Integrand size = 717, antiderivative size = 26 \[ \text {the integral} =\left (3+\frac {\left (-1+x-\frac {64 \log ^2(2)}{(4+2 x)^2}\right )^2}{x}\right )^4 \] Output:
((x-16*ln(2)^2/(2+x)^2-1)^2/x+3)^4
Leaf count is larger than twice the leaf count of optimal. \(711\) vs. \(2(26)=52\).
Time = 0.55 (sec) , antiderivative size = 711, normalized size of antiderivative = 27.35 \[ \text {the integral} =\text {Too large to display} \] Input:
Integrate[(-524288 - 6029312*x - 33816576*x^2 - 122421248*x^3 - 318636032* x^4 - 627376128*x^5 - 953286656*x^6 - 1107525632*x^7 - 919941120*x^8 - 385 378304*x^9 + 294787072*x^10 + 834330624*x^11 + 1048039936*x^12 + 944780032 *x^13 + 671757312*x^14 + 389319040*x^15 + 186202360*x^16 + 73676772*x^17 + 24022348*x^18 + 6392524*x^19 + 1366512*x^20 + 229024*x^21 + 28984*x^22 + 2604*x^23 + 148*x^24 + 4*x^25 + (-16777216 - 155189248*x - 692060160*x^2 - 1974468608*x^3 - 4028628992*x^4 - 6230900736*x^5 - 7583563776*x^6 - 75074 76480*x^7 - 6314655744*x^8 - 4819566592*x^9 - 3588702208*x^10 - 2665648128 *x^11 - 1876140032*x^12 - 1163537408*x^13 - 604044288*x^14 - 254886144*x^1 5 - 85735680*x^16 - 22563072*x^17 - 4534144*x^18 - 670720*x^19 - 68736*x^2 0 - 4352*x^21 - 128*x^22)*Log[2]^2 + (-234881024 - 1719664640*x - 59265515 52*x^2 - 12821987328*x^3 - 19465764864*x^4 - 21851799552*x^5 - 18554290176 *x^6 - 11922309120*x^7 - 5668208640*x^8 - 1961197568*x^9 - 692240384*x^10 - 598818816*x^11 - 628064256*x^12 - 463816704*x^13 - 235607040*x^14 - 8357 6832*x^15 - 20511744*x^16 - 3336192*x^17 - 324608*x^18 - 14336*x^19)*Log[2 ]^4 + (-1879048192 - 10737418240*x - 27279753216*x^2 - 41842376704*x^3 - 4 3780145152*x^4 - 32967229440*x^5 - 18098421760*x^6 - 6245318656*x^7 + 1830 813696*x^8 + 6824132608*x^9 + 7933394944*x^10 + 5707530240*x^11 + 27314421 76*x^12 + 872218624*x^13 + 179208192*x^14 + 21495808*x^15 + 1146880*x^16)* Log[2]^6 + (-9395240960 - 41607495680*x - 71068286976*x^2 - 66504884224*x^ 3 - 41641050112*x^4 - 17817403392*x^5 - 6165626880*x^6 - 12507414528*x^7 - 22866296832*x^8 - 20920139776*x^9 - 10779099136*x^10 - 3228303360*x^11 - 528220160*x^12 - 36700160*x^13)*Log[2]^8 + (-30064771072 - 104152956928*x - 96636764160*x^2 - 23353884672*x^3 - 13690208256*x^4 - 11475615744*x^5 + 31809601536*x^6 + 48570040320*x^7 + 26575110144*x^8 + 6660554752*x^9 + 645 922816*x^10)*Log[2]^10 + (-60129542144 - 169651208192*x - 41875931136*x^2 + 84825604096*x^3 - 18253611008*x^4 - 87375740928*x^5 - 43419435008*x^6 - 6576668672*x^7)*Log[2]^12 + (-68719476736 - 171798691840*x + 25769803776*x ^2 + 120259084288*x^3 + 36507222016*x^4)*Log[2]^14 + (-34359738368 - 85899 345920*x)*Log[2]^16)/(131072*x^5 + 1114112*x^6 + 4456448*x^7 + 11141120*x^ 8 + 19496960*x^9 + 25346048*x^10 + 25346048*x^11 + 19914752*x^12 + 1244672 0*x^13 + 6223360*x^14 + 2489344*x^15 + 792064*x^16 + 198016*x^17 + 38080*x ^18 + 5440*x^19 + 544*x^20 + 34*x^21 + x^22),x]
Output:
4*((5*x^2)/2 + x^3 + x^4/4 + (67108864*Log[2]^16)/(2 + x)^16 + (134217728* Log[2]^16)/(2 + x)^15 + (167772160*Log[2]^14*(1 + Log[2]^2))/(2 + x)^13 + (1 + 4*Log[2]^2)^8/(4*x^4) + (33554432*Log[2]^14*(3 + 5*Log[2]^2))/(2 + x) ^14 - 4*x*(-1 + 8*Log[2]^2) - ((1 + 4*Log[2]^2)^6*(-1 + 16*Log[2]^2 + 32*L og[2]^4))/x^3 + (1048576*Log[2]^12*(75 + 160*Log[2]^2 + 112*Log[2]^4))/(2 + x)^11 + (1048576*Log[2]^12*(57 + 176*Log[2]^2 + 140*Log[2]^4))/(2 + x)^1 2 + (262144*Log[2]^10*(63 + 236*Log[2]^2 + 392*Log[2]^4 + 240*Log[2]^6))/( 2 + x)^9 + (131072*Log[2]^10*(135 + 572*Log[2]^2 + 1040*Log[2]^4 + 672*Log [2]^6))/(2 + x)^10 + (16384*Log[2]^8*(81 + 628*Log[2]^2 + 2044*Log[2]^4 + 3072*Log[2]^6 + 1760*Log[2]^8))/(2 + x)^7 + ((1 + 4*Log[2]^2)^4*(5 - 52*Lo g[2]^2 + 912*Log[2]^4 + 4160*Log[2]^6 + 4352*Log[2]^8))/(2*x^2) + (2048*Lo g[2]^8*(1323 + 6624*Log[2]^2 + 22880*Log[2]^4 + 35840*Log[2]^6 + 21120*Log [2]^8))/(2 + x)^8 + (512*Log[2]^6*(-27 + 1506*Log[2]^2 + 9920*Log[2]^4 + 2 9696*Log[2]^6 + 42240*Log[2]^8 + 23296*Log[2]^10))/(2 + x)^5 + (512*Log[2] ^6*(405 + 2034*Log[2]^2 + 14416*Log[2]^4 + 44800*Log[2]^6 + 65280*Log[2]^8 + 36608*Log[2]^10))/(2 + x)^6 - (4*(1 + 4*Log[2]^2)^2*(-1 + 10*Log[2]^2 + 44*Log[2]^4 + 2792*Log[2]^6 + 17056*Log[2]^8 + 36224*Log[2]^10 + 26112*Lo g[2]^12))/x + (16*Log[2]^4*(-351 + 1632*Log[2]^2 + 23312*Log[2]^4 + 137216 *Log[2]^6 + 387840*Log[2]^8 + 532480*Log[2]^10 + 286720*Log[2]^12))/(2 + x )^3 + (16*Log[2]^4*(513 + 2160*Log[2]^2 + 34120*Log[2]^4 + 211456*Log[2...
Leaf count is larger than twice the leaf count of optimal. \(700\) vs. \(2(26)=52\).
Time = 4.96 (sec) , antiderivative size = 700, normalized size of antiderivative = 26.92, number of steps used = 4, number of rules used = 4, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.006, Rules used = {2026, 2007, 2123, 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 {4 x^{25}+148 x^{24}+2604 x^{23}+28984 x^{22}+229024 x^{21}+1366512 x^{20}+6392524 x^{19}+24022348 x^{18}+73676772 x^{17}+186202360 x^{16}+389319040 x^{15}+671757312 x^{14}+944780032 x^{13}+1048039936 x^{12}+834330624 x^{11}+294787072 x^{10}-385378304 x^9-919941120 x^8-1107525632 x^7-953286656 x^6-627376128 x^5-318636032 x^4-122421248 x^3-33816576 x^2+\left (36507222016 x^4+120259084288 x^3+25769803776 x^2-171798691840 x-68719476736\right ) \log ^{14}(2)+\left (-6576668672 x^7-43419435008 x^6-87375740928 x^5-18253611008 x^4+84825604096 x^3-41875931136 x^2-169651208192 x-60129542144\right ) \log ^{12}(2)+\left (645922816 x^{10}+6660554752 x^9+26575110144 x^8+48570040320 x^7+31809601536 x^6-11475615744 x^5-13690208256 x^4-23353884672 x^3-96636764160 x^2-104152956928 x-30064771072\right ) \log ^{10}(2)-6029312 x+(-85899345920 x-34359738368) \log ^{16}(2)+\left (-36700160 x^{13}-528220160 x^{12}-3228303360 x^{11}-10779099136 x^{10}-20920139776 x^9-22866296832 x^8-12507414528 x^7-6165626880 x^6-17817403392 x^5-41641050112 x^4-66504884224 x^3-71068286976 x^2-41607495680 x-9395240960\right ) \log ^8(2)+\left (1146880 x^{16}+21495808 x^{15}+179208192 x^{14}+872218624 x^{13}+2731442176 x^{12}+5707530240 x^{11}+7933394944 x^{10}+6824132608 x^9+1830813696 x^8-6245318656 x^7-18098421760 x^6-32967229440 x^5-43780145152 x^4-41842376704 x^3-27279753216 x^2-10737418240 x-1879048192\right ) \log ^6(2)+\left (-14336 x^{19}-324608 x^{18}-3336192 x^{17}-20511744 x^{16}-83576832 x^{15}-235607040 x^{14}-463816704 x^{13}-628064256 x^{12}-598818816 x^{11}-692240384 x^{10}-1961197568 x^9-5668208640 x^8-11922309120 x^7-18554290176 x^6-21851799552 x^5-19465764864 x^4-12821987328 x^3-5926551552 x^2-1719664640 x-234881024\right ) \log ^4(2)+\left (-128 x^{22}-4352 x^{21}-68736 x^{20}-670720 x^{19}-4534144 x^{18}-22563072 x^{17}-85735680 x^{16}-254886144 x^{15}-604044288 x^{14}-1163537408 x^{13}-1876140032 x^{12}-2665648128 x^{11}-3588702208 x^{10}-4819566592 x^9-6314655744 x^8-7507476480 x^7-7583563776 x^6-6230900736 x^5-4028628992 x^4-1974468608 x^3-692060160 x^2-155189248 x-16777216\right ) \log ^2(2)-524288}{x^{22}+34 x^{21}+544 x^{20}+5440 x^{19}+38080 x^{18}+198016 x^{17}+792064 x^{16}+2489344 x^{15}+6223360 x^{14}+12446720 x^{13}+19914752 x^{12}+25346048 x^{11}+25346048 x^{10}+19496960 x^9+11141120 x^8+4456448 x^7+1114112 x^6+131072 x^5} \, dx\) |
| \(\Big \downarrow \) 2026 |
| \(\displaystyle \int \frac {4 x^{25}+148 x^{24}+2604 x^{23}+28984 x^{22}+229024 x^{21}+1366512 x^{20}+6392524 x^{19}+24022348 x^{18}+73676772 x^{17}+186202360 x^{16}+389319040 x^{15}+671757312 x^{14}+944780032 x^{13}+1048039936 x^{12}+834330624 x^{11}+294787072 x^{10}-385378304 x^9-919941120 x^8-1107525632 x^7-953286656 x^6-627376128 x^5-318636032 x^4-122421248 x^3-33816576 x^2+\left (36507222016 x^4+120259084288 x^3+25769803776 x^2-171798691840 x-68719476736\right ) \log ^{14}(2)+\left (-6576668672 x^7-43419435008 x^6-87375740928 x^5-18253611008 x^4+84825604096 x^3-41875931136 x^2-169651208192 x-60129542144\right ) \log ^{12}(2)+\left (645922816 x^{10}+6660554752 x^9+26575110144 x^8+48570040320 x^7+31809601536 x^6-11475615744 x^5-13690208256 x^4-23353884672 x^3-96636764160 x^2-104152956928 x-30064771072\right ) \log ^{10}(2)-6029312 x+(-85899345920 x-34359738368) \log ^{16}(2)+\left (-36700160 x^{13}-528220160 x^{12}-3228303360 x^{11}-10779099136 x^{10}-20920139776 x^9-22866296832 x^8-12507414528 x^7-6165626880 x^6-17817403392 x^5-41641050112 x^4-66504884224 x^3-71068286976 x^2-41607495680 x-9395240960\right ) \log ^8(2)+\left (1146880 x^{16}+21495808 x^{15}+179208192 x^{14}+872218624 x^{13}+2731442176 x^{12}+5707530240 x^{11}+7933394944 x^{10}+6824132608 x^9+1830813696 x^8-6245318656 x^7-18098421760 x^6-32967229440 x^5-43780145152 x^4-41842376704 x^3-27279753216 x^2-10737418240 x-1879048192\right ) \log ^6(2)+\left (-14336 x^{19}-324608 x^{18}-3336192 x^{17}-20511744 x^{16}-83576832 x^{15}-235607040 x^{14}-463816704 x^{13}-628064256 x^{12}-598818816 x^{11}-692240384 x^{10}-1961197568 x^9-5668208640 x^8-11922309120 x^7-18554290176 x^6-21851799552 x^5-19465764864 x^4-12821987328 x^3-5926551552 x^2-1719664640 x-234881024\right ) \log ^4(2)+\left (-128 x^{22}-4352 x^{21}-68736 x^{20}-670720 x^{19}-4534144 x^{18}-22563072 x^{17}-85735680 x^{16}-254886144 x^{15}-604044288 x^{14}-1163537408 x^{13}-1876140032 x^{12}-2665648128 x^{11}-3588702208 x^{10}-4819566592 x^9-6314655744 x^8-7507476480 x^7-7583563776 x^6-6230900736 x^5-4028628992 x^4-1974468608 x^3-692060160 x^2-155189248 x-16777216\right ) \log ^2(2)-524288}{x^5 \left (x^{17}+34 x^{16}+544 x^{15}+5440 x^{14}+38080 x^{13}+198016 x^{12}+792064 x^{11}+2489344 x^{10}+6223360 x^9+12446720 x^8+19914752 x^7+25346048 x^6+25346048 x^5+19496960 x^4+11141120 x^3+4456448 x^2+1114112 x+131072\right )}dx\) |
| \(\Big \downarrow \) 2007 |
| \(\displaystyle \int \frac {4 x^{25}+148 x^{24}+2604 x^{23}+28984 x^{22}+229024 x^{21}+1366512 x^{20}+6392524 x^{19}+24022348 x^{18}+73676772 x^{17}+186202360 x^{16}+389319040 x^{15}+671757312 x^{14}+944780032 x^{13}+1048039936 x^{12}+834330624 x^{11}+294787072 x^{10}-385378304 x^9-919941120 x^8-1107525632 x^7-953286656 x^6-627376128 x^5-318636032 x^4-122421248 x^3-33816576 x^2+\left (36507222016 x^4+120259084288 x^3+25769803776 x^2-171798691840 x-68719476736\right ) \log ^{14}(2)+\left (-6576668672 x^7-43419435008 x^6-87375740928 x^5-18253611008 x^4+84825604096 x^3-41875931136 x^2-169651208192 x-60129542144\right ) \log ^{12}(2)+\left (645922816 x^{10}+6660554752 x^9+26575110144 x^8+48570040320 x^7+31809601536 x^6-11475615744 x^5-13690208256 x^4-23353884672 x^3-96636764160 x^2-104152956928 x-30064771072\right ) \log ^{10}(2)-6029312 x+(-85899345920 x-34359738368) \log ^{16}(2)+\left (-36700160 x^{13}-528220160 x^{12}-3228303360 x^{11}-10779099136 x^{10}-20920139776 x^9-22866296832 x^8-12507414528 x^7-6165626880 x^6-17817403392 x^5-41641050112 x^4-66504884224 x^3-71068286976 x^2-41607495680 x-9395240960\right ) \log ^8(2)+\left (1146880 x^{16}+21495808 x^{15}+179208192 x^{14}+872218624 x^{13}+2731442176 x^{12}+5707530240 x^{11}+7933394944 x^{10}+6824132608 x^9+1830813696 x^8-6245318656 x^7-18098421760 x^6-32967229440 x^5-43780145152 x^4-41842376704 x^3-27279753216 x^2-10737418240 x-1879048192\right ) \log ^6(2)+\left (-14336 x^{19}-324608 x^{18}-3336192 x^{17}-20511744 x^{16}-83576832 x^{15}-235607040 x^{14}-463816704 x^{13}-628064256 x^{12}-598818816 x^{11}-692240384 x^{10}-1961197568 x^9-5668208640 x^8-11922309120 x^7-18554290176 x^6-21851799552 x^5-19465764864 x^4-12821987328 x^3-5926551552 x^2-1719664640 x-234881024\right ) \log ^4(2)+\left (-128 x^{22}-4352 x^{21}-68736 x^{20}-670720 x^{19}-4534144 x^{18}-22563072 x^{17}-85735680 x^{16}-254886144 x^{15}-604044288 x^{14}-1163537408 x^{13}-1876140032 x^{12}-2665648128 x^{11}-3588702208 x^{10}-4819566592 x^9-6314655744 x^8-7507476480 x^7-7583563776 x^6-6230900736 x^5-4028628992 x^4-1974468608 x^3-692060160 x^2-155189248 x-16777216\right ) \log ^2(2)-524288}{x^5 (x+2)^{17}}dx\) |
| \(\Big \downarrow \) 2123 |
| \(\displaystyle \int \left (-\frac {4 \left (1+4 \log ^2(2)\right )^8}{x^5}+\frac {12 \left (1+4 \log ^2(2)\right )^6 \left (-1+32 \log ^4(2)+16 \log ^2(2)\right )}{x^4}+4 x^3-\frac {4 \left (1+4 \log ^2(2)\right )^4 \left (5+4352 \log ^8(2)+4160 \log ^6(2)+912 \log ^4(2)-52 \log ^2(2)\right )}{x^3}+12 x^2+\frac {16 \left (1+4 \log ^2(2)\right )^2 \left (-1+26112 \log ^{12}(2)+36224 \log ^{10}(2)+17056 \log ^8(2)+2792 \log ^6(2)+44 \log ^4(2)+10 \log ^2(2)\right )}{x^2}+20 x-\frac {8053063680 \log ^{16}(2)}{(x+2)^{16}}-\frac {4294967296 \log ^{16}(2)}{(x+2)^{17}}-\frac {8724152320 \left (\log ^{16}(2)+\log ^{14}(2)\right )}{(x+2)^{14}}-\frac {1879048192 \log ^{14}(2) \left (3+5 \log ^2(2)\right )}{(x+2)^{15}}-\frac {50331648 \log ^{12}(2) \left (57+140 \log ^4(2)+176 \log ^2(2)\right )}{(x+2)^{13}}-\frac {46137344 \log ^{12}(2) \left (75+112 \log ^4(2)+160 \log ^2(2)\right )}{(x+2)^{12}}-\frac {5242880 \log ^{10}(2) \left (135+672 \log ^6(2)+1040 \log ^4(2)+572 \log ^2(2)\right )}{(x+2)^{11}}-\frac {9437184 \log ^{10}(2) \left (63+240 \log ^6(2)+392 \log ^4(2)+236 \log ^2(2)\right )}{(x+2)^{10}}-\frac {65536 \log ^8(2) \left (1323+21120 \log ^8(2)+35840 \log ^6(2)+22880 \log ^4(2)+6624 \log ^2(2)\right )}{(x+2)^9}-\frac {458752 \log ^8(2) \left (81+1760 \log ^8(2)+3072 \log ^6(2)+2044 \log ^4(2)+628 \log ^2(2)\right )}{(x+2)^8}-\frac {12288 \log ^6(2) \left (405+36608 \log ^{10}(2)+65280 \log ^8(2)+44800 \log ^6(2)+14416 \log ^4(2)+2034 \log ^2(2)\right )}{(x+2)^7}-\frac {10240 \log ^6(2) \left (-27+23296 \log ^{10}(2)+42240 \log ^8(2)+29696 \log ^6(2)+9920 \log ^4(2)+1506 \log ^2(2)\right )}{(x+2)^6}-\frac {256 \log ^4(2) \left (513+465920 \log ^{12}(2)+856064 \log ^{10}(2)+613632 \log ^8(2)+211456 \log ^6(2)+34120 \log ^4(2)+2160 \log ^2(2)\right )}{(x+2)^5}-\frac {192 \log ^4(2) \left (-351+286720 \log ^{12}(2)+532480 \log ^{10}(2)+387840 \log ^8(2)+137216 \log ^6(2)+23312 \log ^4(2)+1632 \log ^2(2)\right )}{(x+2)^4}-\frac {16 \log ^2(2) \left (81+1392640 \log ^{14}(2)+2609152 \log ^{12}(2)+1926144 \log ^{10}(2)+697088 \log ^8(2)+123776 \log ^6(2)+9456 \log ^4(2)+1188 \log ^2(2)\right )}{(x+2)^3}-\frac {32 \log ^2(2) \left (-27+208896 \log ^{14}(2)+394240 \log ^{12}(2)+294400 \log ^{10}(2)+108672 \log ^8(2)+20048 \log ^6(2)+1652 \log ^4(2)+54 \log ^2(2)\right )}{(x+2)^2}-16 \left (8 \log ^2(2)-1\right )\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle x^4+\frac {\left (1+4 \log ^2(2)\right )^8}{x^4}+4 x^3+\frac {4 \left (1+4 \log ^2(2)\right )^6 \left (1-32 \log ^4(2)-16 \log ^2(2)\right )}{x^3}+10 x^2+\frac {2 \left (1+4 \log ^2(2)\right )^4 \left (5+4352 \log ^8(2)+4160 \log ^6(2)+912 \log ^4(2)-52 \log ^2(2)\right )}{x^2}+\frac {536870912 \log ^{16}(2)}{(x+2)^{15}}+\frac {268435456 \log ^{16}(2)}{(x+2)^{16}}+16 x \left (1-8 \log ^2(2)\right )+\frac {134217728 \log ^{14}(2) \left (3+5 \log ^2(2)\right )}{(x+2)^{14}}+\frac {671088640 \log ^{14}(2) \left (1+\log ^2(2)\right )}{(x+2)^{13}}+\frac {4194304 \log ^{12}(2) \left (57+140 \log ^4(2)+176 \log ^2(2)\right )}{(x+2)^{12}}+\frac {4194304 \log ^{12}(2) \left (75+112 \log ^4(2)+160 \log ^2(2)\right )}{(x+2)^{11}}+\frac {524288 \log ^{10}(2) \left (135+672 \log ^6(2)+1040 \log ^4(2)+572 \log ^2(2)\right )}{(x+2)^{10}}+\frac {1048576 \log ^{10}(2) \left (63+240 \log ^6(2)+392 \log ^4(2)+236 \log ^2(2)\right )}{(x+2)^9}+\frac {8192 \log ^8(2) \left (1323+21120 \log ^8(2)+35840 \log ^6(2)+22880 \log ^4(2)+6624 \log ^2(2)\right )}{(x+2)^8}+\frac {65536 \log ^8(2) \left (81+1760 \log ^8(2)+3072 \log ^6(2)+2044 \log ^4(2)+628 \log ^2(2)\right )}{(x+2)^7}+\frac {2048 \log ^6(2) \left (405+36608 \log ^{10}(2)+65280 \log ^8(2)+44800 \log ^6(2)+14416 \log ^4(2)+2034 \log ^2(2)\right )}{(x+2)^6}-\frac {2048 \log ^6(2) \left (27-23296 \log ^{10}(2)-42240 \log ^8(2)-29696 \log ^6(2)-9920 \log ^4(2)-1506 \log ^2(2)\right )}{(x+2)^5}+\frac {64 \log ^4(2) \left (513+465920 \log ^{12}(2)+856064 \log ^{10}(2)+613632 \log ^8(2)+211456 \log ^6(2)+34120 \log ^4(2)+2160 \log ^2(2)\right )}{(x+2)^4}-\frac {64 \log ^4(2) \left (351-286720 \log ^{12}(2)-532480 \log ^{10}(2)-387840 \log ^8(2)-137216 \log ^6(2)-23312 \log ^4(2)-1632 \log ^2(2)\right )}{(x+2)^3}+\frac {16 \left (1+4 \log ^2(2)\right )^2 \left (1-26112 \log ^{12}(2)-36224 \log ^{10}(2)-17056 \log ^8(2)-2792 \log ^6(2)-44 \log ^4(2)-10 \log ^2(2)\right )}{x}+\frac {8 \log ^2(2) \left (81+1392640 \log ^{14}(2)+2609152 \log ^{12}(2)+1926144 \log ^{10}(2)+697088 \log ^8(2)+123776 \log ^6(2)+9456 \log ^4(2)+1188 \log ^2(2)\right )}{(x+2)^2}-\frac {32 \log ^2(2) \left (27-208896 \log ^{14}(2)-394240 \log ^{12}(2)-294400 \log ^{10}(2)-108672 \log ^8(2)-20048 \log ^6(2)-1652 \log ^4(2)-54 \log ^2(2)\right )}{x+2}\) |
Input:
Int[(-524288 - 6029312*x - 33816576*x^2 - 122421248*x^3 - 318636032*x^4 - 627376128*x^5 - 953286656*x^6 - 1107525632*x^7 - 919941120*x^8 - 385378304 *x^9 + 294787072*x^10 + 834330624*x^11 + 1048039936*x^12 + 944780032*x^13 + 671757312*x^14 + 389319040*x^15 + 186202360*x^16 + 73676772*x^17 + 24022 348*x^18 + 6392524*x^19 + 1366512*x^20 + 229024*x^21 + 28984*x^22 + 2604*x ^23 + 148*x^24 + 4*x^25 + (-16777216 - 155189248*x - 692060160*x^2 - 19744 68608*x^3 - 4028628992*x^4 - 6230900736*x^5 - 7583563776*x^6 - 7507476480* x^7 - 6314655744*x^8 - 4819566592*x^9 - 3588702208*x^10 - 2665648128*x^11 - 1876140032*x^12 - 1163537408*x^13 - 604044288*x^14 - 254886144*x^15 - 85 735680*x^16 - 22563072*x^17 - 4534144*x^18 - 670720*x^19 - 68736*x^20 - 43 52*x^21 - 128*x^22)*Log[2]^2 + (-234881024 - 1719664640*x - 5926551552*x^2 - 12821987328*x^3 - 19465764864*x^4 - 21851799552*x^5 - 18554290176*x^6 - 11922309120*x^7 - 5668208640*x^8 - 1961197568*x^9 - 692240384*x^10 - 5988 18816*x^11 - 628064256*x^12 - 463816704*x^13 - 235607040*x^14 - 83576832*x ^15 - 20511744*x^16 - 3336192*x^17 - 324608*x^18 - 14336*x^19)*Log[2]^4 + (-1879048192 - 10737418240*x - 27279753216*x^2 - 41842376704*x^3 - 4378014 5152*x^4 - 32967229440*x^5 - 18098421760*x^6 - 6245318656*x^7 + 1830813696 *x^8 + 6824132608*x^9 + 7933394944*x^10 + 5707530240*x^11 + 2731442176*x^1 2 + 872218624*x^13 + 179208192*x^14 + 21495808*x^15 + 1146880*x^16)*Log[2] ^6 + (-9395240960 - 41607495680*x - 71068286976*x^2 - 66504884224*x^3 - 41 641050112*x^4 - 17817403392*x^5 - 6165626880*x^6 - 12507414528*x^7 - 22866 296832*x^8 - 20920139776*x^9 - 10779099136*x^10 - 3228303360*x^11 - 528220 160*x^12 - 36700160*x^13)*Log[2]^8 + (-30064771072 - 104152956928*x - 9663 6764160*x^2 - 23353884672*x^3 - 13690208256*x^4 - 11475615744*x^5 + 318096 01536*x^6 + 48570040320*x^7 + 26575110144*x^8 + 6660554752*x^9 + 645922816 *x^10)*Log[2]^10 + (-60129542144 - 169651208192*x - 41875931136*x^2 + 8482 5604096*x^3 - 18253611008*x^4 - 87375740928*x^5 - 43419435008*x^6 - 657666 8672*x^7)*Log[2]^12 + (-68719476736 - 171798691840*x + 25769803776*x^2 + 1 20259084288*x^3 + 36507222016*x^4)*Log[2]^14 + (-34359738368 - 85899345920 *x)*Log[2]^16)/(131072*x^5 + 1114112*x^6 + 4456448*x^7 + 11141120*x^8 + 19 496960*x^9 + 25346048*x^10 + 25346048*x^11 + 19914752*x^12 + 12446720*x^13 + 6223360*x^14 + 2489344*x^15 + 792064*x^16 + 198016*x^17 + 38080*x^18 + 5440*x^19 + 544*x^20 + 34*x^21 + x^22),x]
Output:
10*x^2 + 4*x^3 + x^4 + (268435456*Log[2]^16)/(2 + x)^16 + (536870912*Log[2 ]^16)/(2 + x)^15 + 16*x*(1 - 8*Log[2]^2) + (671088640*Log[2]^14*(1 + Log[2 ]^2))/(2 + x)^13 + (1 + 4*Log[2]^2)^8/x^4 + (134217728*Log[2]^14*(3 + 5*Lo g[2]^2))/(2 + x)^14 + (4*(1 + 4*Log[2]^2)^6*(1 - 16*Log[2]^2 - 32*Log[2]^4 ))/x^3 + (4194304*Log[2]^12*(75 + 160*Log[2]^2 + 112*Log[2]^4))/(2 + x)^11 + (4194304*Log[2]^12*(57 + 176*Log[2]^2 + 140*Log[2]^4))/(2 + x)^12 + (10 48576*Log[2]^10*(63 + 236*Log[2]^2 + 392*Log[2]^4 + 240*Log[2]^6))/(2 + x) ^9 + (524288*Log[2]^10*(135 + 572*Log[2]^2 + 1040*Log[2]^4 + 672*Log[2]^6) )/(2 + x)^10 + (65536*Log[2]^8*(81 + 628*Log[2]^2 + 2044*Log[2]^4 + 3072*L og[2]^6 + 1760*Log[2]^8))/(2 + x)^7 + (2*(1 + 4*Log[2]^2)^4*(5 - 52*Log[2] ^2 + 912*Log[2]^4 + 4160*Log[2]^6 + 4352*Log[2]^8))/x^2 + (8192*Log[2]^8*( 1323 + 6624*Log[2]^2 + 22880*Log[2]^4 + 35840*Log[2]^6 + 21120*Log[2]^8))/ (2 + x)^8 - (2048*Log[2]^6*(27 - 1506*Log[2]^2 - 9920*Log[2]^4 - 29696*Log [2]^6 - 42240*Log[2]^8 - 23296*Log[2]^10))/(2 + x)^5 + (2048*Log[2]^6*(405 + 2034*Log[2]^2 + 14416*Log[2]^4 + 44800*Log[2]^6 + 65280*Log[2]^8 + 3660 8*Log[2]^10))/(2 + x)^6 - (64*Log[2]^4*(351 - 1632*Log[2]^2 - 23312*Log[2] ^4 - 137216*Log[2]^6 - 387840*Log[2]^8 - 532480*Log[2]^10 - 286720*Log[2]^ 12))/(2 + x)^3 + (16*(1 + 4*Log[2]^2)^2*(1 - 10*Log[2]^2 - 44*Log[2]^4 - 2 792*Log[2]^6 - 17056*Log[2]^8 - 36224*Log[2]^10 - 26112*Log[2]^12))/x + (6 4*Log[2]^4*(513 + 2160*Log[2]^2 + 34120*Log[2]^4 + 211456*Log[2]^6 + 61...
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[(Fx_.)*(Px_)^(p_.), x_Symbol] :> With[{r = Expon[Px, x, Min]}, Int[x^(p *r)*ExpandToSum[Px/x^r, x]^p*Fx, x] /; IGtQ[r, 0]] /; PolyQ[Px, x] && Integ erQ[p] && !MonomialQ[Px, x] && (ILtQ[p, 0] || !PolyQ[u, x])
Int[(Px_)*((a_.) + (b_.)*(x_))^(m_.)*((c_.) + (d_.)*(x_))^(n_.), x_Symbol] :> Int[ExpandIntegrand[Px*(a + b*x)^m*(c + d*x)^n, x], x] /; FreeQ[{a, b, c , d, m, n}, x] && PolyQ[Px, x] && (IntegersQ[m, n] || IGtQ[m, -2])
Leaf count of result is larger than twice the leaf count of optimal. \(682\) vs. \(2(24)=48\).
Time = 1.80 (sec) , antiderivative size = 683, normalized size of antiderivative = 26.27
| method | result | size |
| norman | \(\text {Expression too large to display}\) | \(683\) |
| risch | \(\text {Expression too large to display}\) | \(757\) |
| default | \(\text {Expression too large to display}\) | \(783\) |
| gosper | \(\text {Expression too large to display}\) | \(972\) |
| parallelrisch | \(\text {Expression too large to display}\) | \(972\) |
Input:
int((-524288-6029312*x+(645922816*x^10+6660554752*x^9+26575110144*x^8+4857 0040320*x^7+31809601536*x^6-11475615744*x^5-13690208256*x^4-23353884672*x^ 3-96636764160*x^2-104152956928*x-30064771072)*ln(2)^10+(-36700160*x^13-528 220160*x^12-3228303360*x^11-10779099136*x^10-20920139776*x^9-22866296832*x ^8-12507414528*x^7-6165626880*x^6-17817403392*x^5-41641050112*x^4-66504884 224*x^3-71068286976*x^2-41607495680*x-9395240960)*ln(2)^8+(1146880*x^16+21 495808*x^15+179208192*x^14+872218624*x^13+2731442176*x^12+5707530240*x^11+ 7933394944*x^10+6824132608*x^9+1830813696*x^8-6245318656*x^7-18098421760*x ^6-32967229440*x^5-43780145152*x^4-41842376704*x^3-27279753216*x^2-1073741 8240*x-1879048192)*ln(2)^6+(-14336*x^19-324608*x^18-3336192*x^17-20511744* x^16-83576832*x^15-235607040*x^14-463816704*x^13-628064256*x^12-598818816* x^11-692240384*x^10-1961197568*x^9-5668208640*x^8-11922309120*x^7-18554290 176*x^6-21851799552*x^5-19465764864*x^4-12821987328*x^3-5926551552*x^2-171 9664640*x-234881024)*ln(2)^4+(-128*x^22-4352*x^21-68736*x^20-670720*x^19-4 534144*x^18-22563072*x^17-85735680*x^16-254886144*x^15-604044288*x^14-1163 537408*x^13-1876140032*x^12-2665648128*x^11-3588702208*x^10-4819566592*x^9 -6314655744*x^8-7507476480*x^7-7583563776*x^6-6230900736*x^5-4028628992*x^ 4-1974468608*x^3-692060160*x^2-155189248*x-16777216)*ln(2)^2+(-85899345920 *x-34359738368)*ln(2)^16+(36507222016*x^4+120259084288*x^3+25769803776*x^2 -171798691840*x-68719476736)*ln(2)^14+(-6576668672*x^7-43419435008*x^6-873 75740928*x^5-18253611008*x^4+84825604096*x^3-41875931136*x^2-169651208192* x-60129542144)*ln(2)^12+4*x^25+148*x^24+2604*x^23+28984*x^22+229024*x^21+1 366512*x^20+6392524*x^19+24022348*x^18+73676772*x^17+186202360*x^16+389319 040*x^15+671757312*x^14+944780032*x^13+1048039936*x^12+834330624*x^11-9199 41120*x^8-385378304*x^9+294787072*x^10-1107525632*x^7-953286656*x^6-338165 76*x^2-122421248*x^3-318636032*x^4-627376128*x^5)/(x^22+34*x^21+544*x^20+5 440*x^19+38080*x^18+198016*x^17+792064*x^16+2489344*x^15+6223360*x^14+1244 6720*x^13+19914752*x^12+25346048*x^11+25346048*x^10+19496960*x^9+11141120* x^8+4456448*x^7+1114112*x^6+131072*x^5),x,method=_RETURNVERBOSE)
Output:
(65536+(1006632960*ln(2)^6+3019898880*ln(2)^8+188743680*ln(2)^4+18874368*l n(2)^2+786432+4831838208*ln(2)^10+3221225472*ln(2)^12)*x+234881024*ln(2)^6 +1174405120*ln(2)^8+x^24+36*x^23+618*x^22+29360128*ln(2)^4+2097152*ln(2)^2 +4294967296*ln(2)^16+(2038431744*ln(2)^6+3422552064*ln(2)^8+585105408*ln(2 )^4+83361792*ln(2)^2+4718592+1207959552*ln(2)^10-4831838208*ln(2)^12-64424 50944*ln(2)^14)*x^2+(2575302656*ln(2)^6+2449473536*ln(2)^8+1145044992*ln(2 )^4+236978176*ln(2)^2+18743296+805306368*ln(2)^10+1073741824*ln(2)^12-2147 483648*ln(2)^14)*x^3+(6736-128*ln(2)^2)*x^21+(-3377086464+2202009600*ln(2) ^6+1245708288*ln(2)^8+1568931840*ln(2)^4+729415680*ln(2)^2+301989888*ln(2) ^10+5838471168*ln(2)^12)*x^4+(-27330379776+1132462080*ln(2)^6+1056964608*l n(2)^8+1625554944*ln(2)^4+2719875072*ln(2)^2-3321888768*ln(2)^10+301989888 0*ln(2)^12)*x^5+(-277872640*ln(2)^6+2422210560*ln(2)^8+1457258496*ln(2)^4+ 8303640576*ln(2)^2-102727245824-4504682496*ln(2)^10+469762048*ln(2)^12)*x^ 6+(-1689255936*ln(2)^6+3567255552*ln(2)^8+1413218304*ln(2)^4+18123915264*l n(2)^2-239881494528-2415919104*ln(2)^10)*x^7+(-389922421248-2516189184*ln( 2)^6+2938503168*ln(2)^8+1587953664*ln(2)^4+28662030336*ln(2)^2-603979776*l n(2)^10)*x^8+(-467945443328-2337013760*ln(2)^6+1434189824*ln(2)^8+17094246 40*ln(2)^4+33912479744*ln(2)^2-58720256*ln(2)^10)*x^9+(-428925424128+30787 381248*ln(2)^2+1509285888*ln(2)^4-1481146368*ln(2)^6+416415744*ln(2)^8)*x^ 10+(-306315707904+21800583168*ln(2)^2+1035288576*ln(2)^4-650280960*ln(2...
Leaf count of result is larger than twice the leaf count of optimal. 666 vs. \(2 (24) = 48\).
Time = 0.09 (sec) , antiderivative size = 666, normalized size of antiderivative = 25.62 \[ \text {the integral} =\text {Too large to display} \] Input:
integrate((-524288-6029312*x+671757312*x^14+186202360*x^16-627376128*x^5+1 48*x^24+2604*x^23+28984*x^22+229024*x^21-33816576*x^2-953286656*x^6-110752 5632*x^7+1048039936*x^12-318636032*x^4-122421248*x^3+(-6576668672*x^7-4341 9435008*x^6-87375740928*x^5-18253611008*x^4+84825604096*x^3-41875931136*x^ 2-169651208192*x-60129542144)*log(2)^12+(645922816*x^10+6660554752*x^9+265 75110144*x^8+48570040320*x^7+31809601536*x^6-11475615744*x^5-13690208256*x ^4-23353884672*x^3-96636764160*x^2-104152956928*x-30064771072)*log(2)^10+( 1146880*x^16+21495808*x^15+179208192*x^14+872218624*x^13+2731442176*x^12+5 707530240*x^11+7933394944*x^10+6824132608*x^9+1830813696*x^8-6245318656*x^ 7-18098421760*x^6-32967229440*x^5-43780145152*x^4-41842376704*x^3-27279753 216*x^2-10737418240*x-1879048192)*log(2)^6+(-14336*x^19-324608*x^18-333619 2*x^17-20511744*x^16-83576832*x^15-235607040*x^14-463816704*x^13-628064256 *x^12-598818816*x^11-692240384*x^10-1961197568*x^9-5668208640*x^8-11922309 120*x^7-18554290176*x^6-21851799552*x^5-19465764864*x^4-12821987328*x^3-59 26551552*x^2-1719664640*x-234881024)*log(2)^4+(-128*x^22-4352*x^21-68736*x ^20-670720*x^19-4534144*x^18-22563072*x^17-85735680*x^16-254886144*x^15-60 4044288*x^14-1163537408*x^13-1876140032*x^12-2665648128*x^11-3588702208*x^ 10-4819566592*x^9-6314655744*x^8-7507476480*x^7-7583563776*x^6-6230900736* x^5-4028628992*x^4-1974468608*x^3-692060160*x^2-155189248*x-16777216)*log( 2)^2+(-85899345920*x-34359738368)*log(2)^16+(36507222016*x^4+120259084288* x^3+25769803776*x^2-171798691840*x-68719476736)*log(2)^14+(-36700160*x^13- 528220160*x^12-3228303360*x^11-10779099136*x^10-20920139776*x^9-2286629683 2*x^8-12507414528*x^7-6165626880*x^6-17817403392*x^5-41641050112*x^4-66504 884224*x^3-71068286976*x^2-41607495680*x-9395240960)*log(2)^8+4*x^25+63925 24*x^19+24022348*x^18+834330624*x^11+294787072*x^10-385378304*x^9-91994112 0*x^8+944780032*x^13+389319040*x^15+73676772*x^17+1366512*x^20)/(x^22+34*x ^21+544*x^20+5440*x^19+38080*x^18+198016*x^17+792064*x^16+2489344*x^15+622 3360*x^14+12446720*x^13+19914752*x^12+25346048*x^11+25346048*x^10+19496960 *x^9+11141120*x^8+4456448*x^7+1114112*x^6+131072*x^5),x, algorithm="fricas ")
Output:
(x^24 + 36*x^23 + 618*x^22 + 6736*x^21 + 52352*x^20 + 308752*x^19 + 143501 8*x^18 + 5386052*x^17 + 16590145*x^16 + 4294967296*log(2)^16 + 42392224*x^ 15 - 2147483648*(x^3 + 3*x^2 - 4)*log(2)^14 + 90551648*x^14 + 162753664*x^ 13 + 67108864*(7*x^6 + 45*x^5 + 87*x^4 + 16*x^3 - 72*x^2 + 48*x + 112)*log (2)^12 + 248098240*x^12 + 324614656*x^11 - 8388608*(7*x^9 + 72*x^8 + 288*x ^7 + 537*x^6 + 396*x^5 - 36*x^4 - 96*x^3 - 144*x^2 - 576*x - 448)*log(2)^1 0 + 371027456*x^10 + 377958400*x^9 + 131072*(35*x^12 + 510*x^11 + 3177*x^1 0 + 10942*x^9 + 22419*x^8 + 27216*x^7 + 18480*x^6 + 8064*x^5 + 9504*x^4 + 18688*x^3 + 26112*x^2 + 23040*x + 8960)*log(2)^8 + 347080192*x^8 + 2843525 12*x^7 - 32768*(7*x^15 + 135*x^14 + 1167*x^13 + 5953*x^12 + 19845*x^11 + 4 5201*x^10 + 71320*x^9 + 76788*x^8 + 51552*x^7 + 8480*x^6 - 34560*x^5 - 672 00*x^4 - 78592*x^3 - 62208*x^2 - 30720*x - 7168)*log(2)^6 + 200974336*x^6 + 117145600*x^5 + 1024*(7*x^18 + 171*x^17 + 1926*x^16 + 13251*x^15 + 62190 *x^14 + 210555*x^13 + 530367*x^12 + 1011024*x^11 + 1473912*x^10 + 1669360* x^9 + 1550736*x^8 + 1380096*x^7 + 1423104*x^6 + 1587456*x^5 + 1532160*x^4 + 1118208*x^3 + 571392*x^2 + 184320*x + 28672)*log(2)^4 + 53854208*x^4 + 1 8743296*x^3 - 128*(x^21 + 32*x^20 + 487*x^19 + 4685*x^18 + 31919*x^17 + 16 3405*x^16 + 650382*x^15 + 2052851*x^14 + 5191132*x^13 + 10543780*x^12 + 17 115904*x^11 + 21879728*x^10 + 21320000*x^9 + 14628928*x^8 + 5207552*x^7 - 1957632*x^6 - 4471808*x^5 - 3601408*x^4 - 1851392*x^3 - 651264*x^2 - 14...
Timed out. \[ \text {the integral} =\text {Timed out} \] Input:
integrate((-524288-6029312*x-33816576*x**2+834330624*x**11+944780032*x**13 +389319040*x**15+73676772*x**17+1366512*x**20+294787072*x**10-385378304*x* *9+1048039936*x**12-1107525632*x**7+148*x**24+2604*x**23+28984*x**22+22902 4*x**21-627376128*x**5+(-36700160*x**13-528220160*x**12-3228303360*x**11-1 0779099136*x**10-20920139776*x**9-22866296832*x**8-12507414528*x**7-616562 6880*x**6-17817403392*x**5-41641050112*x**4-66504884224*x**3-71068286976*x **2-41607495680*x-9395240960)*ln(2)**8+(1146880*x**16+21495808*x**15+17920 8192*x**14+872218624*x**13+2731442176*x**12+5707530240*x**11+7933394944*x* *10+6824132608*x**9+1830813696*x**8-6245318656*x**7-18098421760*x**6-32967 229440*x**5-43780145152*x**4-41842376704*x**3-27279753216*x**2-10737418240 *x-1879048192)*ln(2)**6+(-14336*x**19-324608*x**18-3336192*x**17-20511744* x**16-83576832*x**15-235607040*x**14-463816704*x**13-628064256*x**12-59881 8816*x**11-692240384*x**10-1961197568*x**9-5668208640*x**8-11922309120*x** 7-18554290176*x**6-21851799552*x**5-19465764864*x**4-12821987328*x**3-5926 551552*x**2-1719664640*x-234881024)*ln(2)**4-122421248*x**3+186202360*x**1 6+6392524*x**19+24022348*x**18+671757312*x**14+4*x**25-919941120*x**8-3186 36032*x**4-953286656*x**6+(-128*x**22-4352*x**21-68736*x**20-670720*x**19- 4534144*x**18-22563072*x**17-85735680*x**16-254886144*x**15-604044288*x**1 4-1163537408*x**13-1876140032*x**12-2665648128*x**11-3588702208*x**10-4819 566592*x**9-6314655744*x**8-7507476480*x**7-7583563776*x**6-6230900736*x** 5-4028628992*x**4-1974468608*x**3-692060160*x**2-155189248*x-16777216)*ln( 2)**2+(-85899345920*x-34359738368)*ln(2)**16+(36507222016*x**4+12025908428 8*x**3+25769803776*x**2-171798691840*x-68719476736)*ln(2)**14+(-6576668672 *x**7-43419435008*x**6-87375740928*x**5-18253611008*x**4+84825604096*x**3- 41875931136*x**2-169651208192*x-60129542144)*ln(2)**12+(645922816*x**10+66 60554752*x**9+26575110144*x**8+48570040320*x**7+31809601536*x**6-114756157 44*x**5-13690208256*x**4-23353884672*x**3-96636764160*x**2-104152956928*x- 30064771072)*ln(2)**10)/(x**22+34*x**21+544*x**20+5440*x**19+38080*x**18+1 98016*x**17+792064*x**16+2489344*x**15+6223360*x**14+12446720*x**13+199147 52*x**12+25346048*x**11+25346048*x**10+19496960*x**9+11141120*x**8+4456448 *x**7+1114112*x**6+131072*x**5),x)
Output:
Timed out
Leaf count of result is larger than twice the leaf count of optimal. 780 vs. \(2 (24) = 48\).
Time = 0.08 (sec) , antiderivative size = 780, normalized size of antiderivative = 30.00 \[ \text {the integral} =\text {Too large to display} \] Input:
integrate((-524288-6029312*x+671757312*x^14+186202360*x^16-627376128*x^5+1 48*x^24+2604*x^23+28984*x^22+229024*x^21-33816576*x^2-953286656*x^6-110752 5632*x^7+1048039936*x^12-318636032*x^4-122421248*x^3+(-6576668672*x^7-4341 9435008*x^6-87375740928*x^5-18253611008*x^4+84825604096*x^3-41875931136*x^ 2-169651208192*x-60129542144)*log(2)^12+(645922816*x^10+6660554752*x^9+265 75110144*x^8+48570040320*x^7+31809601536*x^6-11475615744*x^5-13690208256*x ^4-23353884672*x^3-96636764160*x^2-104152956928*x-30064771072)*log(2)^10+( 1146880*x^16+21495808*x^15+179208192*x^14+872218624*x^13+2731442176*x^12+5 707530240*x^11+7933394944*x^10+6824132608*x^9+1830813696*x^8-6245318656*x^ 7-18098421760*x^6-32967229440*x^5-43780145152*x^4-41842376704*x^3-27279753 216*x^2-10737418240*x-1879048192)*log(2)^6+(-14336*x^19-324608*x^18-333619 2*x^17-20511744*x^16-83576832*x^15-235607040*x^14-463816704*x^13-628064256 *x^12-598818816*x^11-692240384*x^10-1961197568*x^9-5668208640*x^8-11922309 120*x^7-18554290176*x^6-21851799552*x^5-19465764864*x^4-12821987328*x^3-59 26551552*x^2-1719664640*x-234881024)*log(2)^4+(-128*x^22-4352*x^21-68736*x ^20-670720*x^19-4534144*x^18-22563072*x^17-85735680*x^16-254886144*x^15-60 4044288*x^14-1163537408*x^13-1876140032*x^12-2665648128*x^11-3588702208*x^ 10-4819566592*x^9-6314655744*x^8-7507476480*x^7-7583563776*x^6-6230900736* x^5-4028628992*x^4-1974468608*x^3-692060160*x^2-155189248*x-16777216)*log( 2)^2+(-85899345920*x-34359738368)*log(2)^16+(36507222016*x^4+120259084288* x^3+25769803776*x^2-171798691840*x-68719476736)*log(2)^14+(-36700160*x^13- 528220160*x^12-3228303360*x^11-10779099136*x^10-20920139776*x^9-2286629683 2*x^8-12507414528*x^7-6165626880*x^6-17817403392*x^5-41641050112*x^4-66504 884224*x^3-71068286976*x^2-41607495680*x-9395240960)*log(2)^8+4*x^25+63925 24*x^19+24022348*x^18+834330624*x^11+294787072*x^10-385378304*x^9-91994112 0*x^8+944780032*x^13+389319040*x^15+73676772*x^17+1366512*x^20)/(x^22+34*x ^21+544*x^20+5440*x^19+38080*x^18+198016*x^17+792064*x^16+2489344*x^15+622 3360*x^14+12446720*x^13+19914752*x^12+25346048*x^11+25346048*x^10+19496960 *x^9+11141120*x^8+4456448*x^7+1114112*x^6+131072*x^5),x, algorithm="maxima ")
Output:
x^4 + 4*x^3 - 16*(8*log(2)^2 - 1)*x + 10*x^2 - (16*(56*log(2)^2 - 1)*x^19 - 2*(3584*log(2)^4 - 13120*log(2)^2 + 261)*x^18 - 12*(14592*log(2)^4 - 298 56*log(2)^2 + 667)*x^17 - (1972224*log(2)^4 - 3024512*log(2)^2 + 76609)*x^ 16 + 32*(7168*log(2)^6 - 424032*log(2)^4 + 551480*log(2)^2 - 16021)*x^15 - 4294967296*log(2)^16 + 96*(46080*log(2)^6 - 663360*log(2)^4 + 784708*log( 2)^2 - 26521)*x^14 + 128*(298752*log(2)^6 - 1684440*log(2)^4 + 1896412*log (2)^2 - 75929)*x^13 - 8589934592*log(2)^14 - 64*(71680*log(2)^8 - 3047936* log(2)^6 + 8485872*log(2)^4 - 9373000*log(2)^2 + 455351)*x^12 - 1536*(4352 0*log(2)^8 - 423360*log(2)^6 + 674016*log(2)^4 - 742976*log(2)^2 + 45279)* x^11 - 7516192768*log(2)^12 - 512*(813312*log(2)^8 - 2892864*log(2)^6 + 29 47824*log(2)^4 - 3233516*log(2)^2 + 259831)*x^10 + 4096*(14336*log(2)^10 - 350144*log(2)^8 + 570560*log(2)^6 - 417340*log(2)^4 + 433290*log(2)^2 - 4 9907)*x^9 - 3758096384*log(2)^10 + 1536*(393216*log(2)^10 - 1913088*log(2) ^8 + 1638144*log(2)^6 - 1033824*log(2)^4 + 836784*log(2)^2 - 163969)*x^8 + 8192*(294912*log(2)^10 - 435456*log(2)^8 + 206208*log(2)^6 - 172512*log(2 )^4 + 50648*log(2)^2 - 30199)*x^7 - 1174405120*log(2)^8 - 8192*(57344*log( 2)^12 - 549888*log(2)^10 + 295680*log(2)^8 - 33920*log(2)^6 + 177888*log(2 )^4 + 38780*log(2)^2 + 23429)*x^6 - 98304*(30720*log(2)^12 - 33792*log(2)^ 10 + 10752*log(2)^8 + 11520*log(2)^6 + 16536*log(2)^4 + 5908*log(2)^2 + 11 81)*x^5 - 234881024*log(2)^6 - 16384*(356352*log(2)^12 + 18432*log(2)^1...
Leaf count of result is larger than twice the leaf count of optimal. 1412 vs. \(2 (24) = 48\).
Time = 0.13 (sec) , antiderivative size = 1412, normalized size of antiderivative = 54.31 \[ \text {the integral} =\text {Too large to display} \] Input:
integrate((-524288-6029312*x+671757312*x^14+186202360*x^16-627376128*x^5+1 48*x^24+2604*x^23+28984*x^22+229024*x^21-33816576*x^2-953286656*x^6-110752 5632*x^7+1048039936*x^12-318636032*x^4-122421248*x^3+(-6576668672*x^7-4341 9435008*x^6-87375740928*x^5-18253611008*x^4+84825604096*x^3-41875931136*x^ 2-169651208192*x-60129542144)*log(2)^12+(645922816*x^10+6660554752*x^9+265 75110144*x^8+48570040320*x^7+31809601536*x^6-11475615744*x^5-13690208256*x ^4-23353884672*x^3-96636764160*x^2-104152956928*x-30064771072)*log(2)^10+( 1146880*x^16+21495808*x^15+179208192*x^14+872218624*x^13+2731442176*x^12+5 707530240*x^11+7933394944*x^10+6824132608*x^9+1830813696*x^8-6245318656*x^ 7-18098421760*x^6-32967229440*x^5-43780145152*x^4-41842376704*x^3-27279753 216*x^2-10737418240*x-1879048192)*log(2)^6+(-14336*x^19-324608*x^18-333619 2*x^17-20511744*x^16-83576832*x^15-235607040*x^14-463816704*x^13-628064256 *x^12-598818816*x^11-692240384*x^10-1961197568*x^9-5668208640*x^8-11922309 120*x^7-18554290176*x^6-21851799552*x^5-19465764864*x^4-12821987328*x^3-59 26551552*x^2-1719664640*x-234881024)*log(2)^4+(-128*x^22-4352*x^21-68736*x ^20-670720*x^19-4534144*x^18-22563072*x^17-85735680*x^16-254886144*x^15-60 4044288*x^14-1163537408*x^13-1876140032*x^12-2665648128*x^11-3588702208*x^ 10-4819566592*x^9-6314655744*x^8-7507476480*x^7-7583563776*x^6-6230900736* x^5-4028628992*x^4-1974468608*x^3-692060160*x^2-155189248*x-16777216)*log( 2)^2+(-85899345920*x-34359738368)*log(2)^16+(36507222016*x^4+120259084288* x^3+25769803776*x^2-171798691840*x-68719476736)*log(2)^14+(-36700160*x^13- 528220160*x^12-3228303360*x^11-10779099136*x^10-20920139776*x^9-2286629683 2*x^8-12507414528*x^7-6165626880*x^6-17817403392*x^5-41641050112*x^4-66504 884224*x^3-71068286976*x^2-41607495680*x-9395240960)*log(2)^8+4*x^25+63925 24*x^19+24022348*x^18+834330624*x^11+294787072*x^10-385378304*x^9-91994112 0*x^8+944780032*x^13+389319040*x^15+73676772*x^17+1366512*x^20)/(x^22+34*x ^21+544*x^20+5440*x^19+38080*x^18+198016*x^17+792064*x^16+2489344*x^15+622 3360*x^14+12446720*x^13+19914752*x^12+25346048*x^11+25346048*x^10+19496960 *x^9+11141120*x^8+4456448*x^7+1114112*x^6+131072*x^5),x, algorithm="giac")
Output:
x^4 + 4*x^3 - 128*x*log(2)^2 + 10*x^2 + 16*x - (6684672*x^3*log(2)^16 - 22 28224*x^2*log(2)^16 + 12615680*x^3*log(2)^14 + 524288*x*log(2)^16 - 435814 4*x^2*log(2)^14 - 65536*log(2)^16 + 9420800*x^3*log(2)^12 + 1048576*x*log( 2)^14 - 3432448*x^2*log(2)^12 - 131072*log(2)^14 + 3477504*x^3*log(2)^10 + 868352*x*log(2)^12 - 1378304*x^2*log(2)^10 - 114688*log(2)^12 + 641536*x^ 3*log(2)^8 + 385024*x*log(2)^10 - 292864*x^2*log(2)^8 - 57344*log(2)^10 + 52864*x^3*log(2)^6 + 97280*x*log(2)^8 - 30080*x^2*log(2)^6 - 17920*log(2)^ 8 + 1728*x^3*log(2)^4 + 13312*x*log(2)^6 - 1120*x^2*log(2)^4 - 3584*log(2) ^6 + 32*x^3*log(2)^2 + 704*x*log(2)^4 - 56*x^2*log(2)^2 - 448*log(2)^4 - 1 6*x^3 - 32*x*log(2)^2 - 10*x^2 - 32*log(2)^2 - 4*x - 1)/x^4 + 8*(835584*x^ 15*log(2)^16 + 26460160*x^14*log(2)^16 + 1576960*x^15*log(2)^14 + 39223296 0*x^13*log(2)^16 + 49917952*x^14*log(2)^14 + 3611811840*x^12*log(2)^16 + 1 177600*x^15*log(2)^12 + 739639296*x^13*log(2)^14 + 23115595776*x^11*log(2) ^16 + 37254144*x^14*log(2)^12 + 6807470080*x^12*log(2)^14 + 108973522944*x ^10*log(2)^16 + 434688*x^15*log(2)^10 + 551626752*x^13*log(2)^12 + 4354290 4832*x^11*log(2)^14 + 391187005440*x^9*log(2)^16 + 13737728*x^14*log(2)^10 + 5073160192*x^12*log(2)^12 + 205136855040*x^10*log(2)^14 + 1089735229440 *x^8*log(2)^16 + 80192*x^15*log(2)^8 + 203185152*x^13*log(2)^10 + 32421183 488*x^11*log(2)^12 + 735808847872*x^9*log(2)^14 + 2377604136960*x^7*log(2) ^16 + 2529536*x^14*log(2)^8 + 1866236928*x^12*log(2)^10 + 152585502720*...
Time = 2.86 (sec) , antiderivative size = 767, normalized size of antiderivative = 29.50 \[ \text {the integral} =\text {Too large to display} \] Input:
int((log(2)^6*(1830813696*x^8 - 27279753216*x^2 - 41842376704*x^3 - 437801 45152*x^4 - 32967229440*x^5 - 18098421760*x^6 - 6245318656*x^7 - 107374182 40*x + 6824132608*x^9 + 7933394944*x^10 + 5707530240*x^11 + 2731442176*x^1 2 + 872218624*x^13 + 179208192*x^14 + 21495808*x^15 + 1146880*x^16 - 18790 48192) - log(2)^4*(1719664640*x + 5926551552*x^2 + 12821987328*x^3 + 19465 764864*x^4 + 21851799552*x^5 + 18554290176*x^6 + 11922309120*x^7 + 5668208 640*x^8 + 1961197568*x^9 + 692240384*x^10 + 598818816*x^11 + 628064256*x^1 2 + 463816704*x^13 + 235607040*x^14 + 83576832*x^15 + 20511744*x^16 + 3336 192*x^17 + 324608*x^18 + 14336*x^19 + 234881024) - 6029312*x - log(2)^16*( 85899345920*x + 34359738368) - log(2)^2*(155189248*x + 692060160*x^2 + 197 4468608*x^3 + 4028628992*x^4 + 6230900736*x^5 + 7583563776*x^6 + 750747648 0*x^7 + 6314655744*x^8 + 4819566592*x^9 + 3588702208*x^10 + 2665648128*x^1 1 + 1876140032*x^12 + 1163537408*x^13 + 604044288*x^14 + 254886144*x^15 + 85735680*x^16 + 22563072*x^17 + 4534144*x^18 + 670720*x^19 + 68736*x^20 + 4352*x^21 + 128*x^22 + 16777216) + log(2)^14*(25769803776*x^2 - 1717986918 40*x + 120259084288*x^3 + 36507222016*x^4 - 68719476736) - log(2)^8*(41607 495680*x + 71068286976*x^2 + 66504884224*x^3 + 41641050112*x^4 + 178174033 92*x^5 + 6165626880*x^6 + 12507414528*x^7 + 22866296832*x^8 + 20920139776* x^9 + 10779099136*x^10 + 3228303360*x^11 + 528220160*x^12 + 36700160*x^13 + 9395240960) - 33816576*x^2 - 122421248*x^3 - 318636032*x^4 - 627376128*x ^5 - 953286656*x^6 - 1107525632*x^7 - 919941120*x^8 - 385378304*x^9 + 2947 87072*x^10 + 834330624*x^11 + 1048039936*x^12 + 944780032*x^13 + 671757312 *x^14 + 389319040*x^15 + 186202360*x^16 + 73676772*x^17 + 24022348*x^18 + 6392524*x^19 + 1366512*x^20 + 229024*x^21 + 28984*x^22 + 2604*x^23 + 148*x ^24 + 4*x^25 - log(2)^12*(169651208192*x + 41875931136*x^2 - 84825604096*x ^3 + 18253611008*x^4 + 87375740928*x^5 + 43419435008*x^6 + 6576668672*x^7 + 60129542144) - log(2)^10*(104152956928*x + 96636764160*x^2 + 23353884672 *x^3 + 13690208256*x^4 + 11475615744*x^5 - 31809601536*x^6 - 48570040320*x ^7 - 26575110144*x^8 - 6660554752*x^9 - 645922816*x^10 + 30064771072) - 52 4288)/(131072*x^5 + 1114112*x^6 + 4456448*x^7 + 11141120*x^8 + 19496960*x^ 9 + 25346048*x^10 + 25346048*x^11 + 19914752*x^12 + 12446720*x^13 + 622336 0*x^14 + 2489344*x^15 + 792064*x^16 + 198016*x^17 + 38080*x^18 + 5440*x^19 + 544*x^20 + 34*x^21 + x^22),x)
Output:
(x*(18874368*log(2)^2 + 188743680*log(2)^4 + 1006632960*log(2)^6 + 3019898 880*log(2)^8 + 4831838208*log(2)^10 + 3221225472*log(2)^12 + 786432) - x^1 5*(17647360*log(2)^2 - 13569024*log(2)^4 + 229376*log(2)^6 - 512672) + x^2 *(83361792*log(2)^2 + 585105408*log(2)^4 + 2038431744*log(2)^6 + 342255206 4*log(2)^8 + 1207959552*log(2)^10 - 4831838208*log(2)^12 - 6442450944*log( 2)^14 + 4718592) - x^14*(75331968*log(2)^2 - 63682560*log(2)^4 + 4423680*l og(2)^6 - 2546016) + x^5*(580780032*log(2)^2 + 1625554944*log(2)^4 + 11324 62080*log(2)^6 + 1056964608*log(2)^8 - 3321888768*log(2)^10 + 3019898880*l og(2)^12 + 116097024) - x^9*(1774755840*log(2)^2 - 1709424640*log(2)^4 + 2 337013760*log(2)^6 - 1434189824*log(2)^8 + 58720256*log(2)^10 - 204419072) + x^3*(236978176*log(2)^2 + 1145044992*log(2)^4 + 2575302656*log(2)^6 + 2 449473536*log(2)^8 + 805306368*log(2)^10 + 1073741824*log(2)^12 - 21474836 48*log(2)^14 + 18743296) - x^13*(242740736*log(2)^2 - 215608320*log(2)^4 + 38240256*log(2)^6 - 9718912) + x^4*(460980224*log(2)^2 + 1568931840*log(2 )^4 + 2202009600*log(2)^6 + 1245708288*log(2)^8 + 301989888*log(2)^10 + 58 38471168*log(2)^12 + 53854208) + x^10*(1509285888*log(2)^4 - 1655560192*lo g(2)^2 - 1481146368*log(2)^6 + 416415744*log(2)^8 + 133033472) - x^8*(1285 300224*log(2)^2 - 1587953664*log(2)^4 + 2516189184*log(2)^6 - 2938503168*l og(2)^8 + 603979776*log(2)^10 - 251856384) + x^12*(543095808*log(2)^4 - 59 9872000*log(2)^2 - 195067904*log(2)^6 + 4587520*log(2)^8 + 29142464) - ...
Time = 0.18 (sec) , antiderivative size = 974, normalized size of antiderivative = 37.46 \[ \text {the integral} =\text {Too large to display} \] Input:
int((-524288+186202360*x^16+671757312*x^14+148*x^24+2604*x^23+28984*x^22+2 29024*x^21-6029312*x-627376128*x^5+(-36700160*x^13-528220160*x^12-32283033 60*x^11-10779099136*x^10-20920139776*x^9-22866296832*x^8-12507414528*x^7-6 165626880*x^6-17817403392*x^5-41641050112*x^4-66504884224*x^3-71068286976* x^2-41607495680*x-9395240960)*log(2)^8+(1146880*x^16+21495808*x^15+1792081 92*x^14+872218624*x^13+2731442176*x^12+5707530240*x^11+7933394944*x^10+682 4132608*x^9+1830813696*x^8-6245318656*x^7-18098421760*x^6-32967229440*x^5- 43780145152*x^4-41842376704*x^3-27279753216*x^2-10737418240*x-1879048192)* log(2)^6-33816576*x^2+(-14336*x^19-324608*x^18-3336192*x^17-20511744*x^16- 83576832*x^15-235607040*x^14-463816704*x^13-628064256*x^12-598818816*x^11- 692240384*x^10-1961197568*x^9-5668208640*x^8-11922309120*x^7-18554290176*x ^6-21851799552*x^5-19465764864*x^4-12821987328*x^3-5926551552*x^2-17196646 40*x-234881024)*log(2)^4+(-128*x^22-4352*x^21-68736*x^20-670720*x^19-45341 44*x^18-22563072*x^17-85735680*x^16-254886144*x^15-604044288*x^14-11635374 08*x^13-1876140032*x^12-2665648128*x^11-3588702208*x^10-4819566592*x^9-631 4655744*x^8-7507476480*x^7-7583563776*x^6-6230900736*x^5-4028628992*x^4-19 74468608*x^3-692060160*x^2-155189248*x-16777216)*log(2)^2+(-85899345920*x- 34359738368)*log(2)^16+(36507222016*x^4+120259084288*x^3+25769803776*x^2-1 71798691840*x-68719476736)*log(2)^14+(-6576668672*x^7-43419435008*x^6-8737 5740928*x^5-18253611008*x^4+84825604096*x^3-41875931136*x^2-169651208192*x -60129542144)*log(2)^12+(645922816*x^10+6660554752*x^9+26575110144*x^8+485 70040320*x^7+31809601536*x^6-11475615744*x^5-13690208256*x^4-23353884672*x ^3-96636764160*x^2-104152956928*x-30064771072)*log(2)^10+1366512*x^20+4*x^ 25+6392524*x^19+24022348*x^18-953286656*x^6-919941120*x^8+834330624*x^11+2 94787072*x^10+1048039936*x^12-1107525632*x^7-318636032*x^4-122421248*x^3+9 44780032*x^13+389319040*x^15+73676772*x^17-385378304*x^9)/(x^22+34*x^21+54 4*x^20+5440*x^19+38080*x^18+198016*x^17+792064*x^16+2489344*x^15+6223360*x ^14+12446720*x^13+19914752*x^12+25346048*x^11+25346048*x^10+19496960*x^9+1 1141120*x^8+4456448*x^7+1114112*x^6+131072*x^5),x)
Output:
(8589934592*log(2)**16 - 4294967296*log(2)**14*x**3 - 12884901888*log(2)** 14*x**2 + 17179869184*log(2)**14 + 939524096*log(2)**12*x**6 + 6039797760* log(2)**12*x**5 + 11676942336*log(2)**12*x**4 + 2147483648*log(2)**12*x**3 - 9663676416*log(2)**12*x**2 + 6442450944*log(2)**12*x + 15032385536*log( 2)**12 - 117440512*log(2)**10*x**9 - 1207959552*log(2)**10*x**8 - 48318382 08*log(2)**10*x**7 - 9009364992*log(2)**10*x**6 - 6643777536*log(2)**10*x* *5 + 603979776*log(2)**10*x**4 + 1610612736*log(2)**10*x**3 + 2415919104*l og(2)**10*x**2 + 9663676416*log(2)**10*x + 7516192768*log(2)**10 + 9175040 *log(2)**8*x**12 + 133693440*log(2)**8*x**11 + 832831488*log(2)**8*x**10 + 2868379648*log(2)**8*x**9 + 5877006336*log(2)**8*x**8 + 7134511104*log(2) **8*x**7 + 4844421120*log(2)**8*x**6 + 2113929216*log(2)**8*x**5 + 2491416 576*log(2)**8*x**4 + 4898947072*log(2)**8*x**3 + 6845104128*log(2)**8*x**2 + 6039797760*log(2)**8*x + 2348810240*log(2)**8 - 458752*log(2)**6*x**15 - 8847360*log(2)**6*x**14 - 76480512*log(2)**6*x**13 - 390135808*log(2)**6 *x**12 - 1300561920*log(2)**6*x**11 - 2962292736*log(2)**6*x**10 - 4674027 520*log(2)**6*x**9 - 5032378368*log(2)**6*x**8 - 3378511872*log(2)**6*x**7 - 555745280*log(2)**6*x**6 + 2264924160*log(2)**6*x**5 + 4404019200*log(2 )**6*x**4 + 5150605312*log(2)**6*x**3 + 4076863488*log(2)**6*x**2 + 201326 5920*log(2)**6*x + 469762048*log(2)**6 + 14336*log(2)**4*x**18 + 350208*lo g(2)**4*x**17 + 3944448*log(2)**4*x**16 + 27138048*log(2)**4*x**15 + 12...