log(2)^10+256*(-4762800*x^7+5 7153600*x^6-257191200*x^5+514382400*x^4-385786800*x^3)*log(2)^8+64*(-17146 080*x^6+77157360*x^5+231472080*x^4-1620304560*x^3+2083248720*x^2)*log(2)^6 +16*(-363741840*x^4+1636838280*x^3-4910514840*x)*log(2)^4+4*(-2837186352*x ^2+7092965880*x+4255779528)*log(2)^2-7737780960)*log(5)^4-8*log(5)^16+384* log(5)^15)/(x^9-27*x^8+324*x^7-2268*x^6+10206*x^5-30618*x^4+61236*x^3-7873 2*x^2+59049*x-19683)/log(2)^16,x, algorithm="fricas")
Output:
1/65536*(65536*(x^16 - 24*x^15 + 252*x^14 - 1512*x^13 + 5670*x^12 - 13608* x^11 + 20412*x^10 - 17497*x^9 + 6585*x^8 - 252*x^7 + 1512*x^6 - 5670*x^5 + 13608*x^4 - 20412*x^3 + 17496*x^2 - 6561*x)*log(2)^16 + log(5)^16 + 8*(4* (x^2 - 3*x)*log(2)^2 + 135)*log(5)^14 - 48*log(5)^15 + 1179648*(x^14 - 21* x^13 + 189*x^12 - 945*x^11 + 2835*x^10 - 5103*x^9 + 4374*x^8 + 15309*x^7 - 183708*x^6 + 1102248*x^5 - 4133430*x^4 + 9920232*x^3 - 14880348*x^2 + 127 54584*x - 4782969)*log(2)^14 - 336*(4*(x^2 - 3*x)*log(2)^2 + 45)*log(5)^13 + 28*(16*(x^4 - 6*x^3 + 9*x^2)*log(2)^4 + 936*(x^2 - 3*x)*log(2)^2 + 5265 )*log(5)^12 + 9289728*(x^12 - 18*x^11 + 135*x^10 - 540*x^9 + 810*x^8 + 826 2*x^7 - 101331*x^6 + 612360*x^5 - 2296350*x^4 + 5511240*x^3 - 8266860*x^2 + 7085880*x - 2657205)*log(2)^12 - 1008*(16*(x^4 - 6*x^3 + 9*x^2)*log(2)^4 + 312*(x^2 - 3*x)*log(2)^2 + 1053)*log(5)^11 + 56*(64*(x^6 - 9*x^5 + 27*x ^4 - 27*x^3)*log(2)^6 + 4752*(x^4 - 6*x^3 + 9*x^2)*log(2)^4 + 46332*(x^2 - 3*x)*log(2)^2 + 104247)*log(5)^10 + 41803776*(x^10 - 15*x^9 + 36*x^8 + 10 26*x^7 - 13203*x^6 + 81405*x^5 - 306180*x^4 + 734832*x^3 - 1102248*x^2 + 9 44784*x - 354294)*log(2)^10 - 48*(2240*(x^6 - 9*x^5 + 27*x^4 - 27*x^3)*log (2)^6 + 55440*(x^4 - 6*x^3 + 9*x^2)*log(2)^4 + 324324*(x^2 - 3*x)*log(2)^2 + 521235)*log(5)^9 + 6*(8960*(4*x^7 - 66*x^6 + 468*x^5 - 1863*x^4 + 4536* x^3 - 6804*x^2 + 5832*x - 2187)*log(2)^8 + 241920*(x^6 - 9*x^5 + 27*x^4 - 27*x^3)*log(2)^6 + 2993760*(x^4 - 6*x^3 + 9*x^2)*log(2)^4 + 11675664*(x...
Timed out. \[ \text {the integral} =\text {Timed out} \] Input:
integrate(1/65536*(-344373768+(256*(-840*x**7+10080*x**6-45360*x**5+90720* x**4-68040*x**3)*ln(2)**8+64*(-45360*x**6+204120*x**5+612360*x**4-4286520* x**3+5511240*x**2)*ln(2)**6+16*(-4490640*x**4+20207880*x**3-60623640*x)*ln (2)**4+4*(-105080976*x**2+262702440*x+157621464)*ln(2)**2-675520560)*ln(5) **8+(1024*(112*x**10-2520*x**9+22680*x**8-105840*x**7+272160*x**6-367416*x **5+204120*x**4)*ln(2)**10+256*(-211680*x**7+2540160*x**6-11430720*x**5+22 861440*x**4-17146080*x**3)*ln(2)**8+64*(-1905120*x**6+8573040*x**5+2571912 0*x**4-180033840*x**3+231472080*x**2)*ln(2)**6+16*(-75442752*x**4+33949238 4*x**3-1018477152*x)*ln(2)**4+4*(-945728784*x**2+2364321960*x+1418593176)* ln(2)**2-3782915136)*ln(5)**6+(1024*(-2016*x**10+45360*x**9-408240*x**8+19 05120*x**7-4898880*x**6+6613488*x**5-3674160*x**4)*ln(2)**10+256*(1270080* x**7-15240960*x**6+68584320*x**5-137168640*x**4+102876480*x**3)*ln(2)**8+6 4*(6858432*x**6-30862944*x**5-92588832*x**4+648121824*x**3-833299488*x**2) *ln(2)**6+16*(193995648*x**4-872980416*x**3+2618941248*x)*ln(2)**4+4*(1891 457568*x**2-4728643920*x-2837186352)*ln(2)**2+6190224768)*ln(5)**5+(4*(-48 *x**2+120*x+72)*ln(2)**2-8640)*ln(5)**14+(4*(2016*x**2-5040*x-3024)*ln(2)* *2+120960)*ln(5)**13+(16*(-112*x**4+504*x**3-1512*x)*ln(2)**4+4*(-39312*x* *2+98280*x+58968)*ln(2)**2-1179360)*ln(5)**12+(16*(4032*x**4-18144*x**3+54 432*x)*ln(2)**4+4*(471744*x**2-1179360*x-707616)*ln(2)**2+8491392)*ln(5)** 11+(64*(-112*x**6+504*x**5+1512*x**4-10584*x**3+13608*x**2)*ln(2)**6+16*(- 66528*x**4+299376*x**3-898128*x)*ln(2)**4+4*(-3891888*x**2+9729720*x+58378 32)*ln(2)**2-46702656)*ln(5)**10+(16384*(-288*x**14+7056*x**13-75600*x**12 +462672*x**11-1769040*x**10+4327344*x**9-6613488*x**8+5773680*x**7-2204496 *x**6)*ln(2)**14+4096*(-12096*x**12+272160*x**11-2612736*x**10+13880160*x* *9-44089920*x**8+83770848*x**7-88179840*x**6+39680928*x**5)*ln(2)**12+1024 *(-163296*x**10+3674160*x**9-33067440*x**8+154314720*x**7-396809280*x**6+5 35692528*x**5-297606960*x**4)*ln(2)**10+256*(14696640*x**7-176359680*x**6+ 793618560*x**5-1587237120*x**4+1190427840*x**3)*ln(2)**8+64*(22044960*x**6 -99202320*x**5-297606960*x**4+2083248720*x**3-2678462640*x**2)*ln(2)**6+16 *(238085568*x**4-1071385056*x**3+3214155168*x)*ln(2)**4+4*(1071385056*x**2 -2678462640*x-1607077584)*ln(2)**2+1836660096)*ln(5)+(4096*(112*x**12-2520 *x**11+24192*x**10-128520*x**9+408240*x**8-775656*x**7+816480*x**6-367416* x**5)*ln(2)**12+1024*(15120*x**10-340200*x**9+3061800*x**8-14288400*x**7+3 6741600*x**6-49601160*x**5+27556200*x**4)*ln(2)**10+256*(-4762800*x**7+571 53600*x**6-257191200*x**5+514382400*x**4-385786800*x**3)*ln(2)**8+64*(-171 46080*x**6+77157360*x**5+231472080*x**4-1620304560*x**3+2083248720*x**2)*l n(2)**6+16*(-363741840*x**4+1636838280*x**3-4910514840*x)*ln(2)**4+4*(-283 7186352*x**2+7092965880*x+4255779528)*ln(2)**2-7737780960)*ln(5)**4+(4096* (-1344*x**12+30240*x**11-290304*x**10+1542240*x**9-4898880*x**8+9307872*x* *7-9797760*x**6+4408992*x**5)*ln(2)**12+1024*(-60480*x**10+1360800*x**9-12 247200*x**8+57153600*x**7-146966400*x**6+198404640*x**5-110224800*x**4)*ln (2)**10+256*(11430720*x**7-137168640*x**6+617258880*x**5-1234517760*x**4+9 25888320*x**3)*ln(2)**8+64*(29393280*x**6-132269760*x**5-396809280*x**4+27 77664960*x**3-3571283520*x**2)*ln(2)**6+16*(484989120*x**4-2182451040*x**3 +6547353120*x)*ln(2)**4+4*(3095112384*x**2-7737780960*x-4642668576)*ln(2)* *2+7142567040)*ln(5)**3+(16384*(48*x**14-1176*x**13+12600*x**12-77112*x**1 1+294840*x**10-721224*x**9+1102248*x**8-962280*x**7+367416*x**6)*ln(2)**14 +4096*(6048*x**12-136080*x**11+1306368*x**10-6940080*x**9+22044960*x**8-41 885424*x**7+44089920*x**6-19840464*x**5)*ln(2)**12+1024*(136080*x**10-3061 800*x**9+27556200*x**8-128595600*x**7+330674400*x**6-446410440*x**5+248005 800*x**4)*ln(2)**10+256*(-17146080*x**7+205752960*x**6-925888320*x**5+1851 776640*x**4-1388832480*x**3)*ln(2)**8+64*(-33067440*x**6+148803480*x**5+44 6410440*x**4-3124873080*x**3+4017693960*x**2)*ln(2)**6+16*(-436490208*x**4 +1964205936*x**3-5892617808*x)*ln(2)**4+4*(-2321334288*x**2+5803335720*x+3 482001432)*ln(2)**2-4591650240)*ln(5)**2+(256*(20160*x**7-241920*x**6+1088 640*x**5-2177280*x**4+1632960*x**3)*ln(2)**8+64*(362880*x**6-1632960*x**5- 4898880*x**4+34292160*x**3-44089920*x**2)*ln(2)**6+16*(21555072*x**4-96997 824*x**3+290993472*x)*ln(2)**4+4*(360277632*x**2-900694080*x-540416448)*ln (2)**2+1801388160)*ln(5)**7+(64*(3360*x**6-15120*x**5-45360*x**4+317520*x* *3-408240*x**2)*ln(2)**6+16*(665280*x**4-2993760*x**3+8981280*x)*ln(2)**4+ 4*(23351328*x**2-58378320*x-35026992)*ln(2)**2+200154240)*ln(5)**9-8*ln(5) **16+384*ln(5)**15+65536*(8*x**16-216*x**15+2592*x**14-18144*x**13+81648*x **12-244944*x**11+489888*x**10-629857*x**9+472419*x**8-157788*x**7+2268*x* *6-10206*x**5+30618*x**4-61236*x**3+78732*x**2-59049*x+19683)*ln(2)**16+16 384*(432*x**14-10584*x**13+113400*x**12-694008*x**11+2653560*x**10-6491016 *x**9+9920232*x**8-8660520*x**7+3306744*x**6)*ln(2)**14+4096*(9072*x**12-2 04120*x**11+1959552*x**10-10410120*x**9+33067440*x**8-62828136*x**7+661348 80*x**6-29760696*x**5)*ln(2)**12+1024*(81648*x**10-1837080*x**9+16533720*x **8-77157360*x**7+198404640*x**6-267846264*x**5+148803480*x**4)*ln(2)**10+ 256*(-5511240*x**7+66134880*x**6-297606960*x**5+595213920*x**4-446410440*x **3)*ln(2)**8+64*(-6613488*x**6+29760696*x**5+89282088*x**4-624974616*x**3 +803538792*x**2)*ln(2)**6+16*(-59521392*x**4+267846264*x**3-803538792*x)*l n(2)**4+4*(-229582512*x**2+573956280*x+344373768)*ln(2)**2)/(x**9-27*x**8+ 324*x**7-2268*x**6+10206*x**5-30618*x**4+61236*x**3-78732*x**2+59049*x-196 83)/ln(2)**16,x)
Output:
Timed out
Leaf count of result is larger than twice the leaf count of optimal. 2993 vs. \(2 (28) = 56\).
Time = 0.11 (sec) , antiderivative size = 2993, normalized size of antiderivative = 103.21 \[ \text {the integral} =\text {Too large to display} \] Input:
integrate(1/65536*(-344373768+65536*(8*x^16-216*x^15+2592*x^14-18144*x^13+ 81648*x^12-244944*x^11+489888*x^10-629857*x^9+472419*x^8-157788*x^7+2268*x ^6-10206*x^5+30618*x^4-61236*x^3+78732*x^2-59049*x+19683)*log(2)^16+16384* (432*x^14-10584*x^13+113400*x^12-694008*x^11+2653560*x^10-6491016*x^9+9920 232*x^8-8660520*x^7+3306744*x^6)*log(2)^14+4096*(9072*x^12-204120*x^11+195 9552*x^10-10410120*x^9+33067440*x^8-62828136*x^7+66134880*x^6-29760696*x^5 )*log(2)^12+1024*(81648*x^10-1837080*x^9+16533720*x^8-77157360*x^7+1984046 40*x^6-267846264*x^5+148803480*x^4)*log(2)^10+256*(-5511240*x^7+66134880*x ^6-297606960*x^5+595213920*x^4-446410440*x^3)*log(2)^8+64*(-6613488*x^6+29 760696*x^5+89282088*x^4-624974616*x^3+803538792*x^2)*log(2)^6+16*(-5952139 2*x^4+267846264*x^3-803538792*x)*log(2)^4+4*(-229582512*x^2+573956280*x+34 4373768)*log(2)^2+(256*(-840*x^7+10080*x^6-45360*x^5+90720*x^4-68040*x^3)* log(2)^8+64*(-45360*x^6+204120*x^5+612360*x^4-4286520*x^3+5511240*x^2)*log (2)^6+16*(-4490640*x^4+20207880*x^3-60623640*x)*log(2)^4+4*(-105080976*x^2 +262702440*x+157621464)*log(2)^2-675520560)*log(5)^8+(1024*(112*x^10-2520* x^9+22680*x^8-105840*x^7+272160*x^6-367416*x^5+204120*x^4)*log(2)^10+256*( -211680*x^7+2540160*x^6-11430720*x^5+22861440*x^4-17146080*x^3)*log(2)^8+6 4*(-1905120*x^6+8573040*x^5+25719120*x^4-180033840*x^3+231472080*x^2)*log( 2)^6+16*(-75442752*x^4+339492384*x^3-1018477152*x)*log(2)^4+4*(-945728784* x^2+2364321960*x+1418593176)*log(2)^2-3782915136)*log(5)^6+(1024*(-2016*x^ 10+45360*x^9-408240*x^8+1905120*x^7-4898880*x^6+6613488*x^5-3674160*x^4)*l og(2)^10+256*(1270080*x^7-15240960*x^6+68584320*x^5-137168640*x^4+10287648 0*x^3)*log(2)^8+64*(6858432*x^6-30862944*x^5-92588832*x^4+648121824*x^3-83 3299488*x^2)*log(2)^6+16*(193995648*x^4-872980416*x^3+2618941248*x)*log(2) ^4+4*(1891457568*x^2-4728643920*x-2837186352)*log(2)^2+6190224768)*log(5)^ 5+(4*(-48*x^2+120*x+72)*log(2)^2-8640)*log(5)^14+(4*(2016*x^2-5040*x-3024) *log(2)^2+120960)*log(5)^13+(16*(-112*x^4+504*x^3-1512*x)*log(2)^4+4*(-393 12*x^2+98280*x+58968)*log(2)^2-1179360)*log(5)^12+(16*(4032*x^4-18144*x^3+ 54432*x)*log(2)^4+4*(471744*x^2-1179360*x-707616)*log(2)^2+8491392)*log(5) ^11+(64*(-112*x^6+504*x^5+1512*x^4-10584*x^3+13608*x^2)*log(2)^6+16*(-6652 8*x^4+299376*x^3-898128*x)*log(2)^4+4*(-3891888*x^2+9729720*x+5837832)*log (2)^2-46702656)*log(5)^10+(4096*(-1344*x^12+30240*x^11-290304*x^10+1542240 *x^9-4898880*x^8+9307872*x^7-9797760*x^6+4408992*x^5)*log(2)^12+1024*(-604 80*x^10+1360800*x^9-12247200*x^8+57153600*x^7-146966400*x^6+198404640*x^5- 110224800*x^4)*log(2)^10+256*(11430720*x^7-137168640*x^6+617258880*x^5-123 4517760*x^4+925888320*x^3)*log(2)^8+64*(29393280*x^6-132269760*x^5-3968092 80*x^4+2777664960*x^3-3571283520*x^2)*log(2)^6+16*(484989120*x^4-218245104 0*x^3+6547353120*x)*log(2)^4+4*(3095112384*x^2-7737780960*x-4642668576)*lo g(2)^2+7142567040)*log(5)^3+(16384*(48*x^14-1176*x^13+12600*x^12-77112*x^1 1+294840*x^10-721224*x^9+1102248*x^8-962280*x^7+367416*x^6)*log(2)^14+4096 *(6048*x^12-136080*x^11+1306368*x^10-6940080*x^9+22044960*x^8-41885424*x^7 +44089920*x^6-19840464*x^5)*log(2)^12+1024*(136080*x^10-3061800*x^9+275562 00*x^8-128595600*x^7+330674400*x^6-446410440*x^5+248005800*x^4)*log(2)^10+ 256*(-17146080*x^7+205752960*x^6-925888320*x^5+1851776640*x^4-1388832480*x ^3)*log(2)^8+64*(-33067440*x^6+148803480*x^5+446410440*x^4-3124873080*x^3+ 4017693960*x^2)*log(2)^6+16*(-436490208*x^4+1964205936*x^3-5892617808*x)*l og(2)^4+4*(-2321334288*x^2+5803335720*x+3482001432)*log(2)^2-4591650240)*l og(5)^2+(256*(20160*x^7-241920*x^6+1088640*x^5-2177280*x^4+1632960*x^3)*lo g(2)^8+64*(362880*x^6-1632960*x^5-4898880*x^4+34292160*x^3-44089920*x^2)*l og(2)^6+16*(21555072*x^4-96997824*x^3+290993472*x)*log(2)^4+4*(360277632*x ^2-900694080*x-540416448)*log(2)^2+1801388160)*log(5)^7+(64*(3360*x^6-1512 0*x^5-45360*x^4+317520*x^3-408240*x^2)*log(2)^6+16*(665280*x^4-2993760*x^3 +8981280*x)*log(2)^4+4*(23351328*x^2-58378320*x-35026992)*log(2)^2+2001542 40)*log(5)^9+(16384*(-288*x^14+7056*x^13-75600*x^12+462672*x^11-1769040*x^ 10+4327344*x^9-6613488*x^8+5773680*x^7-2204496*x^6)*log(2)^14+4096*(-12096 *x^12+272160*x^11-2612736*x^10+13880160*x^9-44089920*x^8+83770848*x^7-8817 9840*x^6+39680928*x^5)*log(2)^12+1024*(-163296*x^10+3674160*x^9-33067440*x ^8+154314720*x^7-396809280*x^6+535692528*x^5-297606960*x^4)*log(2)^10+256* (14696640*x^7-176359680*x^6+793618560*x^5-1587237120*x^4+1190427840*x^3)*l og(2)^8+64*(22044960*x^6-99202320*x^5-297606960*x^4+2083248720*x^3-2678462 640*x^2)*log(2)^6+16*(238085568*x^4-1071385056*x^3+3214155168*x)*log(2)^4+ 4*(1071385056*x^2-2678462640*x-1607077584)*log(2)^2+1836660096)*log(5)+(40 96*(112*x^12-2520*x^11+24192*x^10-128520*x^9+408240*x^8-775656*x^7+816480* x^6-367416*x^5)*log(2)^12+1024*(15120*x^10-340200*x^9+3061800*x^8-14288400 *x^7+36741600*x^6-49601160*x^5+27556200*x^4)*log(2)^10+256*(-4762800*x^7+5 7153600*x^6-257191200*x^5+514382400*x^4-385786800*x^3)*log(2)^8+64*(-17146 080*x^6+77157360*x^5+231472080*x^4-1620304560*x^3+2083248720*x^2)*log(2)^6 +16*(-363741840*x^4+1636838280*x^3-4910514840*x)*log(2)^4+4*(-2837186352*x ^2+7092965880*x+4255779528)*log(2)^2-7737780960)*log(5)^4-8*log(5)^16+384* log(5)^15)/(x^9-27*x^8+324*x^7-2268*x^6+10206*x^5-30618*x^4+61236*x^3-7873 2*x^2+59049*x-19683)/log(2)^16,x, algorithm="maxima")
Output:
1/65536*(65536*x^8*log(2)^16 + 131072*(log(5)^2*log(2)^14 - 6*log(5)*log(2 )^14 + 9*log(2)^14)*x^6 + 393216*(log(5)^2*log(2)^14 - 6*log(5)*log(2)^14 + 9*log(2)^14)*x^5 + 16384*(7*log(5)^4*log(2)^12 - 84*log(5)^3*log(2)^12 + 648*log(2)^14 + 567*log(2)^12 + 18*(4*log(2)^14 + 21*log(2)^12)*log(5)^2 - 108*(4*log(2)^14 + 7*log(2)^12)*log(5))*x^4 + 98304*(7*log(5)^4*log(2)^1 2 - 84*log(5)^3*log(2)^12 + 324*log(2)^14 + 567*log(2)^12 + 18*(2*log(2)^1 4 + 21*log(2)^12)*log(5)^2 - 108*(2*log(2)^14 + 7*log(2)^12)*log(5))*x^3 + 8192*(7*log(5)^6*log(2)^10 - 126*log(5)^5*log(2)^10 + 11664*log(2)^14 + 3 0618*log(2)^12 + 5103*log(2)^10 + 189*(2*log(2)^12 + 5*log(2)^10)*log(5)^4 - 756*(6*log(2)^12 + 5*log(2)^10)*log(5)^3 + 81*(16*log(2)^14 + 252*log(2 )^12 + 105*log(2)^10)*log(5)^2 - 486*(16*log(2)^14 + 84*log(2)^12 + 21*log (2)^10)*log(5))*x^2 + 8192*(63*log(5)^6*log(2)^10 - 8*log(2)^16 - 1134*log (5)^5*log(2)^10 + 34992*log(2)^14 + 122472*log(2)^12 + 45927*log(2)^10 + 1 89*(8*log(2)^12 + 45*log(2)^10)*log(5)^4 - 2268*(8*log(2)^12 + 15*log(2)^1 0)*log(5)^3 + 243*(16*log(2)^14 + 336*log(2)^12 + 315*log(2)^10)*log(5)^2 - 1458*(16*log(2)^14 + 112*log(2)^12 + 63*log(2)^10)*log(5))*x + (log(5)^1 6 - 48*log(5)^15 + 1080*log(5)^14 - 5642219814912*log(2)^14 - 15120*log(5) ^13 + 147420*log(5)^12 - 24684711690240*log(2)^12 - 1061424*log(5)^11 + 58 37832*log(5)^10 - 14810827014144*log(2)^10 - 65610*(1792*log(2)^8 - 1287)* log(5)^8 - 25019280*log(5)^9 + 6144*(35*log(5)^8*log(2)^8 - 840*log(5)^...
Leaf count of result is larger than twice the leaf count of optimal. 4266 vs. \(2 (28) = 56\).
Time = 0.16 (sec) , antiderivative size = 4266, normalized size of antiderivative = 147.10 \[ \text {the integral} =\text {Too large to display} \] Input:
integrate(1/65536*(-344373768+65536*(8*x^16-216*x^15+2592*x^14-18144*x^13+ 81648*x^12-244944*x^11+489888*x^10-629857*x^9+472419*x^8-157788*x^7+2268*x ^6-10206*x^5+30618*x^4-61236*x^3+78732*x^2-59049*x+19683)*log(2)^16+16384* (432*x^14-10584*x^13+113400*x^12-694008*x^11+2653560*x^10-6491016*x^9+9920 232*x^8-8660520*x^7+3306744*x^6)*log(2)^14+4096*(9072*x^12-204120*x^11+195 9552*x^10-10410120*x^9+33067440*x^8-62828136*x^7+66134880*x^6-29760696*x^5 )*log(2)^12+1024*(81648*x^10-1837080*x^9+16533720*x^8-77157360*x^7+1984046 40*x^6-267846264*x^5+148803480*x^4)*log(2)^10+256*(-5511240*x^7+66134880*x ^6-297606960*x^5+595213920*x^4-446410440*x^3)*log(2)^8+64*(-6613488*x^6+29 760696*x^5+89282088*x^4-624974616*x^3+803538792*x^2)*log(2)^6+16*(-5952139 2*x^4+267846264*x^3-803538792*x)*log(2)^4+4*(-229582512*x^2+573956280*x+34 4373768)*log(2)^2+(256*(-840*x^7+10080*x^6-45360*x^5+90720*x^4-68040*x^3)* log(2)^8+64*(-45360*x^6+204120*x^5+612360*x^4-4286520*x^3+5511240*x^2)*log (2)^6+16*(-4490640*x^4+20207880*x^3-60623640*x)*log(2)^4+4*(-105080976*x^2 +262702440*x+157621464)*log(2)^2-675520560)*log(5)^8+(1024*(112*x^10-2520* x^9+22680*x^8-105840*x^7+272160*x^6-367416*x^5+204120*x^4)*log(2)^10+256*( -211680*x^7+2540160*x^6-11430720*x^5+22861440*x^4-17146080*x^3)*log(2)^8+6 4*(-1905120*x^6+8573040*x^5+25719120*x^4-180033840*x^3+231472080*x^2)*log( 2)^6+16*(-75442752*x^4+339492384*x^3-1018477152*x)*log(2)^4+4*(-945728784* x^2+2364321960*x+1418593176)*log(2)^2-3782915136)*log(5)^6+(1024*(-2016*x^ 10+45360*x^9-408240*x^8+1905120*x^7-4898880*x^6+6613488*x^5-3674160*x^4)*l og(2)^10+256*(1270080*x^7-15240960*x^6+68584320*x^5-137168640*x^4+10287648 0*x^3)*log(2)^8+64*(6858432*x^6-30862944*x^5-92588832*x^4+648121824*x^3-83 3299488*x^2)*log(2)^6+16*(193995648*x^4-872980416*x^3+2618941248*x)*log(2) ^4+4*(1891457568*x^2-4728643920*x-2837186352)*log(2)^2+6190224768)*log(5)^ 5+(4*(-48*x^2+120*x+72)*log(2)^2-8640)*log(5)^14+(4*(2016*x^2-5040*x-3024) *log(2)^2+120960)*log(5)^13+(16*(-112*x^4+504*x^3-1512*x)*log(2)^4+4*(-393 12*x^2+98280*x+58968)*log(2)^2-1179360)*log(5)^12+(16*(4032*x^4-18144*x^3+ 54432*x)*log(2)^4+4*(471744*x^2-1179360*x-707616)*log(2)^2+8491392)*log(5) ^11+(64*(-112*x^6+504*x^5+1512*x^4-10584*x^3+13608*x^2)*log(2)^6+16*(-6652 8*x^4+299376*x^3-898128*x)*log(2)^4+4*(-3891888*x^2+9729720*x+5837832)*log (2)^2-46702656)*log(5)^10+(4096*(-1344*x^12+30240*x^11-290304*x^10+1542240 *x^9-4898880*x^8+9307872*x^7-9797760*x^6+4408992*x^5)*log(2)^12+1024*(-604 80*x^10+1360800*x^9-12247200*x^8+57153600*x^7-146966400*x^6+198404640*x^5- 110224800*x^4)*log(2)^10+256*(11430720*x^7-137168640*x^6+617258880*x^5-123 4517760*x^4+925888320*x^3)*log(2)^8+64*(29393280*x^6-132269760*x^5-3968092 80*x^4+2777664960*x^3-3571283520*x^2)*log(2)^6+16*(484989120*x^4-218245104 0*x^3+6547353120*x)*log(2)^4+4*(3095112384*x^2-7737780960*x-4642668576)*lo g(2)^2+7142567040)*log(5)^3+(16384*(48*x^14-1176*x^13+12600*x^12-77112*x^1 1+294840*x^10-721224*x^9+1102248*x^8-962280*x^7+367416*x^6)*log(2)^14+4096 *(6048*x^12-136080*x^11+1306368*x^10-6940080*x^9+22044960*x^8-41885424*x^7 +44089920*x^6-19840464*x^5)*log(2)^12+1024*(136080*x^10-3061800*x^9+275562 00*x^8-128595600*x^7+330674400*x^6-446410440*x^5+248005800*x^4)*log(2)^10+ 256*(-17146080*x^7+205752960*x^6-925888320*x^5+1851776640*x^4-1388832480*x ^3)*log(2)^8+64*(-33067440*x^6+148803480*x^5+446410440*x^4-3124873080*x^3+ 4017693960*x^2)*log(2)^6+16*(-436490208*x^4+1964205936*x^3-5892617808*x)*l og(2)^4+4*(-2321334288*x^2+5803335720*x+3482001432)*log(2)^2-4591650240)*l og(5)^2+(256*(20160*x^7-241920*x^6+1088640*x^5-2177280*x^4+1632960*x^3)*lo g(2)^8+64*(362880*x^6-1632960*x^5-4898880*x^4+34292160*x^3-44089920*x^2)*l og(2)^6+16*(21555072*x^4-96997824*x^3+290993472*x)*log(2)^4+4*(360277632*x ^2-900694080*x-540416448)*log(2)^2+1801388160)*log(5)^7+(64*(3360*x^6-1512 0*x^5-45360*x^4+317520*x^3-408240*x^2)*log(2)^6+16*(665280*x^4-2993760*x^3 +8981280*x)*log(2)^4+4*(23351328*x^2-58378320*x-35026992)*log(2)^2+2001542 40)*log(5)^9+(16384*(-288*x^14+7056*x^13-75600*x^12+462672*x^11-1769040*x^ 10+4327344*x^9-6613488*x^8+5773680*x^7-2204496*x^6)*log(2)^14+4096*(-12096 *x^12+272160*x^11-2612736*x^10+13880160*x^9-44089920*x^8+83770848*x^7-8817 9840*x^6+39680928*x^5)*log(2)^12+1024*(-163296*x^10+3674160*x^9-33067440*x ^8+154314720*x^7-396809280*x^6+535692528*x^5-297606960*x^4)*log(2)^10+256* (14696640*x^7-176359680*x^6+793618560*x^5-1587237120*x^4+1190427840*x^3)*l og(2)^8+64*(22044960*x^6-99202320*x^5-297606960*x^4+2083248720*x^3-2678462 640*x^2)*log(2)^6+16*(238085568*x^4-1071385056*x^3+3214155168*x)*log(2)^4+ 4*(1071385056*x^2-2678462640*x-1607077584)*log(2)^2+1836660096)*log(5)+(40 96*(112*x^12-2520*x^11+24192*x^10-128520*x^9+408240*x^8-775656*x^7+816480* x^6-367416*x^5)*log(2)^12+1024*(15120*x^10-340200*x^9+3061800*x^8-14288400 *x^7+36741600*x^6-49601160*x^5+27556200*x^4)*log(2)^10+256*(-4762800*x^7+5 7153600*x^6-257191200*x^5+514382400*x^4-385786800*x^3)*log(2)^8+64*(-17146 080*x^6+77157360*x^5+231472080*x^4-1620304560*x^3+2083248720*x^2)*log(2)^6 +16*(-363741840*x^4+1636838280*x^3-4910514840*x)*log(2)^4+4*(-2837186352*x ^2+7092965880*x+4255779528)*log(2)^2-7737780960)*log(5)^4-8*log(5)^16+384* log(5)^15)/(x^9-27*x^8+324*x^7-2268*x^6+10206*x^5-30618*x^4+61236*x^3-7873 2*x^2+59049*x-19683)/log(2)^16,x, algorithm="giac")
Output:
1/65536*(65536*x^8*log(2)^16 + 131072*x^6*log(5)^2*log(2)^14 - 786432*x^6* log(5)*log(2)^14 + 393216*x^5*log(5)^2*log(2)^14 + 114688*x^4*log(5)^4*log (2)^12 + 1179648*x^6*log(2)^14 - 2359296*x^5*log(5)*log(2)^14 + 1179648*x^ 4*log(5)^2*log(2)^14 - 1376256*x^4*log(5)^3*log(2)^12 + 688128*x^3*log(5)^ 4*log(2)^12 + 3538944*x^5*log(2)^14 - 7077888*x^4*log(5)*log(2)^14 + 35389 44*x^3*log(5)^2*log(2)^14 + 57344*x^2*log(5)^6*log(2)^10 + 6193152*x^4*log (5)^2*log(2)^12 - 8257536*x^3*log(5)^3*log(2)^12 + 3096576*x^2*log(5)^4*lo g(2)^12 + 10616832*x^4*log(2)^14 - 21233664*x^3*log(5)*log(2)^14 + 1061683 2*x^2*log(5)^2*log(2)^14 - 1032192*x^2*log(5)^5*log(2)^10 + 516096*x*log(5 )^6*log(2)^10 - 12386304*x^4*log(5)*log(2)^12 + 37158912*x^3*log(5)^2*log( 2)^12 - 37158912*x^2*log(5)^3*log(2)^12 + 12386304*x*log(5)^4*log(2)^12 + 31850496*x^3*log(2)^14 - 63700992*x^2*log(5)*log(2)^14 + 31850496*x*log(5) ^2*log(2)^14 - 65536*x*log(2)^16 + 7741440*x^2*log(5)^4*log(2)^10 - 928972 8*x*log(5)^5*log(2)^10 + 9289728*x^4*log(2)^12 - 74317824*x^3*log(5)*log(2 )^12 + 167215104*x^2*log(5)^2*log(2)^12 - 148635648*x*log(5)^3*log(2)^12 + 95551488*x^2*log(2)^14 - 191102976*x*log(5)*log(2)^14 - 30965760*x^2*log( 5)^3*log(2)^10 + 69672960*x*log(5)^4*log(2)^10 + 55738368*x^3*log(2)^12 - 334430208*x^2*log(5)*log(2)^12 + 668860416*x*log(5)^2*log(2)^12 + 28665446 4*x*log(2)^14 + 69672960*x^2*log(5)^2*log(2)^10 - 278691840*x*log(5)^3*log (2)^10 + 250822656*x^2*log(2)^12 - 1337720832*x*log(5)*log(2)^12 - 8360...
Time = 6.19 (sec) , antiderivative size = 4377, normalized size of antiderivative = 150.93 \[ \text {the integral} =\text {Too large to display} \] Input:
int(((log(5)^7*(256*log(2)^8*(1632960*x^3 - 2177280*x^4 + 1088640*x^5 - 24 1920*x^6 + 20160*x^7) - 4*log(2)^2*(900694080*x - 360277632*x^2 + 54041644 8) - 64*log(2)^6*(44089920*x^2 - 34292160*x^3 + 4898880*x^4 + 1632960*x^5 - 362880*x^6) + 16*log(2)^4*(290993472*x - 96997824*x^3 + 21555072*x^4) + 1801388160))/65536 - (log(2)^4*(803538792*x - 267846264*x^3 + 59521392*x^4 ))/4096 + (log(5)^14*(4*log(2)^2*(120*x - 48*x^2 + 72) - 8640))/65536 - (l og(5)^13*(4*log(2)^2*(5040*x - 2016*x^2 + 3024) - 120960))/65536 - (log(5) ^5*(1024*log(2)^10*(3674160*x^4 - 6613488*x^5 + 4898880*x^6 - 1905120*x^7 + 408240*x^8 - 45360*x^9 + 2016*x^10) - 16*log(2)^4*(2618941248*x - 872980 416*x^3 + 193995648*x^4) - 256*log(2)^8*(102876480*x^3 - 137168640*x^4 + 6 8584320*x^5 - 15240960*x^6 + 1270080*x^7) + 4*log(2)^2*(4728643920*x - 189 1457568*x^2 + 2837186352) + 64*log(2)^6*(833299488*x^2 - 648121824*x^3 + 9 2588832*x^4 + 30862944*x^5 - 6858432*x^6) - 6190224768))/65536 + (log(2)^1 0*(148803480*x^4 - 267846264*x^5 + 198404640*x^6 - 77157360*x^7 + 16533720 *x^8 - 1837080*x^9 + 81648*x^10))/64 - (log(2)^12*(29760696*x^5 - 66134880 *x^6 + 62828136*x^7 - 33067440*x^8 + 10410120*x^9 - 1959552*x^10 + 204120* x^11 - 9072*x^12))/16 + (log(5)^3*(4096*log(2)^12*(4408992*x^5 - 9797760*x ^6 + 9307872*x^7 - 4898880*x^8 + 1542240*x^9 - 290304*x^10 + 30240*x^11 - 1344*x^12) - 4*log(2)^2*(7737780960*x - 3095112384*x^2 + 4642668576) - 64* log(2)^6*(3571283520*x^2 - 2777664960*x^3 + 396809280*x^4 + 132269760*x^5 - 29393280*x^6) - 1024*log(2)^10*(110224800*x^4 - 198404640*x^5 + 14696640 0*x^6 - 57153600*x^7 + 12247200*x^8 - 1360800*x^9 + 60480*x^10) + 256*log( 2)^8*(925888320*x^3 - 1234517760*x^4 + 617258880*x^5 - 137168640*x^6 + 114 30720*x^7) + 16*log(2)^4*(6547353120*x - 2182451040*x^3 + 484989120*x^4) + 7142567040))/65536 - (log(5)^4*(4096*log(2)^12*(367416*x^5 - 816480*x^6 + 775656*x^7 - 408240*x^8 + 128520*x^9 - 24192*x^10 + 2520*x^11 - 112*x^12) - 1024*log(2)^10*(27556200*x^4 - 49601160*x^5 + 36741600*x^6 - 14288400*x ^7 + 3061800*x^8 - 340200*x^9 + 15120*x^10) + 16*log(2)^4*(4910514840*x - 1636838280*x^3 + 363741840*x^4) - 64*log(2)^6*(2083248720*x^2 - 1620304560 *x^3 + 231472080*x^4 + 77157360*x^5 - 17146080*x^6) + 256*log(2)^8*(385786 800*x^3 - 514382400*x^4 + 257191200*x^5 - 57153600*x^6 + 4762800*x^7) - 4* log(2)^2*(7092965880*x - 2837186352*x^2 + 4255779528) + 7737780960))/65536 + (log(2)^14*(3306744*x^6 - 8660520*x^7 + 9920232*x^8 - 6491016*x^9 + 265 3560*x^10 - 694008*x^11 + 113400*x^12 - 10584*x^13 + 432*x^14))/4 - (log(5 )^8*(256*log(2)^8*(68040*x^3 - 90720*x^4 + 45360*x^5 - 10080*x^6 + 840*x^7 ) - 64*log(2)^6*(5511240*x^2 - 4286520*x^3 + 612360*x^4 + 204120*x^5 - 453 60*x^6) - 4*log(2)^2*(262702440*x - 105080976*x^2 + 157621464) + 16*log(2) ^4*(60623640*x - 20207880*x^3 + 4490640*x^4) + 675520560))/65536 + (log(5) ^10*(4*log(2)^2*(9729720*x - 3891888*x^2 + 5837832) + 64*log(2)^6*(13608*x ^2 - 10584*x^3 + 1512*x^4 + 504*x^5 - 112*x^6) - 16*log(2)^4*(898128*x - 2 99376*x^3 + 66528*x^4) - 46702656))/65536 + log(2)^16*(78732*x^2 - 59049*x - 61236*x^3 + 30618*x^4 - 10206*x^5 + 2268*x^6 - 157788*x^7 + 472419*x^8 - 629857*x^9 + 489888*x^10 - 244944*x^11 + 81648*x^12 - 18144*x^13 + 2592* x^14 - 216*x^15 + 8*x^16 + 19683) - (log(5)^9*(64*log(2)^6*(408240*x^2 - 3 17520*x^3 + 45360*x^4 + 15120*x^5 - 3360*x^6) + 4*log(2)^2*(58378320*x - 2 3351328*x^2 + 35026992) - 16*log(2)^4*(8981280*x - 2993760*x^3 + 665280*x^ 4) - 200154240))/65536 + (log(5)^6*(1024*log(2)^10*(204120*x^4 - 367416*x^ 5 + 272160*x^6 - 105840*x^7 + 22680*x^8 - 2520*x^9 + 112*x^10) - 16*log(2) ^4*(1018477152*x - 339492384*x^3 + 75442752*x^4) - 256*log(2)^8*(17146080* x^3 - 22861440*x^4 + 11430720*x^5 - 2540160*x^6 + 211680*x^7) + 4*log(2)^2 *(2364321960*x - 945728784*x^2 + 1418593176) + 64*log(2)^6*(231472080*x^2 - 180033840*x^3 + 25719120*x^4 + 8573040*x^5 - 1905120*x^6) - 3782915136)) /65536 + (log(5)*(4096*log(2)^12*(39680928*x^5 - 88179840*x^6 + 83770848*x ^7 - 44089920*x^8 + 13880160*x^9 - 2612736*x^10 + 272160*x^11 - 12096*x^12 ) - 1024*log(2)^10*(297606960*x^4 - 535692528*x^5 + 396809280*x^6 - 154314 720*x^7 + 33067440*x^8 - 3674160*x^9 + 163296*x^10) - 16384*log(2)^14*(220 4496*x^6 - 5773680*x^7 + 6613488*x^8 - 4327344*x^9 + 1769040*x^10 - 462672 *x^11 + 75600*x^12 - 7056*x^13 + 288*x^14) + 256*log(2)^8*(1190427840*x^3 - 1587237120*x^4 + 793618560*x^5 - 176359680*x^6 + 14696640*x^7) - 64*log( 2)^6*(2678462640*x^2 - 2083248720*x^3 + 297606960*x^4 + 99202320*x^5 - 220 44960*x^6) - 4*log(2)^2*(2678462640*x - 1071385056*x^2 + 1607077584) + 16* log(2)^4*(3214155168*x - 1071385056*x^3 + 238085568*x^4) + 1836660096))/65 536 - (log(5)^2*(4096*log(2)^12*(19840464*x^5 - 44089920*x^6 + 41885424*x^ 7 - 22044960*x^8 + 6940080*x^9 - 1306368*x^10 + 136080*x^11 - 6048*x^12) - 4*log(2)^2*(5803335720*x - 2321334288*x^2 + 3482001432) - 1024*log(2)^10* (248005800*x^4 - 446410440*x^5 + 330674400*x^6 - 128595600*x^7 + 27556200* x^8 - 3061800*x^9 + 136080*x^10) - 64*log(2)^6*(4017693960*x^2 - 312487308 0*x^3 + 446410440*x^4 + 148803480*x^5 - 33067440*x^6) - 16384*log(2)^14*(3 67416*x^6 - 962280*x^7 + 1102248*x^8 - 721224*x^9 + 294840*x^10 - 77112*x^ 11 + 12600*x^12 - 1176*x^13 + 48*x^14) + 256*log(2)^8*(1388832480*x^3 - 18 51776640*x^4 + 925888320*x^5 - 205752960*x^6 + 17146080*x^7) + 16*log(2)^4 *(5892617808*x - 1964205936*x^3 + 436490208*x^4) + 4591650240))/65536 + (3 *log(5)^15)/512 - log(5)^16/8192 + (log(2)^2*(573956280*x - 229582512*x^2 + 344373768))/16384 - (log(2)^8*(446410440*x^3 - 595213920*x^4 + 297606960 *x^5 - 66134880*x^6 + 5511240*x^7))/256 - (log(5)^12*(16*log(2)^4*(1512*x - 504*x^3 + 112*x^4) - 4*log(2)^2*(98280*x - 39312*x^2 + 58968) + 1179360) )/65536 + (log(5)^11*(16*log(2)^4*(54432*x - 18144*x^3 + 4032*x^4) - 4*log (2)^2*(1179360*x - 471744*x^2 + 707616) + 8491392))/65536 + (log(2)^6*(803 538792*x^2 - 624974616*x^3 + 89282088*x^4 + 29760696*x^5 - 6613488*x^6))/1 024 - 43046721/8192)/(log(2)^16*(59049*x - 78732*x^2 + 61236*x^3 - 30618*x ^4 + 10206*x^5 - 2268*x^6 + 324*x^7 - 27*x^8 + x^9 - 19683)),x)
Output:
x^2*((405*(4644864*log(2)^12 + 232243200*log(2)^14 + 668860416*log(2)^16 + 3096576*log(2)^12*log(5)^2 - 688128*log(2)^12*log(5)^3 + 57344*log(2)^12* log(5)^4 + 25804800*log(2)^14*log(5)^2 - 6193152*log(2)^12*log(5)*(25*log( 2)^2 + 1)))/(16384*log(2)^16) + (7*(69984*log(2)^2 - 1458*log(5) + 379080* log(2)^4 + 1215*log(5)^2 + 279936*log(2)^6 - 540*log(5)^3 + 135*log(5)^4 - 18*log(5)^5 + log(5)^6 + 46656*log(2)^2*log(5)^2 - 10368*log(2)^2*log(5)^ 3 + 864*log(2)^2*log(5)^4 + 42120*log(2)^4*log(5)^2 - 3888*log(2)^2*log(5) *(65*log(2)^2 + 24) + 729))/(8*log(2)^6) + (40095*(884736*log(2)^14 - 5898 24*log(2)^14*log(5) + 21233664*log(2)^16 + 98304*log(2)^14*log(5)^2))/(163 84*log(2)^16) - (4455*(21676032*log(2)^14 - 14450688*log(2)^14*log(5) + 14 8635648*log(2)^16 + 2408448*log(2)^14*log(5)^2))/(16384*log(2)^16) - (27*( 104509440*log(2)^12 + 1421328384*log(2)^14 + 2006581248*log(2)^16 + 696729 60*log(2)^12*log(5)^2 - 15482880*log(2)^12*log(5)^3 + 1290240*log(2)^12*lo g(5)^4 + 157925376*log(2)^14*log(5)^2 - 27869184*log(2)^12*log(5)*(34*log( 2)^2 + 5)))/(16384*log(2)^16) - 25019280) + x^6*((884736*log(2)^14 - 58982 4*log(2)^14*log(5) + 21233664*log(2)^16 + 98304*log(2)^14*log(5)^2)/(49152 *log(2)^16) - 432) - x*((40095*(21676032*log(2)^14 - 14450688*log(2)^14*lo g(5) + 148635648*log(2)^16 + 2408448*log(2)^14*log(5)^2))/(8192*log(2)^16) - (189*(69984*log(2)^2 - 1458*log(5) + 379080*log(2)^4 + 1215*log(5)^2 + 279936*log(2)^6 - 540*log(5)^3 + 135*log(5)^4 - 18*log(5)^5 + log(5)^6 ...
Time = 0.20 (sec) , antiderivative size = 4452, normalized size of antiderivative = 153.52 \[ \text {the integral} =\text {Too large to display} \] Input:
int(1/65536*(-344373768+(256*(20160*x^7-241920*x^6+1088640*x^5-2177280*x^4 +1632960*x^3)*log(2)^8+64*(362880*x^6-1632960*x^5-4898880*x^4+34292160*x^3 -44089920*x^2)*log(2)^6+16*(21555072*x^4-96997824*x^3+290993472*x)*log(2)^ 4+4*(360277632*x^2-900694080*x-540416448)*log(2)^2+1801388160)*log(5)^7+(6 4*(3360*x^6-15120*x^5-45360*x^4+317520*x^3-408240*x^2)*log(2)^6+16*(665280 *x^4-2993760*x^3+8981280*x)*log(2)^4+4*(23351328*x^2-58378320*x-35026992)* log(2)^2+200154240)*log(5)^9+(256*(-840*x^7+10080*x^6-45360*x^5+90720*x^4- 68040*x^3)*log(2)^8+64*(-45360*x^6+204120*x^5+612360*x^4-4286520*x^3+55112 40*x^2)*log(2)^6+16*(-4490640*x^4+20207880*x^3-60623640*x)*log(2)^4+4*(-10 5080976*x^2+262702440*x+157621464)*log(2)^2-675520560)*log(5)^8+(1024*(112 *x^10-2520*x^9+22680*x^8-105840*x^7+272160*x^6-367416*x^5+204120*x^4)*log( 2)^10+256*(-211680*x^7+2540160*x^6-11430720*x^5+22861440*x^4-17146080*x^3) *log(2)^8+64*(-1905120*x^6+8573040*x^5+25719120*x^4-180033840*x^3+23147208 0*x^2)*log(2)^6+16*(-75442752*x^4+339492384*x^3-1018477152*x)*log(2)^4+4*( -945728784*x^2+2364321960*x+1418593176)*log(2)^2-3782915136)*log(5)^6+(102 4*(-2016*x^10+45360*x^9-408240*x^8+1905120*x^7-4898880*x^6+6613488*x^5-367 4160*x^4)*log(2)^10+256*(1270080*x^7-15240960*x^6+68584320*x^5-137168640*x ^4+102876480*x^3)*log(2)^8+64*(6858432*x^6-30862944*x^5-92588832*x^4+64812 1824*x^3-833299488*x^2)*log(2)^6+16*(193995648*x^4-872980416*x^3+261894124 8*x)*log(2)^4+4*(1891457568*x^2-4728643920*x-2837186352)*log(2)^2+61902247 68)*log(5)^5+(4*(-48*x^2+120*x+72)*log(2)^2-8640)*log(5)^14+(4*(2016*x^2-5 040*x-3024)*log(2)^2+120960)*log(5)^13+(16*(-112*x^4+504*x^3-1512*x)*log(2 )^4+4*(-39312*x^2+98280*x+58968)*log(2)^2-1179360)*log(5)^12+(16*(4032*x^4 -18144*x^3+54432*x)*log(2)^4+4*(471744*x^2-1179360*x-707616)*log(2)^2+8491 392)*log(5)^11+(16384*(-288*x^14+7056*x^13-75600*x^12+462672*x^11-1769040* x^10+4327344*x^9-6613488*x^8+5773680*x^7-2204496*x^6)*log(2)^14+4096*(-120 96*x^12+272160*x^11-2612736*x^10+13880160*x^9-44089920*x^8+83770848*x^7-88 179840*x^6+39680928*x^5)*log(2)^12+1024*(-163296*x^10+3674160*x^9-33067440 *x^8+154314720*x^7-396809280*x^6+535692528*x^5-297606960*x^4)*log(2)^10+25 6*(14696640*x^7-176359680*x^6+793618560*x^5-1587237120*x^4+1190427840*x^3) *log(2)^8+64*(22044960*x^6-99202320*x^5-297606960*x^4+2083248720*x^3-26784 62640*x^2)*log(2)^6+16*(238085568*x^4-1071385056*x^3+3214155168*x)*log(2)^ 4+4*(1071385056*x^2-2678462640*x-1607077584)*log(2)^2+1836660096)*log(5)-8 *log(5)^16+384*log(5)^15+65536*(8*x^16-216*x^15+2592*x^14-18144*x^13+81648 *x^12-244944*x^11+489888*x^10-629857*x^9+472419*x^8-157788*x^7+2268*x^6-10 206*x^5+30618*x^4-61236*x^3+78732*x^2-59049*x+19683)*log(2)^16+16384*(432* x^14-10584*x^13+113400*x^12-694008*x^11+2653560*x^10-6491016*x^9+9920232*x ^8-8660520*x^7+3306744*x^6)*log(2)^14+4096*(9072*x^12-204120*x^11+1959552* x^10-10410120*x^9+33067440*x^8-62828136*x^7+66134880*x^6-29760696*x^5)*log (2)^12+1024*(81648*x^10-1837080*x^9+16533720*x^8-77157360*x^7+198404640*x^ 6-267846264*x^5+148803480*x^4)*log(2)^10+256*(-5511240*x^7+66134880*x^6-29 7606960*x^5+595213920*x^4-446410440*x^3)*log(2)^8+64*(-6613488*x^6+2976069 6*x^5+89282088*x^4-624974616*x^3+803538792*x^2)*log(2)^6+16*(-59521392*x^4 +267846264*x^3-803538792*x)*log(2)^4+4*(-229582512*x^2+573956280*x+3443737 68)*log(2)^2+(64*(-112*x^6+504*x^5+1512*x^4-10584*x^3+13608*x^2)*log(2)^6+ 16*(-66528*x^4+299376*x^3-898128*x)*log(2)^4+4*(-3891888*x^2+9729720*x+583 7832)*log(2)^2-46702656)*log(5)^10+(4096*(112*x^12-2520*x^11+24192*x^10-12 8520*x^9+408240*x^8-775656*x^7+816480*x^6-367416*x^5)*log(2)^12+1024*(1512 0*x^10-340200*x^9+3061800*x^8-14288400*x^7+36741600*x^6-49601160*x^5+27556 200*x^4)*log(2)^10+256*(-4762800*x^7+57153600*x^6-257191200*x^5+514382400* x^4-385786800*x^3)*log(2)^8+64*(-17146080*x^6+77157360*x^5+231472080*x^4-1 620304560*x^3+2083248720*x^2)*log(2)^6+16*(-363741840*x^4+1636838280*x^3-4 910514840*x)*log(2)^4+4*(-2837186352*x^2+7092965880*x+4255779528)*log(2)^2 -7737780960)*log(5)^4+(4096*(-1344*x^12+30240*x^11-290304*x^10+1542240*x^9 -4898880*x^8+9307872*x^7-9797760*x^6+4408992*x^5)*log(2)^12+1024*(-60480*x ^10+1360800*x^9-12247200*x^8+57153600*x^7-146966400*x^6+198404640*x^5-1102 24800*x^4)*log(2)^10+256*(11430720*x^7-137168640*x^6+617258880*x^5-1234517 760*x^4+925888320*x^3)*log(2)^8+64*(29393280*x^6-132269760*x^5-396809280*x ^4+2777664960*x^3-3571283520*x^2)*log(2)^6+16*(484989120*x^4-2182451040*x^ 3+6547353120*x)*log(2)^4+4*(3095112384*x^2-7737780960*x-4642668576)*log(2) ^2+7142567040)*log(5)^3+(16384*(48*x^14-1176*x^13+12600*x^12-77112*x^11+29 4840*x^10-721224*x^9+1102248*x^8-962280*x^7+367416*x^6)*log(2)^14+4096*(60 48*x^12-136080*x^11+1306368*x^10-6940080*x^9+22044960*x^8-41885424*x^7+440 89920*x^6-19840464*x^5)*log(2)^12+1024*(136080*x^10-3061800*x^9+27556200*x ^8-128595600*x^7+330674400*x^6-446410440*x^5+248005800*x^4)*log(2)^10+256* (-17146080*x^7+205752960*x^6-925888320*x^5+1851776640*x^4-1388832480*x^3)* log(2)^8+64*(-33067440*x^6+148803480*x^5+446410440*x^4-3124873080*x^3+4017 693960*x^2)*log(2)^6+16*(-436490208*x^4+1964205936*x^3-5892617808*x)*log(2 )^4+4*(-2321334288*x^2+5803335720*x+3482001432)*log(2)^2-4591650240)*log(5 )^2)/(x^9-27*x^8+324*x^7-2268*x^6+10206*x^5-30618*x^4+61236*x^3-78732*x^2+ 59049*x-19683)/log(2)^16,x)
Output:
(log(5)**16 - 48*log(5)**15 + 32*log(5)**14*log(2)**2*x**2 - 96*log(5)**14 *log(2)**2*x + 1080*log(5)**14 - 1344*log(5)**13*log(2)**2*x**2 + 4032*log (5)**13*log(2)**2*x - 15120*log(5)**13 + 448*log(5)**12*log(2)**4*x**4 - 2 688*log(5)**12*log(2)**4*x**3 + 4032*log(5)**12*log(2)**4*x**2 + 26208*log (5)**12*log(2)**2*x**2 - 78624*log(5)**12*log(2)**2*x + 147420*log(5)**12 - 16128*log(5)**11*log(2)**4*x**4 + 96768*log(5)**11*log(2)**4*x**3 - 1451 52*log(5)**11*log(2)**4*x**2 - 314496*log(5)**11*log(2)**2*x**2 + 943488*l og(5)**11*log(2)**2*x - 1061424*log(5)**11 + 3584*log(5)**10*log(2)**6*x** 6 - 32256*log(5)**10*log(2)**6*x**5 + 96768*log(5)**10*log(2)**6*x**4 - 96 768*log(5)**10*log(2)**6*x**3 + 266112*log(5)**10*log(2)**4*x**4 - 1596672 *log(5)**10*log(2)**4*x**3 + 2395008*log(5)**10*log(2)**4*x**2 + 2594592*l og(5)**10*log(2)**2*x**2 - 7783776*log(5)**10*log(2)**2*x + 5837832*log(5) **10 - 107520*log(5)**9*log(2)**6*x**6 + 967680*log(5)**9*log(2)**6*x**5 - 2903040*log(5)**9*log(2)**6*x**4 + 2903040*log(5)**9*log(2)**6*x**3 - 266 1120*log(5)**9*log(2)**4*x**4 + 15966720*log(5)**9*log(2)**4*x**3 - 239500 80*log(5)**9*log(2)**4*x**2 - 15567552*log(5)**9*log(2)**2*x**2 + 46702656 *log(5)**9*log(2)**2*x - 25019280*log(5)**9 + 8960*log(5)**8*log(2)**8*x** 8 - 1290240*log(5)**8*log(2)**8*x**6 + 11612160*log(5)**8*log(2)**8*x**5 - 49351680*log(5)**8*log(2)**8*x**4 + 121927680*log(5)**8*log(2)**8*x**3 - 182891520*log(5)**8*log(2)**8*x**2 + 156764160*log(5)**8*log(2)**8*x - ...