\(\int \frac {-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}+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^6-7507476480 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}-85735680 x^{16}-22563072 x^{17}-4534144 x^{18}-670720 x^{19}-68736 x^{20}-4352 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}-598818816 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 ^4(2)+(-1879048192-10737418240 x-27279753216 x^2-41842376704 x^3-43780145152 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^{12}+872218624 x^{13}+179208192 x^{14}+21495808 x^{15}+1146880 x^{16}) \log ^6(2)+(-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 ^8(2)+(-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+645922816 x^{10}) \log ^{10}(2)+(-60129542144-169651208192 x-41875931136 x^2+84825604096 x^3-18253611008 x^4-87375740928 x^5-43419435008 x^6-6576668672 x^7) \log ^{12}(2)+(-68719476736-171798691840 x+25769803776 x^2+120259084288 x^3+36507222016 x^4) \log ^{14}(2)+(-34359738368-85899345920 x) \log ^{16}(2)}{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}+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}} \, dx\) [5614]
Optimal result
Integrand size = 717, antiderivative size = 26 \[
\int \frac {-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}+24022348 x^{18}+6392524 x^{19}+1366512 x^{20}+229024 x^{21}+28984 x^{22}+2604 x^{23}+148 x^{24}+4 x^{25}+\left (-16777216-155189248 x-692060160 x^2-1974468608 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}-85735680 x^{16}-22563072 x^{17}-4534144 x^{18}-670720 x^{19}-68736 x^{20}-4352 x^{21}-128 x^{22}\right ) \log ^2(2)+\left (-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}-598818816 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}\right ) \log ^4(2)+\left (-1879048192-10737418240 x-27279753216 x^2-41842376704 x^3-43780145152 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^{12}+872218624 x^{13}+179208192 x^{14}+21495808 x^{15}+1146880 x^{16}\right ) \log ^6(2)+\left (-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}\right ) \log ^8(2)+\left (-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+645922816 x^{10}\right ) \log ^{10}(2)+\left (-60129542144-169651208192 x-41875931136 x^2+84825604096 x^3-18253611008 x^4-87375740928 x^5-43419435008 x^6-6576668672 x^7\right ) \log ^{12}(2)+\left (-68719476736-171798691840 x+25769803776 x^2+120259084288 x^3+36507222016 x^4\right ) \log ^{14}(2)+(-34359738368-85899345920 x) \log ^{16}(2)}{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}+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}} \, dx=\left (3+\frac {\left (-1+x-\frac {64 \log ^2(2)}{(4+2 x)^2}\right )^2}{x}\right )^4
\]
[Out]
((x-16*ln(2)^2/(2+x)^2-1)^2/x+3)^4
Rubi [B] (verified)
Leaf count is larger than twice the leaf count of optimal. \(700\) vs. \(2(26)=52\).
Time = 9.59 (sec) , antiderivative size = 700, normalized size of antiderivative = 26.92,
number of steps used = 2, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.001, Rules used = {2099}
\[
\text {integral}=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}
\]
[In]
Int[(-524288 - 6029312*x - 33816576*x^2 - 122421248*x^3 - 318636032*x^4 - 627376128*x^5 - 953286656*x^6 - 1107
525632*x^7 - 919941120*x^8 - 385378304*x^9 + 294787072*x^10 + 834330624*x^11 + 1048039936*x^12 + 944780032*x^1
3 + 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 - 1
974468608*x^3 - 4028628992*x^4 - 6230900736*x^5 - 7583563776*x^6 - 7507476480*x^7 - 6314655744*x^8 - 481956659
2*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^20 - 4352*x^21 - 128*x^22)*Log[2]^2 +
(-234881024 - 1719664640*x - 5926551552*x^2 - 12821987328*x^3 - 19465764864*x^4 - 21851799552*x^5 - 185542901
76*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 - 83576832*x^15 - 20511744*x^16 - 3336192*x^17 - 324608*x^18 - 14336*x^19)*L
og[2]^4 + (-1879048192 - 10737418240*x - 27279753216*x^2 - 41842376704*x^3 - 43780145152*x^4 - 32967229440*x^5
- 18098421760*x^6 - 6245318656*x^7 + 1830813696*x^8 + 6824132608*x^9 + 7933394944*x^10 + 5707530240*x^11 + 27
31442176*x^12 + 872218624*x^13 + 179208192*x^14 + 21495808*x^15 + 1146880*x^16)*Log[2]^6 + (-9395240960 - 4160
7495680*x - 71068286976*x^2 - 66504884224*x^3 - 41641050112*x^4 - 17817403392*x^5 - 6165626880*x^6 - 125074145
28*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 - 11475615
744*x^5 + 31809601536*x^6 + 48570040320*x^7 + 26575110144*x^8 + 6660554752*x^9 + 645922816*x^10)*Log[2]^10 + (
-60129542144 - 169651208192*x - 41875931136*x^2 + 84825604096*x^3 - 18253611008*x^4 - 87375740928*x^5 - 434194
35008*x^6 - 6576668672*x^7)*Log[2]^12 + (-68719476736 - 171798691840*x + 25769803776*x^2 + 120259084288*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 + 19496960*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]
[Out]
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*
Log[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 +
(1048576*Log[2]^10*(63 + 236*Log[2]^2 + 392*Log[2]^4 + 240*Log[2]^6))/(2 + x)^9 + (524288*Log[2]^10*(135 + 57
2*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*Log[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 - 232
96*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 + 36608*Log[2]^10))/(2 + x)^6 - (64*Log[2]^4*(351 - 1632*Log[2]^2 - 23312*Log[2]^4 - 137216*Log[2]^6 - 387
840*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 - 2792*Log[2]^6 - 17056*Log[2]^8 - 36224*Log[2]^10 - 26112*Log[2]^12))/x + (64*Log[2]^4*(513 + 2160*L
og[2]^2 + 34120*Log[2]^4 + 211456*Log[2]^6 + 613632*Log[2]^8 + 856064*Log[2]^10 + 465920*Log[2]^12))/(2 + x)^4
- (32*Log[2]^2*(27 - 54*Log[2]^2 - 1652*Log[2]^4 - 20048*Log[2]^6 - 108672*Log[2]^8 - 294400*Log[2]^10 - 3942
40*Log[2]^12 - 208896*Log[2]^14))/(2 + x) + (8*Log[2]^2*(81 + 1188*Log[2]^2 + 9456*Log[2]^4 + 123776*Log[2]^6
+ 697088*Log[2]^8 + 1926144*Log[2]^10 + 2609152*Log[2]^12 + 1392640*Log[2]^14))/(2 + x)^2
Rule 2099
Int[(P_)^(p_)*(Q_)^(q_.), x_Symbol] :> With[{PP = Factor[P]}, Int[ExpandIntegrand[PP^p*Q^q, x], x] /; !SumQ[N
onfreeFactors[PP, x]]] /; FreeQ[q, x] && PolyQ[P, x] && PolyQ[Q, x] && IntegerQ[p] && NeQ[P, x]
Rubi steps \begin{align*}
\text {integral}& = \int \left (20 x+12 x^2+4 x^3-\frac {4294967296 \log ^{16}(2)}{(2+x)^{17}}-\frac {8053063680 \log ^{16}(2)}{(2+x)^{16}}-\frac {4 \left (1+4 \log ^2(2)\right )^8}{x^5}-\frac {1879048192 \log ^{14}(2) \left (3+5 \log ^2(2)\right )}{(2+x)^{15}}-16 \left (-1+8 \log ^2(2)\right )+\frac {12 \left (1+4 \log ^2(2)\right )^6 \left (-1+16 \log ^2(2)+32 \log ^4(2)\right )}{x^4}-\frac {46137344 \log ^{12}(2) \left (75+160 \log ^2(2)+112 \log ^4(2)\right )}{(2+x)^{12}}-\frac {50331648 \log ^{12}(2) \left (57+176 \log ^2(2)+140 \log ^4(2)\right )}{(2+x)^{13}}-\frac {9437184 \log ^{10}(2) \left (63+236 \log ^2(2)+392 \log ^4(2)+240 \log ^6(2)\right )}{(2+x)^{10}}-\frac {5242880 \log ^{10}(2) \left (135+572 \log ^2(2)+1040 \log ^4(2)+672 \log ^6(2)\right )}{(2+x)^{11}}-\frac {458752 \log ^8(2) \left (81+628 \log ^2(2)+2044 \log ^4(2)+3072 \log ^6(2)+1760 \log ^8(2)\right )}{(2+x)^8}-\frac {4 \left (1+4 \log ^2(2)\right )^4 \left (5-52 \log ^2(2)+912 \log ^4(2)+4160 \log ^6(2)+4352 \log ^8(2)\right )}{x^3}-\frac {65536 \log ^8(2) \left (1323+6624 \log ^2(2)+22880 \log ^4(2)+35840 \log ^6(2)+21120 \log ^8(2)\right )}{(2+x)^9}-\frac {10240 \log ^6(2) \left (-27+1506 \log ^2(2)+9920 \log ^4(2)+29696 \log ^6(2)+42240 \log ^8(2)+23296 \log ^{10}(2)\right )}{(2+x)^6}-\frac {12288 \log ^6(2) \left (405+2034 \log ^2(2)+14416 \log ^4(2)+44800 \log ^6(2)+65280 \log ^8(2)+36608 \log ^{10}(2)\right )}{(2+x)^7}+\frac {16 \left (1+4 \log ^2(2)\right )^2 \left (-1+10 \log ^2(2)+44 \log ^4(2)+2792 \log ^6(2)+17056 \log ^8(2)+36224 \log ^{10}(2)+26112 \log ^{12}(2)\right )}{x^2}-\frac {192 \log ^4(2) \left (-351+1632 \log ^2(2)+23312 \log ^4(2)+137216 \log ^6(2)+387840 \log ^8(2)+532480 \log ^{10}(2)+286720 \log ^{12}(2)\right )}{(2+x)^4}-\frac {256 \log ^4(2) \left (513+2160 \log ^2(2)+34120 \log ^4(2)+211456 \log ^6(2)+613632 \log ^8(2)+856064 \log ^{10}(2)+465920 \log ^{12}(2)\right )}{(2+x)^5}-\frac {32 \log ^2(2) \left (-27+54 \log ^2(2)+1652 \log ^4(2)+20048 \log ^6(2)+108672 \log ^8(2)+294400 \log ^{10}(2)+394240 \log ^{12}(2)+208896 \log ^{14}(2)\right )}{(2+x)^2}-\frac {16 \log ^2(2) \left (81+1188 \log ^2(2)+9456 \log ^4(2)+123776 \log ^6(2)+697088 \log ^8(2)+1926144 \log ^{10}(2)+2609152 \log ^{12}(2)+1392640 \log ^{14}(2)\right )}{(2+x)^3}-\frac {8724152320 \left (\log ^{14}(2)+\log ^{16}(2)\right )}{(2+x)^{14}}\right ) \, dx \\ & = 10 x^2+4 x^3+x^4+\frac {268435456 \log ^{16}(2)}{(2+x)^{16}}+\frac {536870912 \log ^{16}(2)}{(2+x)^{15}}+16 x \left (1-8 \log ^2(2)\right )+\frac {671088640 \log ^{14}(2) \left (1+\log ^2(2)\right )}{(2+x)^{13}}+\frac {\left (1+4 \log ^2(2)\right )^8}{x^4}+\frac {134217728 \log ^{14}(2) \left (3+5 \log ^2(2)\right )}{(2+x)^{14}}+\frac {4 \left (1+4 \log ^2(2)\right )^6 \left (1-16 \log ^2(2)-32 \log ^4(2)\right )}{x^3}+\frac {4194304 \log ^{12}(2) \left (75+160 \log ^2(2)+112 \log ^4(2)\right )}{(2+x)^{11}}+\frac {4194304 \log ^{12}(2) \left (57+176 \log ^2(2)+140 \log ^4(2)\right )}{(2+x)^{12}}+\frac {1048576 \log ^{10}(2) \left (63+236 \log ^2(2)+392 \log ^4(2)+240 \log ^6(2)\right )}{(2+x)^9}+\frac {524288 \log ^{10}(2) \left (135+572 \log ^2(2)+1040 \log ^4(2)+672 \log ^6(2)\right )}{(2+x)^{10}}+\frac {65536 \log ^8(2) \left (81+628 \log ^2(2)+2044 \log ^4(2)+3072 \log ^6(2)+1760 \log ^8(2)\right )}{(2+x)^7}+\frac {2 \left (1+4 \log ^2(2)\right )^4 \left (5-52 \log ^2(2)+912 \log ^4(2)+4160 \log ^6(2)+4352 \log ^8(2)\right )}{x^2}+\frac {8192 \log ^8(2) \left (1323+6624 \log ^2(2)+22880 \log ^4(2)+35840 \log ^6(2)+21120 \log ^8(2)\right )}{(2+x)^8}-\frac {2048 \log ^6(2) \left (27-1506 \log ^2(2)-9920 \log ^4(2)-29696 \log ^6(2)-42240 \log ^8(2)-23296 \log ^{10}(2)\right )}{(2+x)^5}+\frac {2048 \log ^6(2) \left (405+2034 \log ^2(2)+14416 \log ^4(2)+44800 \log ^6(2)+65280 \log ^8(2)+36608 \log ^{10}(2)\right )}{(2+x)^6}-\frac {64 \log ^4(2) \left (351-1632 \log ^2(2)-23312 \log ^4(2)-137216 \log ^6(2)-387840 \log ^8(2)-532480 \log ^{10}(2)-286720 \log ^{12}(2)\right )}{(2+x)^3}+\frac {16 \left (1+4 \log ^2(2)\right )^2 \left (1-10 \log ^2(2)-44 \log ^4(2)-2792 \log ^6(2)-17056 \log ^8(2)-36224 \log ^{10}(2)-26112 \log ^{12}(2)\right )}{x}+\frac {64 \log ^4(2) \left (513+2160 \log ^2(2)+34120 \log ^4(2)+211456 \log ^6(2)+613632 \log ^8(2)+856064 \log ^{10}(2)+465920 \log ^{12}(2)\right )}{(2+x)^4}-\frac {32 \log ^2(2) \left (27-54 \log ^2(2)-1652 \log ^4(2)-20048 \log ^6(2)-108672 \log ^8(2)-294400 \log ^{10}(2)-394240 \log ^{12}(2)-208896 \log ^{14}(2)\right )}{2+x}+\frac {8 \log ^2(2) \left (81+1188 \log ^2(2)+9456 \log ^4(2)+123776 \log ^6(2)+697088 \log ^8(2)+1926144 \log ^{10}(2)+2609152 \log ^{12}(2)+1392640 \log ^{14}(2)\right )}{(2+x)^2} \\
\end{align*}
Mathematica [B] (verified)
Leaf count is larger than twice the leaf count of optimal. \(711\) vs. \(2(26)=52\).
Time = 0.88 (sec) , antiderivative size = 711, normalized size of antiderivative = 27.35
\[
\text {integral}=4 \left (\frac {5 x^2}{2}+x^3+\frac {x^4}{4}+\frac {67108864 \log ^{16}(2)}{(2+x)^{16}}+\frac {134217728 \log ^{16}(2)}{(2+x)^{15}}+\frac {167772160 \log ^{14}(2) \left (1+\log ^2(2)\right )}{(2+x)^{13}}+\frac {\left (1+4 \log ^2(2)\right )^8}{4 x^4}+\frac {33554432 \log ^{14}(2) \left (3+5 \log ^2(2)\right )}{(2+x)^{14}}-4 x \left (-1+8 \log ^2(2)\right )-\frac {\left (1+4 \log ^2(2)\right )^6 \left (-1+16 \log ^2(2)+32 \log ^4(2)\right )}{x^3}+\frac {1048576 \log ^{12}(2) \left (75+160 \log ^2(2)+112 \log ^4(2)\right )}{(2+x)^{11}}+\frac {1048576 \log ^{12}(2) \left (57+176 \log ^2(2)+140 \log ^4(2)\right )}{(2+x)^{12}}+\frac {262144 \log ^{10}(2) \left (63+236 \log ^2(2)+392 \log ^4(2)+240 \log ^6(2)\right )}{(2+x)^9}+\frac {131072 \log ^{10}(2) \left (135+572 \log ^2(2)+1040 \log ^4(2)+672 \log ^6(2)\right )}{(2+x)^{10}}+\frac {16384 \log ^8(2) \left (81+628 \log ^2(2)+2044 \log ^4(2)+3072 \log ^6(2)+1760 \log ^8(2)\right )}{(2+x)^7}+\frac {\left (1+4 \log ^2(2)\right )^4 \left (5-52 \log ^2(2)+912 \log ^4(2)+4160 \log ^6(2)+4352 \log ^8(2)\right )}{2 x^2}+\frac {2048 \log ^8(2) \left (1323+6624 \log ^2(2)+22880 \log ^4(2)+35840 \log ^6(2)+21120 \log ^8(2)\right )}{(2+x)^8}+\frac {512 \log ^6(2) \left (-27+1506 \log ^2(2)+9920 \log ^4(2)+29696 \log ^6(2)+42240 \log ^8(2)+23296 \log ^{10}(2)\right )}{(2+x)^5}+\frac {512 \log ^6(2) \left (405+2034 \log ^2(2)+14416 \log ^4(2)+44800 \log ^6(2)+65280 \log ^8(2)+36608 \log ^{10}(2)\right )}{(2+x)^6}-\frac {4 \left (1+4 \log ^2(2)\right )^2 \left (-1+10 \log ^2(2)+44 \log ^4(2)+2792 \log ^6(2)+17056 \log ^8(2)+36224 \log ^{10}(2)+26112 \log ^{12}(2)\right )}{x}+\frac {16 \log ^4(2) \left (-351+1632 \log ^2(2)+23312 \log ^4(2)+137216 \log ^6(2)+387840 \log ^8(2)+532480 \log ^{10}(2)+286720 \log ^{12}(2)\right )}{(2+x)^3}+\frac {16 \log ^4(2) \left (513+2160 \log ^2(2)+34120 \log ^4(2)+211456 \log ^6(2)+613632 \log ^8(2)+856064 \log ^{10}(2)+465920 \log ^{12}(2)\right )}{(2+x)^4}+\frac {8 \log ^2(2) \left (-27+54 \log ^2(2)+1652 \log ^4(2)+20048 \log ^6(2)+108672 \log ^8(2)+294400 \log ^{10}(2)+394240 \log ^{12}(2)+208896 \log ^{14}(2)\right )}{2+x}+\frac {2 \log ^2(2) \left (81+1188 \log ^2(2)+9456 \log ^4(2)+123776 \log ^6(2)+697088 \log ^8(2)+1926144 \log ^{10}(2)+2609152 \log ^{12}(2)+1392640 \log ^{14}(2)\right )}{(2+x)^2}\right )
\]
[In]
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 - 385378304*x^9 + 294787072*x^10 + 834330624*x^11 + 1048039936*x^12 + 9447800
32*x^13 + 671757312*x^14 + 389319040*x^15 + 186202360*x^16 + 73676772*x^17 + 24022348*x^18 + 6392524*x^19 + 13
66512*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 - 7507476480*x^7 - 6314655744*x^8 - 481
9566592*x^9 - 3588702208*x^10 - 2665648128*x^11 - 1876140032*x^12 - 1163537408*x^13 - 604044288*x^14 - 2548861
44*x^15 - 85735680*x^16 - 22563072*x^17 - 4534144*x^18 - 670720*x^19 - 68736*x^20 - 4352*x^21 - 128*x^22)*Log[
2]^2 + (-234881024 - 1719664640*x - 5926551552*x^2 - 12821987328*x^3 - 19465764864*x^4 - 21851799552*x^5 - 185
54290176*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 - 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 - 43780145152*x^4 - 329672294
40*x^5 - 18098421760*x^6 - 6245318656*x^7 + 1830813696*x^8 + 6824132608*x^9 + 7933394944*x^10 + 5707530240*x^1
1 + 2731442176*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 - 125
07414528*x^7 - 22866296832*x^8 - 20920139776*x^9 - 10779099136*x^10 - 3228303360*x^11 - 528220160*x^12 - 36700
160*x^13)*Log[2]^8 + (-30064771072 - 104152956928*x - 96636764160*x^2 - 23353884672*x^3 - 13690208256*x^4 - 11
475615744*x^5 + 31809601536*x^6 + 48570040320*x^7 + 26575110144*x^8 + 6660554752*x^9 + 645922816*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 - 85899345920*x)*Log[2]^16)/(131072*x^5 + 1114112*x^6 + 44564
48*x^7 + 11141120*x^8 + 19496960*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]
[Out]
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*L
og[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*Log[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)^12 + (262144*Log[2]^10*(63 + 236*Log[2]^2 + 392*Log[2]^4 + 240*Log[2]^6))/(2 + x)^9 + (131072*Log[2]^10*(13
5 + 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*Log[2]^2 + 912*Log[2]^4 + 4160*L
og[2]^6 + 4352*Log[2]^8))/(2*x^2) + (2048*Log[2]^8*(1323 + 6624*Log[2]^2 + 22880*Log[2]^4 + 35840*Log[2]^6 + 2
1120*Log[2]^8))/(2 + x)^8 + (512*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 + (512*Log[2]^6*(405 + 2034*Log[2]^2 + 14416*Log[2]^4 + 44800*Log[2]^6 + 6528
0*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*Log[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]^6 + 613632*Log[2]^8 + 856064*Log[2]^10 + 465920*Log[2]^12))/(
2 + x)^4 + (8*Log[2]^2*(-27 + 54*Log[2]^2 + 1652*Log[2]^4 + 20048*Log[2]^6 + 108672*Log[2]^8 + 294400*Log[2]^1
0 + 394240*Log[2]^12 + 208896*Log[2]^14))/(2 + x) + (2*Log[2]^2*(81 + 1188*Log[2]^2 + 9456*Log[2]^4 + 123776*L
og[2]^6 + 697088*Log[2]^8 + 1926144*Log[2]^10 + 2609152*Log[2]^12 + 1392640*Log[2]^14))/(2 + x)^2)
Maple [B] (verified)
Leaf count of result is larger than twice the leaf count of optimal. \(682\) vs. \(2(24)=48\).
Time = 0.87 (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 |
\(\text {Expression too large to display}\) |
\(972\) |
| | |
|
|
|
|
[In]
int((-524288-6029312*x+(645922816*x^10+6660554752*x^9+26575110144*x^8+48570040320*x^7+31809601536*x^6-11475615
744*x^5-13690208256*x^4-23353884672*x^3-96636764160*x^2-104152956928*x-30064771072)*ln(2)^10+(1146880*x^16+214
95808*x^15+179208192*x^14+872218624*x^13+2731442176*x^12+5707530240*x^11+7933394944*x^10+6824132608*x^9+183081
3696*x^8-6245318656*x^7-18098421760*x^6-32967229440*x^5-43780145152*x^4-41842376704*x^3-27279753216*x^2-107374
18240*x-1879048192)*ln(2)^6+(-14336*x^19-324608*x^18-3336192*x^17-20511744*x^16-83576832*x^15-235607040*x^14-4
63816704*x^13-628064256*x^12-598818816*x^11-692240384*x^10-1961197568*x^9-5668208640*x^8-11922309120*x^7-18554
290176*x^6-21851799552*x^5-19465764864*x^4-12821987328*x^3-5926551552*x^2-1719664640*x-234881024)*ln(2)^4+(-12
8*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)*ln(2)^2+(-8589
9345920*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^6-87375740928*x^5-18253611008*x^4+84825604096*x^3-41875931136*x^2-1696
51208192*x-60129542144)*ln(2)^12+(-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)*ln(2)^8+4*x^25+148*x^24+229024*x^21+28984*x^22+2604*x^23+1366512*x^20+6392524*x^
19+24022348*x^18+73676772*x^17+834330624*x^11+1048039936*x^12+944780032*x^13+671757312*x^14+186202360*x^16+389
319040*x^15-1107525632*x^7-919941120*x^8+294787072*x^10-385378304*x^9-953286656*x^6-627376128*x^5-318636032*x^
4-122421248*x^3-33816576*x^2)/(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+11
14112*x^6+131072*x^5),x,method=_RETURNVERBOSE)
[Out]
(65536+8589934592*ln(2)^14+7516192768*ln(2)^12+3758096384*ln(2)^10+4294967296*ln(2)^16+x^24+234881024*ln(2)^6+
1174405120*ln(2)^8+618*x^22+36*x^23+29360128*ln(2)^4+2097152*ln(2)^2+(786432+3221225472*ln(2)^12+4831838208*ln
(2)^10+1006632960*ln(2)^6+3019898880*ln(2)^8+188743680*ln(2)^4+18874368*ln(2)^2)*x+(4718592-6442450944*ln(2)^1
4-4831838208*ln(2)^12+1207959552*ln(2)^10+2038431744*ln(2)^6+3422552064*ln(2)^8+585105408*ln(2)^4+83361792*ln(
2)^2)*x^2+(-2147483648*ln(2)^14+1073741824*ln(2)^12+18743296+805306368*ln(2)^10+2575302656*ln(2)^6+2449473536*
ln(2)^8+1145044992*ln(2)^4+236978176*ln(2)^2)*x^3+(6736-128*ln(2)^2)*x^21+(5838471168*ln(2)^12-3377086464+3019
89888*ln(2)^10+2202009600*ln(2)^6+1245708288*ln(2)^8+1568931840*ln(2)^4+729415680*ln(2)^2)*x^4+(3019898880*ln(
2)^12-27330379776-3321888768*ln(2)^10+1132462080*ln(2)^6+1056964608*ln(2)^8+1625554944*ln(2)^4+2719875072*ln(2
)^2)*x^5+(-102727245824+469762048*ln(2)^12-4504682496*ln(2)^10-277872640*ln(2)^6+2422210560*ln(2)^8+1457258496
*ln(2)^4+8303640576*ln(2)^2)*x^6+(-2415919104*ln(2)^10-1689255936*ln(2)^6+3567255552*ln(2)^8+1413218304*ln(2)^
4+18123915264*ln(2)^2-239881494528)*x^7+(-389922421248-603979776*ln(2)^10-2516189184*ln(2)^6+2938503168*ln(2)^
8+1587953664*ln(2)^4+28662030336*ln(2)^2)*x^8+(-467945443328-58720256*ln(2)^10-2337013760*ln(2)^6+1434189824*l
n(2)^8+1709424640*ln(2)^4+33912479744*ln(2)^2)*x^9+(-428925424128+30787381248*ln(2)^2+1509285888*ln(2)^4-14811
46368*ln(2)^6+416415744*ln(2)^8)*x^10+(-306315707904+21800583168*ln(2)^2+1035288576*ln(2)^4-650280960*ln(2)^6+
66846720*ln(2)^8)*x^11+(-172237083200+12145569280*ln(2)^2+543095808*ln(2)^4-195067904*ln(2)^6+4587520*ln(2)^8)
*x^12+(-76497326976+5333389824*ln(2)^2+215608320*ln(2)^4-38240256*ln(2)^6)*x^13+(-26740476576+1836484224*ln(2)
^2+63682560*ln(2)^4-4423680*ln(2)^6)*x^14+(-7275160928+489273600*ln(2)^2+13569024*ln(2)^4-229376*ln(2)^6)*x^15
+(-1507900095+98359680*ln(2)^2+1972224*ln(2)^4)*x^16+(-229150908+14264448*ln(2)^2+175104*ln(2)^4)*x^17+(-23693
942+1366400*ln(2)^2+7168*ln(2)^4)*x^18+(-1366512+68736*ln(2)^2)*x^19)/x^4/(2+x)^16
Fricas [B] (verification not implemented)
Leaf count of result is larger than twice the leaf count of optimal. 666 vs. \(2 (24) = 48\).
Time = 0.26 (sec) , antiderivative size = 666, normalized size of antiderivative = 25.62
\[
\text {integral}=\frac {x^{24} + 36 \, x^{23} + 618 \, x^{22} + 6736 \, x^{21} + 52352 \, x^{20} + 308752 \, x^{19} + 1435018 \, x^{18} + 5386052 \, x^{17} + 16590145 \, x^{16} + 4294967296 \, \log \left (2\right )^{16} + 42392224 \, x^{15} - 2147483648 \, {\left (x^{3} + 3 \, x^{2} - 4\right )} \log \left (2\right )^{14} + 90551648 \, x^{14} + 162753664 \, x^{13} + 67108864 \, {\left (7 \, x^{6} + 45 \, x^{5} + 87 \, x^{4} + 16 \, x^{3} - 72 \, x^{2} + 48 \, x + 112\right )} \log \left (2\right )^{12} + 248098240 \, x^{12} + 324614656 \, x^{11} - 8388608 \, {\left (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\right )} \log \left (2\right )^{10} + 371027456 \, x^{10} + 377958400 \, x^{9} + 131072 \, {\left (35 \, x^{12} + 510 \, x^{11} + 3177 \, x^{10} + 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\right )} \log \left (2\right )^{8} + 347080192 \, x^{8} + 284352512 \, x^{7} - 32768 \, {\left (7 \, x^{15} + 135 \, x^{14} + 1167 \, x^{13} + 5953 \, x^{12} + 19845 \, x^{11} + 45201 \, x^{10} + 71320 \, x^{9} + 76788 \, x^{8} + 51552 \, x^{7} + 8480 \, x^{6} - 34560 \, x^{5} - 67200 \, x^{4} - 78592 \, x^{3} - 62208 \, x^{2} - 30720 \, x - 7168\right )} \log \left (2\right )^{6} + 200974336 \, x^{6} + 117145600 \, x^{5} + 1024 \, {\left (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\right )} \log \left (2\right )^{4} + 53854208 \, x^{4} + 18743296 \, x^{3} - 128 \, {\left (x^{21} + 32 \, x^{20} + 487 \, x^{19} + 4685 \, x^{18} + 31919 \, x^{17} + 163405 \, x^{16} + 650382 \, x^{15} + 2052851 \, x^{14} + 5191132 \, x^{13} + 10543780 \, x^{12} + 17115904 \, 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} - 147456 \, x - 16384\right )} \log \left (2\right )^{2} + 4718592 \, x^{2} + 786432 \, x + 65536}{x^{20} + 32 \, x^{19} + 480 \, x^{18} + 4480 \, x^{17} + 29120 \, x^{16} + 139776 \, x^{15} + 512512 \, x^{14} + 1464320 \, x^{13} + 3294720 \, x^{12} + 5857280 \, x^{11} + 8200192 \, x^{10} + 8945664 \, x^{9} + 7454720 \, x^{8} + 4587520 \, x^{7} + 1966080 \, x^{6} + 524288 \, x^{5} + 65536 \, x^{4}}
\]
[In]
integrate((-524288-6029312*x-627376128*x^5-318636032*x^4-33816576*x^2+1048039936*x^12+186202360*x^16+(-3670016
0*x^13-528220160*x^12-3228303360*x^11-10779099136*x^10-20920139776*x^9-22866296832*x^8-12507414528*x^7-6165626
880*x^6-17817403392*x^5-41641050112*x^4-66504884224*x^3-71068286976*x^2-41607495680*x-9395240960)*log(2)^8+(11
46880*x^16+21495808*x^15+179208192*x^14+872218624*x^13+2731442176*x^12+5707530240*x^11+7933394944*x^10+6824132
608*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^18-3336192*x^17-20511744*x^16-83576832*x^15-2
35607040*x^14-463816704*x^13-628064256*x^12-598818816*x^11-692240384*x^10-1961197568*x^9-5668208640*x^8-119223
09120*x^7-18554290176*x^6-21851799552*x^5-19465764864*x^4-12821987328*x^3-5926551552*x^2-1719664640*x-23488102
4)*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^1
5-604044288*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
)*log(2)^2+(-85899345920*x-34359738368)*log(2)^16+(36507222016*x^4+120259084288*x^3+25769803776*x^2-1717986918
40*x-68719476736)*log(2)^14+(-6576668672*x^7-43419435008*x^6-87375740928*x^5-18253611008*x^4+84825604096*x^3-4
1875931136*x^2-169651208192*x-60129542144)*log(2)^12-953286656*x^6+4*x^25-122421248*x^3-385378304*x^9+29478707
2*x^10-1107525632*x^7-919941120*x^8+148*x^24+2604*x^23+28984*x^22+229024*x^21+6392524*x^19+1366512*x^20+240223
48*x^18+73676772*x^17+389319040*x^15+671757312*x^14+944780032*x^13+834330624*x^11+(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)*log(2)^10)/(x^22+34*x^21+544*x^20+5440*x^19+38080*x^18+198016*x^17+792064*x^1
6+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),x, algorithm="fricas")
[Out]
(x^24 + 36*x^23 + 618*x^22 + 6736*x^21 + 52352*x^20 + 308752*x^19 + 1435018*x^18 + 5386052*x^17 + 16590145*x^1
6 + 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 + 32461465
6*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)^10 + 371027456*x^10 + 377958400*x^9 + 131072*(35*x^12 + 510*x^11 + 3177*x^10 + 10942*x^9 + 22419*x^8 + 2721
6*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 + 2
84352512*x^7 - 32768*(7*x^15 + 135*x^14 + 1167*x^13 + 5953*x^12 + 19845*x^11 + 45201*x^10 + 71320*x^9 + 76788*
x^8 + 51552*x^7 + 8480*x^6 - 34560*x^5 - 67200*x^4 - 78592*x^3 - 62208*x^2 - 30720*x - 7168)*log(2)^6 + 200974
336*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 + 15
32160*x^4 + 1118208*x^3 + 571392*x^2 + 184320*x + 28672)*log(2)^4 + 53854208*x^4 + 18743296*x^3 - 128*(x^21 +
32*x^20 + 487*x^19 + 4685*x^18 + 31919*x^17 + 163405*x^16 + 650382*x^15 + 2052851*x^14 + 5191132*x^13 + 105437
80*x^12 + 17115904*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 - 147456*x - 16384)*log(2)^2 + 4718592*x^2 + 786432*x + 65536)/(x^2
0 + 32*x^19 + 480*x^18 + 4480*x^17 + 29120*x^16 + 139776*x^15 + 512512*x^14 + 1464320*x^13 + 3294720*x^12 + 58
57280*x^11 + 8200192*x^10 + 8945664*x^9 + 7454720*x^8 + 4587520*x^7 + 1966080*x^6 + 524288*x^5 + 65536*x^4)
Sympy [F(-1)]
Timed out. \[
\int \frac {-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}+24022348 x^{18}+6392524 x^{19}+1366512 x^{20}+229024 x^{21}+28984 x^{22}+2604 x^{23}+148 x^{24}+4 x^{25}+\left (-16777216-155189248 x-692060160 x^2-1974468608 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}-85735680 x^{16}-22563072 x^{17}-4534144 x^{18}-670720 x^{19}-68736 x^{20}-4352 x^{21}-128 x^{22}\right ) \log ^2(2)+\left (-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}-598818816 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}\right ) \log ^4(2)+\left (-1879048192-10737418240 x-27279753216 x^2-41842376704 x^3-43780145152 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^{12}+872218624 x^{13}+179208192 x^{14}+21495808 x^{15}+1146880 x^{16}\right ) \log ^6(2)+\left (-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}\right ) \log ^8(2)+\left (-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+645922816 x^{10}\right ) \log ^{10}(2)+\left (-60129542144-169651208192 x-41875931136 x^2+84825604096 x^3-18253611008 x^4-87375740928 x^5-43419435008 x^6-6576668672 x^7\right ) \log ^{12}(2)+\left (-68719476736-171798691840 x+25769803776 x^2+120259084288 x^3+36507222016 x^4\right ) \log ^{14}(2)+(-34359738368-85899345920 x) \log ^{16}(2)}{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}+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}} \, dx=\text {Timed out}
\]
[In]
integrate((-524288+1366512*x**20-6029312*x-33816576*x**2-318636032*x**4-385378304*x**9-627376128*x**5-95328665
6*x**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**7-18554290176*x
**6-21851799552*x**5-19465764864*x**4-12821987328*x**3-5926551552*x**2-1719664640*x-234881024)*ln(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**15-60404428
8*x**14-1163537408*x**13-1876140032*x**12-2665648128*x**11-3588702208*x**10-4819566592*x**9-6314655744*x**8-75
07476480*x**7-7583563776*x**6-6230900736*x**5-4028628992*x**4-1974468608*x**3-692060160*x**2-155189248*x-16777
216)*ln(2)**2+(-85899345920*x-34359738368)*ln(2)**16+(36507222016*x**4+120259084288*x**3+25769803776*x**2-1717
98691840*x-68719476736)*ln(2)**14+(-6576668672*x**7-43419435008*x**6-87375740928*x**5-18253611008*x**4+8482560
4096*x**3-41875931136*x**2-169651208192*x-60129542144)*ln(2)**12+(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**2-104
152956928*x-30064771072)*ln(2)**10+24022348*x**18+73676772*x**17+389319040*x**15+671757312*x**14+944780032*x**
13+834330624*x**11+1048039936*x**12+6392524*x**19+186202360*x**16-122421248*x**3+148*x**24+2604*x**23+28984*x*
*22+229024*x**21+(-36700160*x**13-528220160*x**12-3228303360*x**11-10779099136*x**10-20920139776*x**9-22866296
832*x**8-12507414528*x**7-6165626880*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+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**6-3296722
9440*x**5-43780145152*x**4-41842376704*x**3-27279753216*x**2-10737418240*x-1879048192)*ln(2)**6-1107525632*x**
7-919941120*x**8+4*x**25+294787072*x**10)/(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+1
1141120*x**8+4456448*x**7+1114112*x**6+131072*x**5),x)
[Out]
Timed out
Maxima [B] (verification not implemented)
Leaf count of result is larger than twice the leaf count of optimal. 780 vs. \(2 (24) = 48\).
Time = 0.26 (sec) , antiderivative size = 780, normalized size of antiderivative = 30.00
\[
\int \frac {-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}+24022348 x^{18}+6392524 x^{19}+1366512 x^{20}+229024 x^{21}+28984 x^{22}+2604 x^{23}+148 x^{24}+4 x^{25}+\left (-16777216-155189248 x-692060160 x^2-1974468608 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}-85735680 x^{16}-22563072 x^{17}-4534144 x^{18}-670720 x^{19}-68736 x^{20}-4352 x^{21}-128 x^{22}\right ) \log ^2(2)+\left (-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}-598818816 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}\right ) \log ^4(2)+\left (-1879048192-10737418240 x-27279753216 x^2-41842376704 x^3-43780145152 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^{12}+872218624 x^{13}+179208192 x^{14}+21495808 x^{15}+1146880 x^{16}\right ) \log ^6(2)+\left (-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}\right ) \log ^8(2)+\left (-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+645922816 x^{10}\right ) \log ^{10}(2)+\left (-60129542144-169651208192 x-41875931136 x^2+84825604096 x^3-18253611008 x^4-87375740928 x^5-43419435008 x^6-6576668672 x^7\right ) \log ^{12}(2)+\left (-68719476736-171798691840 x+25769803776 x^2+120259084288 x^3+36507222016 x^4\right ) \log ^{14}(2)+(-34359738368-85899345920 x) \log ^{16}(2)}{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}+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}} \, dx=\text {Too large to display}
\]
[In]
integrate((-524288-6029312*x-627376128*x^5-318636032*x^4-33816576*x^2+1048039936*x^12+186202360*x^16+(-3670016
0*x^13-528220160*x^12-3228303360*x^11-10779099136*x^10-20920139776*x^9-22866296832*x^8-12507414528*x^7-6165626
880*x^6-17817403392*x^5-41641050112*x^4-66504884224*x^3-71068286976*x^2-41607495680*x-9395240960)*log(2)^8+(11
46880*x^16+21495808*x^15+179208192*x^14+872218624*x^13+2731442176*x^12+5707530240*x^11+7933394944*x^10+6824132
608*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^18-3336192*x^17-20511744*x^16-83576832*x^15-2
35607040*x^14-463816704*x^13-628064256*x^12-598818816*x^11-692240384*x^10-1961197568*x^9-5668208640*x^8-119223
09120*x^7-18554290176*x^6-21851799552*x^5-19465764864*x^4-12821987328*x^3-5926551552*x^2-1719664640*x-23488102
4)*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^1
5-604044288*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
)*log(2)^2+(-85899345920*x-34359738368)*log(2)^16+(36507222016*x^4+120259084288*x^3+25769803776*x^2-1717986918
40*x-68719476736)*log(2)^14+(-6576668672*x^7-43419435008*x^6-87375740928*x^5-18253611008*x^4+84825604096*x^3-4
1875931136*x^2-169651208192*x-60129542144)*log(2)^12-953286656*x^6+4*x^25-122421248*x^3-385378304*x^9+29478707
2*x^10-1107525632*x^7-919941120*x^8+148*x^24+2604*x^23+28984*x^22+229024*x^21+6392524*x^19+1366512*x^20+240223
48*x^18+73676772*x^17+389319040*x^15+671757312*x^14+944780032*x^13+834330624*x^11+(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)*log(2)^10)/(x^22+34*x^21+544*x^20+5440*x^19+38080*x^18+198016*x^17+792064*x^1
6+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),x, algorithm="maxima")
[Out]
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 - 29856*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 - 93
73000*log(2)^2 + 455351)*x^12 - 1536*(43520*log(2)^8 - 423360*log(2)^6 + 674016*log(2)^4 - 742976*log(2)^2 + 4
5279)*x^11 - 7516192768*log(2)^12 - 512*(813312*log(2)^8 - 2892864*log(2)^6 + 2947824*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 - 49907)*x^9 - 3758096384*log(2)^10 + 1536*(393216*log(2)^10 - 1913088*log(2)^8 + 1638144*log(2)^6 - 1033
824*log(2)^4 + 836784*log(2)^2 - 163969)*x^8 + 8192*(294912*log(2)^10 - 435456*log(2)^8 + 206208*log(2)^6 - 17
2512*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 - 3
3792*log(2)^10 + 10752*log(2)^8 + 11520*log(2)^6 + 16536*log(2)^4 + 5908*log(2)^2 + 1181)*x^5 - 234881024*log(
2)^6 - 16384*(356352*log(2)^12 + 18432*log(2)^10 + 76032*log(2)^8 + 134400*log(2)^6 + 95760*log(2)^4 + 28136*l
og(2)^2 + 3287)*x^4 + 131072*(16384*log(2)^14 - 8192*log(2)^12 - 6144*log(2)^10 - 18688*log(2)^8 - 19648*log(2
)^6 - 8736*log(2)^4 - 1808*log(2)^2 - 143)*x^3 - 29360128*log(2)^4 + 1572864*(4096*log(2)^14 + 3072*log(2)^12
- 768*log(2)^10 - 2176*log(2)^8 - 1296*log(2)^6 - 372*log(2)^4 - 53*log(2)^2 - 3)*x^2 - 786432*(4096*log(2)^12
+ 6144*log(2)^10 + 3840*log(2)^8 + 1280*log(2)^6 + 240*log(2)^4 + 24*log(2)^2 + 1)*x - 2097152*log(2)^2 - 655
36)/(x^20 + 32*x^19 + 480*x^18 + 4480*x^17 + 29120*x^16 + 139776*x^15 + 512512*x^14 + 1464320*x^13 + 3294720*x
^12 + 5857280*x^11 + 8200192*x^10 + 8945664*x^9 + 7454720*x^8 + 4587520*x^7 + 1966080*x^6 + 524288*x^5 + 65536
*x^4)
Giac [B] (verification not implemented)
Leaf count of result is larger than twice the leaf count of optimal. 1412 vs. \(2 (24) = 48\).
Time = 0.30 (sec) , antiderivative size = 1412, normalized size of antiderivative = 54.31
\[
\int \frac {-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}+24022348 x^{18}+6392524 x^{19}+1366512 x^{20}+229024 x^{21}+28984 x^{22}+2604 x^{23}+148 x^{24}+4 x^{25}+\left (-16777216-155189248 x-692060160 x^2-1974468608 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}-85735680 x^{16}-22563072 x^{17}-4534144 x^{18}-670720 x^{19}-68736 x^{20}-4352 x^{21}-128 x^{22}\right ) \log ^2(2)+\left (-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}-598818816 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}\right ) \log ^4(2)+\left (-1879048192-10737418240 x-27279753216 x^2-41842376704 x^3-43780145152 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^{12}+872218624 x^{13}+179208192 x^{14}+21495808 x^{15}+1146880 x^{16}\right ) \log ^6(2)+\left (-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}\right ) \log ^8(2)+\left (-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+645922816 x^{10}\right ) \log ^{10}(2)+\left (-60129542144-169651208192 x-41875931136 x^2+84825604096 x^3-18253611008 x^4-87375740928 x^5-43419435008 x^6-6576668672 x^7\right ) \log ^{12}(2)+\left (-68719476736-171798691840 x+25769803776 x^2+120259084288 x^3+36507222016 x^4\right ) \log ^{14}(2)+(-34359738368-85899345920 x) \log ^{16}(2)}{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}+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}} \, dx=\text {Too large to display}
\]
[In]
integrate((-524288-6029312*x-627376128*x^5-318636032*x^4-33816576*x^2+1048039936*x^12+186202360*x^16+(-3670016
0*x^13-528220160*x^12-3228303360*x^11-10779099136*x^10-20920139776*x^9-22866296832*x^8-12507414528*x^7-6165626
880*x^6-17817403392*x^5-41641050112*x^4-66504884224*x^3-71068286976*x^2-41607495680*x-9395240960)*log(2)^8+(11
46880*x^16+21495808*x^15+179208192*x^14+872218624*x^13+2731442176*x^12+5707530240*x^11+7933394944*x^10+6824132
608*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^18-3336192*x^17-20511744*x^16-83576832*x^15-2
35607040*x^14-463816704*x^13-628064256*x^12-598818816*x^11-692240384*x^10-1961197568*x^9-5668208640*x^8-119223
09120*x^7-18554290176*x^6-21851799552*x^5-19465764864*x^4-12821987328*x^3-5926551552*x^2-1719664640*x-23488102
4)*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^1
5-604044288*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
)*log(2)^2+(-85899345920*x-34359738368)*log(2)^16+(36507222016*x^4+120259084288*x^3+25769803776*x^2-1717986918
40*x-68719476736)*log(2)^14+(-6576668672*x^7-43419435008*x^6-87375740928*x^5-18253611008*x^4+84825604096*x^3-4
1875931136*x^2-169651208192*x-60129542144)*log(2)^12-953286656*x^6+4*x^25-122421248*x^3-385378304*x^9+29478707
2*x^10-1107525632*x^7-919941120*x^8+148*x^24+2604*x^23+28984*x^22+229024*x^21+6392524*x^19+1366512*x^20+240223
48*x^18+73676772*x^17+389319040*x^15+671757312*x^14+944780032*x^13+834330624*x^11+(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)*log(2)^10)/(x^22+34*x^21+544*x^20+5440*x^19+38080*x^18+198016*x^17+792064*x^1
6+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),x, algorithm="giac")
[Out]
x^4 + 4*x^3 - 128*x*log(2)^2 + 10*x^2 + 16*x - (6684672*x^3*log(2)^16 - 2228224*x^2*log(2)^16 + 12615680*x^3*l
og(2)^14 + 524288*x*log(2)^16 - 4358144*x^2*log(2)^14 - 65536*log(2)^16 + 9420800*x^3*log(2)^12 + 1048576*x*lo
g(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)^1
0 + 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 - 16*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*l
og(2)^16 + 1576960*x^15*log(2)^14 + 392232960*x^13*log(2)^16 + 49917952*x^14*log(2)^14 + 3611811840*x^12*log(2
)^16 + 1177600*x^15*log(2)^12 + 739639296*x^13*log(2)^14 + 23115595776*x^11*log(2)^16 + 37254144*x^14*log(2)^1
2 + 6807470080*x^12*log(2)^14 + 108973522944*x^10*log(2)^16 + 434688*x^15*log(2)^10 + 551626752*x^13*log(2)^12
+ 43542904832*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)^1
0 + 32421183488*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*x^10*log(2)^12 + 2047817547776*x^8*log(2)^14 + 4068344856576*x^
6*log(2)^16 + 6608*x^15*log(2)^6 + 37332864*x^13*log(2)^8 + 11909136384*x^11*log(2)^10 + 546658975744*x^9*log(
2)^12 + 4462812856320*x^7*log(2)^14 + 5424459808768*x^5*log(2)^16 + 207696*x^14*log(2)^6 + 342075200*x^12*log(
2)^8 + 55954096128*x^10*log(2)^10 + 1519241265152*x^8*log(2)^12 + 7625372598272*x^6*log(2)^14 + 5547742986240*
x^4*log(2)^16 + 216*x^15*log(2)^4 + 3053184*x^13*log(2)^6 + 2176952320*x^11*log(2)^8 + 200070463488*x^9*log(2)
^10 + 3305213263872*x^7*log(2)^12 + 10148370186240*x^5*log(2)^14 + 4226851799040*x^3*log(2)^16 + 7668*x^14*log
(2)^4 + 27851840*x^12*log(2)^6 + 10196293632*x^10*log(2)^8 + 554741071872*x^8*log(2)^10 + 5635509321728*x^6*lo
g(2)^12 + 10353496817664*x^4*log(2)^14 + 2275997122560*x^2*log(2)^16 - 108*x^15*log(2)^2 + 121176*x^13*log(2)^
4 + 176335872*x^11*log(2)^6 + 36326506496*x^9*log(2)^8 + 1203554746368*x^7*log(2)^10 + 7480074567680*x^5*log(2
)^12 + 7861333655552*x^3*log(2)^14 + 780341870592*x*log(2)^16 - 3159*x^14*log(2)^2 + 1149768*x^12*log(2)^4 + 8
20835328*x^10*log(2)^6 + 100299730944*x^8*log(2)^8 + 2045249716224*x^6*log(2)^10 + 7604611842048*x^4*log(2)^12
+ 4211416760320*x^2*log(2)^14 + 130056978432*log(2)^16 - 43092*x^13*log(2)^2 + 7399296*x^11*log(2)^4 + 290279
0144*x^9*log(2)^6 + 216531763200*x^7*log(2)^8 + 2703450701824*x^5*log(2)^10 + 5746599133184*x^3*log(2)^12 + 14
31834722304*x*log(2)^14 - 363636*x^12*log(2)^2 + 34442496*x^10*log(2)^4 + 7944339456*x^8*log(2)^6 + 3658040442
88*x^6*log(2)^8 + 2733985234944*x^4*log(2)^10 + 3057270128640*x^2*log(2)^12 + 234881024000*log(2)^14 - 2122848
*x^11*log(2)^2 + 120396672*x^9*log(2)^4 + 16974581760*x^7*log(2)^6 + 480129482752*x^5*log(2)^8 + 2051618635776
*x^3*log(2)^10 + 1028250402816*x*log(2)^12 - 9081072*x^10*log(2)^2 + 323097984*x^8*log(2)^4 + 28338638848*x^6*
log(2)^6 + 481389723648*x^4*log(2)^8 + 1080975949824*x^2*log(2)^10 + 165649842176*log(2)^12 - 29405376*x^9*log
(2)^2 + 673339392*x^7*log(2)^4 + 36697767936*x^5*log(2)^6 + 357365972992*x^3*log(2)^8 + 358499745792*x*log(2)^
10 - 73389888*x^8*log(2)^2 + 1092731904*x^6*log(2)^4 + 36236181504*x^4*log(2)^6 + 185693634560*x^2*log(2)^8 +
56560189440*log(2)^10 - 142331904*x^7*log(2)^2 + 1372833792*x^5*log(2)^4 + 26434994176*x^3*log(2)^6 + 60467183
616*x*log(2)^8 - 214486272*x^6*log(2)^2 + 1313667072*x^4*log(2)^4 + 13461749760*x^2*log(2)^6 + 9310830592*log(
2)^8 - 249080832*x^5*log(2)^2 + 928088064*x^3*log(2)^4 + 4281335808*x*log(2)^6 - 218889216*x^4*log(2)^2 + 4574
08512*x^2*log(2)^4 + 641204224*log(2)^6 - 140894208*x^3*log(2)^2 + 140673024*x*log(2)^4 - 62705664*x^2*log(2)^
2 + 20348928*log(2)^4 - 17252352*x*log(2)^2 - 2211840*log(2)^2)/(x + 2)^16
Mupad [B] (verification not implemented)
Time = 11.66 (sec) , antiderivative size = 767, normalized size of antiderivative = 29.50
\[
\int \frac {-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}+24022348 x^{18}+6392524 x^{19}+1366512 x^{20}+229024 x^{21}+28984 x^{22}+2604 x^{23}+148 x^{24}+4 x^{25}+\left (-16777216-155189248 x-692060160 x^2-1974468608 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}-85735680 x^{16}-22563072 x^{17}-4534144 x^{18}-670720 x^{19}-68736 x^{20}-4352 x^{21}-128 x^{22}\right ) \log ^2(2)+\left (-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}-598818816 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}\right ) \log ^4(2)+\left (-1879048192-10737418240 x-27279753216 x^2-41842376704 x^3-43780145152 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^{12}+872218624 x^{13}+179208192 x^{14}+21495808 x^{15}+1146880 x^{16}\right ) \log ^6(2)+\left (-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}\right ) \log ^8(2)+\left (-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+645922816 x^{10}\right ) \log ^{10}(2)+\left (-60129542144-169651208192 x-41875931136 x^2+84825604096 x^3-18253611008 x^4-87375740928 x^5-43419435008 x^6-6576668672 x^7\right ) \log ^{12}(2)+\left (-68719476736-171798691840 x+25769803776 x^2+120259084288 x^3+36507222016 x^4\right ) \log ^{14}(2)+(-34359738368-85899345920 x) \log ^{16}(2)}{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}+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}} \, dx=\text {Too large to display}
\]
[In]
int((log(2)^6*(1830813696*x^8 - 27279753216*x^2 - 41842376704*x^3 - 43780145152*x^4 - 32967229440*x^5 - 180984
21760*x^6 - 6245318656*x^7 - 10737418240*x + 6824132608*x^9 + 7933394944*x^10 + 5707530240*x^11 + 2731442176*x
^12 + 872218624*x^13 + 179208192*x^14 + 21495808*x^15 + 1146880*x^16 - 1879048192) - log(2)^4*(1719664640*x +
5926551552*x^2 + 12821987328*x^3 + 19465764864*x^4 + 21851799552*x^5 + 18554290176*x^6 + 11922309120*x^7 + 566
8208640*x^8 + 1961197568*x^9 + 692240384*x^10 + 598818816*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 + 234881024) - 6029312*x - log(2
)^16*(85899345920*x + 34359738368) - log(2)^2*(155189248*x + 692060160*x^2 + 1974468608*x^3 + 4028628992*x^4 +
6230900736*x^5 + 7583563776*x^6 + 7507476480*x^7 + 6314655744*x^8 + 4819566592*x^9 + 3588702208*x^10 + 266564
8128*x^11 + 1876140032*x^12 + 1163537408*x^13 + 604044288*x^14 + 254886144*x^15 + 85735680*x^16 + 22563072*x^1
7 + 4534144*x^18 + 670720*x^19 + 68736*x^20 + 4352*x^21 + 128*x^22 + 16777216) + log(2)^14*(25769803776*x^2 -
171798691840*x + 120259084288*x^3 + 36507222016*x^4 - 68719476736) - log(2)^8*(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 + 9395240960) - 33816576
*x^2 - 122421248*x^3 - 318636032*x^4 - 627376128*x^5 - 953286656*x^6 - 1107525632*x^7 - 919941120*x^8 - 385378
304*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 + 2
604*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) - 524288)/(131072*x^5 + 1114112*x^6 + 4456448*x^7 + 111411
20*x^8 + 19496960*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)
[Out]
(x*(18874368*log(2)^2 + 188743680*log(2)^4 + 1006632960*log(2)^6 + 3019898880*log(2)^8 + 4831838208*log(2)^10
+ 3221225472*log(2)^12 + 786432) - x^15*(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 + 3422552064*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 + 44236
80*log(2)^6 - 2546016) + x^5*(580780032*log(2)^2 + 1625554944*log(2)^4 + 1132462080*log(2)^6 + 1056964608*log(
2)^8 - 3321888768*log(2)^10 + 3019898880*log(2)^12 + 116097024) - x^9*(1774755840*log(2)^2 - 1709424640*log(2)
^4 + 2337013760*log(2)^6 - 1434189824*log(2)^8 + 58720256*log(2)^10 - 204419072) + x^3*(236978176*log(2)^2 + 1
145044992*log(2)^4 + 2575302656*log(2)^6 + 2449473536*log(2)^8 + 805306368*log(2)^10 + 1073741824*log(2)^12 -
2147483648*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 + 5838471168*log(2)^12 + 53854208) + x^10*(1509285888*log(2)^4 - 1655560192*log(2)^2 - 1481146368*log(2)
^6 + 416415744*log(2)^8 + 133033472) - x^8*(1285300224*log(2)^2 - 1587953664*log(2)^4 + 2516189184*log(2)^6 -
2938503168*log(2)^8 + 603979776*log(2)^10 - 251856384) + x^12*(543095808*log(2)^4 - 599872000*log(2)^2 - 19506
7904*log(2)^6 + 4587520*log(2)^8 + 29142464) - x^7*(414908416*log(2)^2 - 1413218304*log(2)^4 + 1689255936*log(
2)^6 - 3567255552*log(2)^8 + 2415919104*log(2)^10 - 247390208) - x^19*(896*log(2)^2 - 16) + 2097152*log(2)^2 +
29360128*log(2)^4 + 234881024*log(2)^6 + 1174405120*log(2)^8 + 3758096384*log(2)^10 + 7516192768*log(2)^12 +
8589934592*log(2)^14 + 4294967296*log(2)^16 + x^6*(317685760*log(2)^2 + 1457258496*log(2)^4 - 277872640*log(2)
^6 + 2422210560*log(2)^8 - 4504682496*log(2)^10 + 469762048*log(2)^12 + 191930368) + x^18*(7168*log(2)^4 - 262
40*log(2)^2 + 522) + x^17*(175104*log(2)^4 - 358272*log(2)^2 + 8004) + x^16*(1972224*log(2)^4 - 3024512*log(2)
^2 + 76609) + x^11*(1035288576*log(2)^4 - 1141211136*log(2)^2 - 650280960*log(2)^6 + 66846720*log(2)^8 + 69548
544) + 65536)/(65536*x^4 + 524288*x^5 + 1966080*x^6 + 4587520*x^7 + 7454720*x^8 + 8945664*x^9 + 8200192*x^10 +
5857280*x^11 + 3294720*x^12 + 1464320*x^13 + 512512*x^14 + 139776*x^15 + 29120*x^16 + 4480*x^17 + 480*x^18 +
32*x^19 + x^20) - x*(128*log(2)^2 - 16) + 10*x^2 + 4*x^3 + x^4