3.70.15 \(\int \frac {-152587890625-3784179687500 x-43945312500000 x^2-317187500000000 x^3-1592500000000000 x^4-5896800000000000 x^5-16656640000000000 x^6-36608000000000000 x^7-63258624000000000 x^8-86219161600000000 x^9-92366962688000000 x^{10}-76947023462400000 x^{11}-48855252992000000 x^{12}-22849226014720000 x^{13}-7421703487488000 x^{14}-1495335813775360 x^{15}-140737488355328 x^{16}+(732421875000 x^2+15859375000000 x^3+159250000000000 x^4+982800000000000 x^5+4164160000000000 x^6+12812800000000000 x^7+29520691200000000 x^8+51731496960000000 x^9+69275222016000000 x^{10}+70534771507200000 x^{11}+53740778291200000 x^{12}+29703993819136000 x^{13}+11256250289356800 x^{14}+2616837674106880 x^{15}[phone] x^{16}) \log (4)+(-1531250000000 x^4-28350000000000 x^5-240240000000000 x^6-1232000000000000 x^7-4257792000000000 x^8-10445783040000000 x^9-18651021312000000 x^{10}-24415882444800000 x^{11}-23253221376000000 x^{12}-15708842885120000 x^{13}-7143389606707200 x^{14}-1962628255580160 x^{15}-246290604621824 x^{16}) \log ^2(4)+(1820000000000 x^6+28000000000000 x^7+193536000000000 x^8+791347200000000 x^9+2119434240000000 x^{10}+3884344934400000 x^{11}+4932501504000000 x^{12}+4284229877760000 x^{13}+2435246456832000 x^{14}[phone] x^{15}[phone] x^{16}) \log ^3(4)+(-1344000000000 x^8-16486400000000 x^9-88309760000000 x^{10}-269746176000000 x^{11}-513802240000000 x^{12}-624783523840000 x^{13}-473520144384000 x^{14}-204440443289600 x^{15}-38482906972160 x^{16}) \log ^4(4)+(630784000000 x^{10}[phone] x^{11}[phone] x^{12}[phone] x^{13}[phone] x^{14}[phone] x^{15}[phone] x^{16}) \log ^5(4)+(-183500800000 x^{12}-1115684864000 x^{13}-2536715059200 x^{14}-2555505541120 x^{15}-962072674304 x^{16}) \log ^6(4)+(30198988800 x^{14}[phone] x^{15}[phone] x^{16}) \log ^7(4)-2147483648 x^{16} \log ^8(4)}{134217728 x^{33}} \, dx\)

Optimal. Leaf size=22 \[ \frac {\left (\left (2+\frac {5}{4 x}\right )^2-\log (4)\right )^8}{x^{16}} \]

________________________________________________________________________________________

Rubi [B]  time = 0.64, antiderivative size = 341, normalized size of antiderivative = 15.50, number of steps used = 4, number of rules used = 3, integrand size = 451, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.007, Rules used = {6, 12, 14} \begin {gather*} \frac {152587890625}{4294967296 x^{32}}+\frac {30517578125}{33554432 x^{31}}+\frac {6103515625 (60-\log (4))}{33554432 x^{30}}+\frac {8544921875 (20-\log (4))}{2097152 x^{29}}+\frac {1708984375 \left (1040+\log ^2(4)-104 \log (4)\right )}{4194304 x^{28}}+\frac {341796875 \left (624+3 \log ^2(4)-104 \log (4)\right )}{131072 x^{27}}+\frac {68359375 \left (9152-\log ^3(4)+132 \log ^2(4)-2288 \log (4)\right )}{131072 x^{26}}+\frac {1953125 \left (45760-35 \log ^3(4)+1540 \log ^2(4)-16016 \log (4)\right )}{8192 x^{25}}+\frac {390625 \left (1647360+35 \log ^4(4)-5040 \log ^3(4)+110880 \log ^2(4)-768768 \log (4)\right )}{32768 x^{24}}+\frac {78125 (4-\log (4)) \left (45760-35 \log ^3(4)+1540 \log ^2(4)-16016 \log (4)\right )}{512 x^{23}}+\frac {109375 (4-\log (4))^2 \left (9152-\log ^3(4)+132 \log ^2(4)-2288 \log (4)\right )}{512 x^{22}}+\frac {21875 (4-\log (4))^3 \left (624+3 \log ^2(4)-104 \log (4)\right )}{32 x^{21}}+\frac {4375 (4-\log (4))^4 \left (1040+\log ^2(4)-104 \log (4)\right )}{64 x^{20}}+\frac {875 (4-\log (4))^5 (20-\log (4))}{2 x^{19}}+\frac {25 (4-\log (4))^6 (60-\log (4))}{2 x^{18}}+\frac {40 (4-\log (4))^7}{x^{17}}+\frac {(4-\log (4))^8}{x^{16}} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(-152587890625 - 3784179687500*x - 43945312500000*x^2 - 317187500000000*x^3 - 1592500000000000*x^4 - 58968
00000000000*x^5 - 16656640000000000*x^6 - 36608000000000000*x^7 - 63258624000000000*x^8 - 86219161600000000*x^
9 - 92366962688000000*x^10 - 76947023462400000*x^11 - 48855252992000000*x^12 - 22849226014720000*x^13 - 742170
3487488000*x^14 - 1495335813775360*x^15 - 140737488355328*x^16 + (732421875000*x^2 + 15859375000000*x^3 + 1592
50000000000*x^4 + 982800000000000*x^5 + 4164160000000000*x^6 + 12812800000000000*x^7 + 29520691200000000*x^8 +
51731496960000000*x^9 + 69275222016000000*x^10 + 70534771507200000*x^11 + 53740778291200000*x^12 + 2970399381
9136000*x^13 + 11256250289356800*x^14 + 2616837674106880*x^15 + 281474976710656*x^16)*Log[4] + (-1531250000000
*x^4 - 28350000000000*x^5 - 240240000000000*x^6 - 1232000000000000*x^7 - 4257792000000000*x^8 - 10445783040000
000*x^9 - 18651021312000000*x^10 - 24415882444800000*x^11 - 23253221376000000*x^12 - 15708842885120000*x^13 -
7143389606707200*x^14 - 1962628255580160*x^15 - 246290604621824*x^16)*Log[4]^2 + (1820000000000*x^6 + 28000000
000000*x^7 + 193536000000000*x^8 + 791347200000000*x^9 + 2119434240000000*x^10 + 3884344934400000*x^11 + 49325
01504000000*x^12 + 4284229877760000*x^13 + 2435246456832000*x^14 + 817761773158400*x^15 + 123145302310912*x^16
)*Log[4]^3 + (-1344000000000*x^8 - 16486400000000*x^9 - 88309760000000*x^10 - 269746176000000*x^11 - 513802240
000000*x^12 - 624783523840000*x^13 - 473520144384000*x^14 - 204440443289600*x^15 - 38482906972160*x^16)*Log[4]
^4 + (630784000000*x^10 + 5780275200000*x^11 + 22020096000000*x^12 + 44627394560000*x^13 + 50734301184000*x^14
+ 30666066493440*x^15 + 7696581394432*x^16)*Log[4]^5 + (-183500800000*x^12 - 1115684864000*x^13 - 25367150592
00*x^14 - 2555505541120*x^15 - 962072674304*x^16)*Log[4]^6 + (30198988800*x^14 + 91268055040*x^15 + 6871947673
6*x^16)*Log[4]^7 - 2147483648*x^16*Log[4]^8)/(134217728*x^33),x]

[Out]

152587890625/(4294967296*x^32) + 30517578125/(33554432*x^31) + (40*(4 - Log[4])^7)/x^17 + (4 - Log[4])^8/x^16
+ (8544921875*(20 - Log[4]))/(2097152*x^29) + (875*(4 - Log[4])^5*(20 - Log[4]))/(2*x^19) + (6103515625*(60 -
Log[4]))/(33554432*x^30) + (25*(4 - Log[4])^6*(60 - Log[4]))/(2*x^18) + (1708984375*(1040 - 104*Log[4] + Log[4
]^2))/(4194304*x^28) + (4375*(4 - Log[4])^4*(1040 - 104*Log[4] + Log[4]^2))/(64*x^20) + (341796875*(624 - 104*
Log[4] + 3*Log[4]^2))/(131072*x^27) + (21875*(4 - Log[4])^3*(624 - 104*Log[4] + 3*Log[4]^2))/(32*x^21) + (1953
125*(45760 - 16016*Log[4] + 1540*Log[4]^2 - 35*Log[4]^3))/(8192*x^25) + (78125*(4 - Log[4])*(45760 - 16016*Log
[4] + 1540*Log[4]^2 - 35*Log[4]^3))/(512*x^23) + (68359375*(9152 - 2288*Log[4] + 132*Log[4]^2 - Log[4]^3))/(13
1072*x^26) + (109375*(4 - Log[4])^2*(9152 - 2288*Log[4] + 132*Log[4]^2 - Log[4]^3))/(512*x^22) + (390625*(1647
360 - 768768*Log[4] + 110880*Log[4]^2 - 5040*Log[4]^3 + 35*Log[4]^4))/(32768*x^24)

Rule 6

Int[(u_.)*((w_.) + (a_.)*(v_) + (b_.)*(v_))^(p_.), x_Symbol] :> Int[u*((a + b)*v + w)^p, x] /; FreeQ[{a, b}, x
] &&  !FreeQ[v, x]

Rule 12

Int[(a_)*(u_), x_Symbol] :> Dist[a, Int[u, x], x] /; FreeQ[a, x] &&  !MatchQ[u, (b_)*(v_) /; FreeQ[b, x]]

Rule 14

Int[(u_)*((c_.)*(x_))^(m_.), x_Symbol] :> Int[ExpandIntegrand[(c*x)^m*u, x], x] /; FreeQ[{c, m}, x] && SumQ[u]
&&  !LinearQ[u, x] &&  !MatchQ[u, (a_) + (b_.)*(v_) /; FreeQ[{a, b}, x] && InverseFunctionQ[v]]

Rubi steps

too large to display

________________________________________________________________________________________

Mathematica [A]  time = 0.06, size = 23, normalized size = 1.05 \begin {gather*} \frac {\left (25+80 x-16 x^2 (-4+\log (4))\right )^8}{4294967296 x^{32}} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-152587890625 - 3784179687500*x - 43945312500000*x^2 - 317187500000000*x^3 - 1592500000000000*x^4 -
5896800000000000*x^5 - 16656640000000000*x^6 - 36608000000000000*x^7 - 63258624000000000*x^8 - 86219161600000
000*x^9 - 92366962688000000*x^10 - 76947023462400000*x^11 - 48855252992000000*x^12 - 22849226014720000*x^13 -
7421703487488000*x^14 - 1495335813775360*x^15 - 140737488355328*x^16 + (732421875000*x^2 + 15859375000000*x^3
+ 159250000000000*x^4 + 982800000000000*x^5 + 4164160000000000*x^6 + 12812800000000000*x^7 + 29520691200000000
*x^8 + 51731496960000000*x^9 + 69275222016000000*x^10 + 70534771507200000*x^11 + 53740778291200000*x^12 + 2970
3993819136000*x^13 + 11256250289356800*x^14 + 2616837674106880*x^15 + 281474976710656*x^16)*Log[4] + (-1531250
000000*x^4 - 28350000000000*x^5 - 240240000000000*x^6 - 1232000000000000*x^7 - 4257792000000000*x^8 - 10445783
040000000*x^9 - 18651021312000000*x^10 - 24415882444800000*x^11 - 23253221376000000*x^12 - 15708842885120000*x
^13 - 7143389606707200*x^14 - 1962628255580160*x^15 - 246290604621824*x^16)*Log[4]^2 + (1820000000000*x^6 + 28
000000000000*x^7 + 193536000000000*x^8 + 791347200000000*x^9 + 2119434240000000*x^10 + 3884344934400000*x^11 +
4932501504000000*x^12 + 4284229877760000*x^13 + 2435246456832000*x^14 + 817761773158400*x^15 + 12314530231091
2*x^16)*Log[4]^3 + (-1344000000000*x^8 - 16486400000000*x^9 - 88309760000000*x^10 - 269746176000000*x^11 - 513
802240000000*x^12 - 624783523840000*x^13 - 473520144384000*x^14 - 204440443289600*x^15 - 38482906972160*x^16)*
Log[4]^4 + (630784000000*x^10 + 5780275200000*x^11 + 22020096000000*x^12 + 44627394560000*x^13 + 5073430118400
0*x^14 + 30666066493440*x^15 + 7696581394432*x^16)*Log[4]^5 + (-183500800000*x^12 - 1115684864000*x^13 - 25367
15059200*x^14 - 2555505541120*x^15 - 962072674304*x^16)*Log[4]^6 + (30198988800*x^14 + 91268055040*x^15 + 6871
9476736*x^16)*Log[4]^7 - 2147483648*x^16*Log[4]^8)/(134217728*x^33),x]

[Out]

(25 + 80*x - 16*x^2*(-4 + Log[4]))^8/(4294967296*x^32)

________________________________________________________________________________________

fricas [B]  time = 0.62, size = 456, normalized size = 20.73 \begin {gather*} \frac {1099511627776 \, x^{16} \log \relax (2)^{8} + 281474976710656 \, x^{16} + 2814749767106560 \, x^{15} + 13194139533312000 \, x^{14} + 38482906972160000 \, x^{13} + 78168404787200000 \, x^{12} + 117252607180800000 \, x^{11} + 134351945728000000 \, x^{10} + 119957094400000000 \, x^{9} + 84344832000000000 \, x^{8} - 274877906944 \, {\left (64 \, x^{16} + 80 \, x^{15} + 25 \, x^{14}\right )} \log \relax (2)^{7} + 46858240000000000 \, x^{7} + 30064771072 \, {\left (4096 \, x^{16} + 10240 \, x^{15} + 9600 \, x^{14} + 4000 \, x^{13} + 625 \, x^{12}\right )} \log \relax (2)^{6} + 20500480000000000 \, x^{6} - 1879048192 \, {\left (262144 \, x^{16} + 983040 \, x^{15} + 1536000 \, x^{14} + 1280000 \, x^{13} + 600000 \, x^{12} + 150000 \, x^{11} + 15625 \, x^{10}\right )} \log \relax (2)^{5} + 6988800000000000 \, x^{5} + 73400320 \, {\left (16777216 \, x^{16} + 83886080 \, x^{15} + 183500800 \, x^{14} + 229376000 \, x^{13} + 179200000 \, x^{12} + 89600000 \, x^{11} + 28000000 \, x^{10} + 5000000 \, x^{9} + 390625 \, x^{8}\right )} \log \relax (2)^{4} + 1820000000000000 \, x^{4} - 1835008 \, {\left (1073741824 \, x^{16} + 6710886400 \, x^{15} + 18874368000 \, x^{14} + 31457280000 \, x^{13} + 34406400000 \, x^{12} + 25804800000 \, x^{11} + 13440000000 \, x^{10} + 4800000000 \, x^{9} + 1125000000 \, x^{8} + 156250000 \, x^{7} + 9765625 \, x^{6}\right )} \log \relax (2)^{3} + 350000000000000 \, x^{3} + 28672 \, {\left (68719476736 \, x^{16} + 515396075520 \, x^{15} + 1771674009600 \, x^{14} + 3690987520000 \, x^{13} + 5190451200000 \, x^{12} + 5190451200000 \, x^{11} + 3784704000000 \, x^{10} + 2027520000000 \, x^{9} + 792000000000 \, x^{8} + 220000000000 \, x^{7} + 41250000000 \, x^{6} + 4687500000 \, x^{5} + 244140625 \, x^{4}\right )} \log \relax (2)^{2} + 46875000000000 \, x^{2} - 256 \, {\left (4398046511104 \, x^{16} + 38482906972160 \, x^{15} + 156336809574400 \, x^{14} + 390842023936000 \, x^{13} + 671759728640000 \, x^{12} + 839699660800000 \, x^{11} + 787218432000000 \, x^{10} + 562298880000000 \, x^{9} + 307507200000000 \, x^{8} + 128128000000000 \, x^{7} + 40040000000000 \, x^{6} + 9100000000000 \, x^{5} + 1421875000000 \, x^{4} + 136718750000 \, x^{3} + 6103515625 \, x^{2}\right )} \log \relax (2) + 3906250000000 \, x + 152587890625}{4294967296 \, x^{32}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/134217728*(-152587890625-3784179687500*x-549755813888*x^16*log(2)^8+128*(68719476736*x^16+91268055
040*x^15+30198988800*x^14)*log(2)^7+64*(-962072674304*x^16-2555505541120*x^15-2536715059200*x^14-1115684864000
*x^13-183500800000*x^12)*log(2)^6+32*(7696581394432*x^16+30666066493440*x^15+50734301184000*x^14+4462739456000
0*x^13+22020096000000*x^12+5780275200000*x^11+630784000000*x^10)*log(2)^5+16*(-38482906972160*x^16-20444044328
9600*x^15-473520144384000*x^14-624783523840000*x^13-513802240000000*x^12-269746176000000*x^11-88309760000000*x
^10-16486400000000*x^9-1344000000000*x^8)*log(2)^4+8*(123145302310912*x^16+817761773158400*x^15+24352464568320
00*x^14+4284229877760000*x^13+4932501504000000*x^12+3884344934400000*x^11+2119434240000000*x^10+79134720000000
0*x^9+193536000000000*x^8+28000000000000*x^7+1820000000000*x^6)*log(2)^3+4*(-246290604621824*x^16-196262825558
0160*x^15-7143389606707200*x^14-15708842885120000*x^13-23253221376000000*x^12-24415882444800000*x^11-186510213
12000000*x^10-10445783040000000*x^9-4257792000000000*x^8-1232000000000000*x^7-240240000000000*x^6-283500000000
00*x^5-1531250000000*x^4)*log(2)^2+2*(281474976710656*x^16+2616837674106880*x^15+11256250289356800*x^14+297039
93819136000*x^13+53740778291200000*x^12+70534771507200000*x^11+69275222016000000*x^10+51731496960000000*x^9+29
520691200000000*x^8+12812800000000000*x^7+4164160000000000*x^6+982800000000000*x^5+159250000000000*x^4+1585937
5000000*x^3+732421875000*x^2)*log(2)-1592500000000000*x^4-317187500000000*x^3-43945312500000*x^2-1665664000000
0000*x^6-5896800000000000*x^5-36608000000000000*x^7-63258624000000000*x^8-92366962688000000*x^10-8621916160000
0000*x^9-1495335813775360*x^15-140737488355328*x^16-76947023462400000*x^11-48855252992000000*x^12-228492260147
20000*x^13-7421703487488000*x^14)/x^33,x, algorithm="fricas")

[Out]

1/4294967296*(1099511627776*x^16*log(2)^8 + 281474976710656*x^16 + 2814749767106560*x^15 + 13194139533312000*x
^14 + 38482906972160000*x^13 + 78168404787200000*x^12 + 117252607180800000*x^11 + 134351945728000000*x^10 + 11
9957094400000000*x^9 + 84344832000000000*x^8 - 274877906944*(64*x^16 + 80*x^15 + 25*x^14)*log(2)^7 + 468582400
00000000*x^7 + 30064771072*(4096*x^16 + 10240*x^15 + 9600*x^14 + 4000*x^13 + 625*x^12)*log(2)^6 + 205004800000
00000*x^6 - 1879048192*(262144*x^16 + 983040*x^15 + 1536000*x^14 + 1280000*x^13 + 600000*x^12 + 150000*x^11 +
15625*x^10)*log(2)^5 + 6988800000000000*x^5 + 73400320*(16777216*x^16 + 83886080*x^15 + 183500800*x^14 + 22937
6000*x^13 + 179200000*x^12 + 89600000*x^11 + 28000000*x^10 + 5000000*x^9 + 390625*x^8)*log(2)^4 + 182000000000
0000*x^4 - 1835008*(1073741824*x^16 + 6710886400*x^15 + 18874368000*x^14 + 31457280000*x^13 + 34406400000*x^12
+ 25804800000*x^11 + 13440000000*x^10 + 4800000000*x^9 + 1125000000*x^8 + 156250000*x^7 + 9765625*x^6)*log(2)
^3 + 350000000000000*x^3 + 28672*(68719476736*x^16 + 515396075520*x^15 + 1771674009600*x^14 + 3690987520000*x^
13 + 5190451200000*x^12 + 5190451200000*x^11 + 3784704000000*x^10 + 2027520000000*x^9 + 792000000000*x^8 + 220
000000000*x^7 + 41250000000*x^6 + 4687500000*x^5 + 244140625*x^4)*log(2)^2 + 46875000000000*x^2 - 256*(4398046
511104*x^16 + 38482906972160*x^15 + 156336809574400*x^14 + 390842023936000*x^13 + 671759728640000*x^12 + 83969
9660800000*x^11 + 787218432000000*x^10 + 562298880000000*x^9 + 307507200000000*x^8 + 128128000000000*x^7 + 400
40000000000*x^6 + 9100000000000*x^5 + 1421875000000*x^4 + 136718750000*x^3 + 6103515625*x^2)*log(2) + 39062500
00000*x + 152587890625)/x^32

________________________________________________________________________________________

giac [B]  time = 1.10, size = 631, normalized size = 28.68 result too large to display

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/134217728*(-152587890625-3784179687500*x-549755813888*x^16*log(2)^8+128*(68719476736*x^16+91268055
040*x^15+30198988800*x^14)*log(2)^7+64*(-962072674304*x^16-2555505541120*x^15-2536715059200*x^14-1115684864000
*x^13-183500800000*x^12)*log(2)^6+32*(7696581394432*x^16+30666066493440*x^15+50734301184000*x^14+4462739456000
0*x^13+22020096000000*x^12+5780275200000*x^11+630784000000*x^10)*log(2)^5+16*(-38482906972160*x^16-20444044328
9600*x^15-473520144384000*x^14-624783523840000*x^13-513802240000000*x^12-269746176000000*x^11-88309760000000*x
^10-16486400000000*x^9-1344000000000*x^8)*log(2)^4+8*(123145302310912*x^16+817761773158400*x^15+24352464568320
00*x^14+4284229877760000*x^13+4932501504000000*x^12+3884344934400000*x^11+2119434240000000*x^10+79134720000000
0*x^9+193536000000000*x^8+28000000000000*x^7+1820000000000*x^6)*log(2)^3+4*(-246290604621824*x^16-196262825558
0160*x^15-7143389606707200*x^14-15708842885120000*x^13-23253221376000000*x^12-24415882444800000*x^11-186510213
12000000*x^10-10445783040000000*x^9-4257792000000000*x^8-1232000000000000*x^7-240240000000000*x^6-283500000000
00*x^5-1531250000000*x^4)*log(2)^2+2*(281474976710656*x^16+2616837674106880*x^15+11256250289356800*x^14+297039
93819136000*x^13+53740778291200000*x^12+70534771507200000*x^11+69275222016000000*x^10+51731496960000000*x^9+29
520691200000000*x^8+12812800000000000*x^7+4164160000000000*x^6+982800000000000*x^5+159250000000000*x^4+1585937
5000000*x^3+732421875000*x^2)*log(2)-1592500000000000*x^4-317187500000000*x^3-43945312500000*x^2-1665664000000
0000*x^6-5896800000000000*x^5-36608000000000000*x^7-63258624000000000*x^8-92366962688000000*x^10-8621916160000
0000*x^9-1495335813775360*x^15-140737488355328*x^16-76947023462400000*x^11-48855252992000000*x^12-228492260147
20000*x^13-7421703487488000*x^14)/x^33,x, algorithm="giac")

[Out]

1/4294967296*(1099511627776*x^16*log(2)^8 - 17592186044416*x^16*log(2)^7 + 123145302310912*x^16*log(2)^6 - 219
90232555520*x^15*log(2)^7 - 492581209243648*x^16*log(2)^5 + 307863255777280*x^15*log(2)^6 - 6871947673600*x^14
*log(2)^7 + 1231453023109120*x^16*log(2)^4 - 1847179534663680*x^15*log(2)^5 + 288621802291200*x^14*log(2)^6 -
1970324836974592*x^16*log(2)^3 + 6157265115545600*x^15*log(2)^4 - 2886218022912000*x^14*log(2)^5 + 12025908428
8000*x^13*log(2)^6 + 1970324836974592*x^16*log(2)^2 - 12314530231091200*x^15*log(2)^3 + 13469017440256000*x^14
*log(2)^4 - 2405181685760000*x^13*log(2)^5 + 18790481920000*x^12*log(2)^6 - 1125899906842624*x^16*log(2) + 147
77436277309440*x^15*log(2)^2 - 34634616274944000*x^14*log(2)^3 + 16836271800320000*x^13*log(2)^4 - 11274289152
00000*x^12*log(2)^5 + 281474976710656*x^16 - 9851624184872960*x^15*log(2) + 50797437203251200*x^14*log(2)^2 -
57724360458240000*x^13*log(2)^3 + 13153337344000000*x^12*log(2)^4 - 281857228800000*x^11*log(2)^5 + 2814749767
106560*x^15 - 40022223251046400*x^14*log(2) + 105827994173440000*x^13*log(2)^2 - 63136019251200000*x^12*log(2)
^3 + 6576668672000000*x^11*log(2)^4 - 29360128000000*x^10*log(2)^5 + 13194139533312000*x^14 - 1000555581276160
00*x^13*log(2) + 148820616806400000*x^12*log(2)^2 - 47352014438400000*x^11*log(2)^3 + 2055208960000000*x^10*lo
g(2)^4 + 38482906972160000*x^13 - 171970490531840000*x^12*log(2) + 148820616806400000*x^11*log(2)^2 - 24662507
520000000*x^10*log(2)^3 + 367001600000000*x^9*log(2)^4 + 78168404787200000*x^12 - 214963113164800000*x^11*log(
2) + 108515033088000000*x^10*log(2)^2 - 8808038400000000*x^9*log(2)^3 + 28672000000000*x^8*log(2)^4 + 11725260
7180800000*x^11 - 201527918592000000*x^10*log(2) + 58133053440000000*x^9*log(2)^2 - 2064384000000000*x^8*log(2
)^3 + 134351945728000000*x^10 - 143948513280000000*x^9*log(2) + 22708224000000000*x^8*log(2)^2 - 2867200000000
00*x^7*log(2)^3 + 119957094400000000*x^9 - 78721843200000000*x^8*log(2) + 6307840000000000*x^7*log(2)^2 - 1792
0000000000*x^6*log(2)^3 + 84344832000000000*x^8 - 32800768000000000*x^7*log(2) + 1182720000000000*x^6*log(2)^2
+ 46858240000000000*x^7 - 10250240000000000*x^6*log(2) + 134400000000000*x^5*log(2)^2 + 20500480000000000*x^6
- 2329600000000000*x^5*log(2) + 7000000000000*x^4*log(2)^2 + 6988800000000000*x^5 - 364000000000000*x^4*log(2
) + 1820000000000000*x^4 - 35000000000000*x^3*log(2) + 350000000000000*x^3 - 1562500000000*x^2*log(2) + 468750
00000000*x^2 + 3906250000000*x + 152587890625)/x^32

________________________________________________________________________________________

maple [B]  time = 0.52, size = 454, normalized size = 20.64

method	result	size
norman	\(\frac {\frac {152587890625}{4294967296}+\left (-\frac {8544921875 \ln \relax (2)}{1048576}+\frac {42724609375}{524288}\right ) x^{3}+\left (-\frac {6103515625 \ln \relax (2)}{16777216}+\frac {91552734375}{8388608}\right ) x^{2}+\left (\frac {1025390625 \ln \relax (2)^{2}}{32768}-\frac {4443359375 \ln \relax (2)}{8192}+\frac {13330078125}{8192}\right ) x^{5}+\left (\frac {1708984375 \ln \relax (2)^{2}}{1048576}-\frac {22216796875 \ln \relax (2)}{262144}+\frac {111083984375}{262144}\right ) x^{4}+\left (-\frac {68359375 \ln \relax (2)^{3}}{1024}+\frac {751953125 \ln \relax (2)^{2}}{512}-\frac {1955078125 \ln \relax (2)}{256}+\frac {1396484375}{128}\right ) x^{7}+\left (-\frac {68359375 \ln \relax (2)^{3}}{16384}+\frac {2255859375 \ln \relax (2)^{2}}{8192}-\frac {9775390625 \ln \relax (2)}{4096}+\frac {9775390625}{2048}\right ) x^{6}+\left (\frac {2734375 \ln \relax (2)^{4}}{32}-\frac {8203125 \ln \relax (2)^{3}}{4}+\frac {54140625 \ln \relax (2)^{2}}{4}-33515625 \ln \relax (2)+\frac {55859375}{2}\right ) x^{9}+\left (\frac {13671875 \ln \relax (2)^{4}}{2048}-\frac {123046875 \ln \relax (2)^{3}}{256}+\frac {1353515625 \ln \relax (2)^{2}}{256}-\frac {1173046875 \ln \relax (2)}{64}+\frac {2513671875}{128}\right ) x^{8}+\left (-65625 \ln \relax (2)^{5}+1531250 \ln \relax (2)^{4}-11025000 \ln \relax (2)^{3}[phone] \ln \relax (2)^{2}-50050000 \ln \relax (2)[phone]\right ) x^{11}+\left (-\frac {109375 \ln \relax (2)^{5}}{16}+\frac {3828125 \ln \relax (2)^{4}}{8}-\frac {11484375 \ln \relax (2)^{3}}{2}[phone] \ln \relax (2)^{2}-46921875 \ln \relax (2)[phone]\right ) x^{10}+\left (4375 \ln \relax (2)^{6}-262500 \ln \relax (2)^{5}+3062500 \ln \relax (2)^{4}-14700000 \ln \relax (2)^{3}[phone] \ln \relax (2)^{2}-40040000 \ln \relax (2)[phone]\right ) x^{12}+\left (28000 \ln \relax (2)^{6}-560000 \ln \relax (2)^{5}+3920000 \ln \relax (2)^{4}-13440000 \ln \relax (2)^{3}[phone] \ln \relax (2)^{2}-23296000 \ln \relax (2)+8960000\right ) x^{13}+\left (-5120 \ln \relax (2)^{7}+71680 \ln \relax (2)^{6}-430080 \ln \relax (2)^{5}+1433600 \ln \relax (2)^{4}-2867200 \ln \relax (2)^{3}+3440640 \ln \relax (2)^{2}-2293760 \ln \relax (2)+655360\right ) x^{15}+\left (-1600 \ln \relax (2)^{7}+67200 \ln \relax (2)^{6}-672000 \ln \relax (2)^{5}+3136000 \ln \relax (2)^{4}-8064000 \ln \relax (2)^{3}[phone] \ln \relax (2)^{2}-9318400 \ln \relax (2)+3072000\right ) x^{14}+\left (256 \ln \relax (2)^{8}-4096 \ln \relax (2)^{7}+28672 \ln \relax (2)^{6}-114688 \ln \relax (2)^{5}+286720 \ln \relax (2)^{4}-458752 \ln \relax (2)^{3}+458752 \ln \relax (2)^{2}-262144 \ln \relax (2)+65536\right ) x^{16}+\frac {30517578125 x}{33554432}}{x^{32}}\)	\(454\)
risch	\(\frac {\left (-687194767360 \ln \relax (2)^{7}[phone] \ln \relax (2)^{6}-57724360458240 \ln \relax (2)^{5}[phone] \ln \relax (2)^{4}-384829069721600 \ln \relax (2)^{3}[phone] \ln \relax (2)^{2}-307863255777280 \ln \relax (2)[phone]\right ) x^{15}+\left (34359738368 \ln \relax (2)^{8}-549755813888 \ln \relax (2)^{7}[phone] \ln \relax (2)^{6}-15393162788864 \ln \relax (2)^{5}[phone] \ln \relax (2)^{4}-61572651155456 \ln \relax (2)^{3}[phone] \ln \relax (2)^{2}-35184372088832 \ln \relax (2)[phone]\right ) x^{16}+\frac {152587890625}{32}[phone] x +\left (-48828125000 \ln \relax (2)[phone]\right ) x^{2}+\left (-1093750000000 \ln \relax (2)[phone]\right ) x^{3}+\left (218750000000 \ln \relax (2)^{2}-11375000000000 \ln \relax (2)[phone]\right ) x^{4}+\left (4200000000000 \ln \relax (2)^{2}-72800000000000 \ln \relax (2)[phone]\right ) x^{5}+\left (-560000000000 \ln \relax (2)^{3}[phone] \ln \relax (2)^{2}-320320000000000 \ln \relax (2)[phone]\right ) x^{6}+\left (-8960000000000 \ln \relax (2)^{3}[phone] \ln \relax (2)^{2}-1025024000000000 \ln \relax (2)+1464320000000000\right ) x^{7}+\left (896000000000 \ln \relax (2)^{4}-64512000000000 \ln \relax (2)^{3}[phone] \ln \relax (2)^{2}-2460057600000000 \ln \relax (2)+2635776000000000\right ) x^{8}+\left (11468800000000 \ln \relax (2)^{4}-275251200000000 \ln \relax (2)^{3}+1816657920000000 \ln \relax (2)^{2}-4498391040000000 \ln \relax (2)+3748659200000000\right ) x^{9}+\left (-917504000000 \ln \relax (2)^{5}[phone] \ln \relax (2)^{4}-770703360000000 \ln \relax (2)^{3}+3391094784000000 \ln \relax (2)^{2}-6297747456000000 \ln \relax (2)+4198498304000000\right ) x^{10}+\left (-8808038400000 \ln \relax (2)^{5}[phone] \ln \relax (2)^{4}-1479750451200000 \ln \relax (2)^{3}+4650644275200000 \ln \relax (2)^{2}-6717597286400000 \ln \relax (2)+3664143974400000\right ) x^{11}+\left (587202560000 \ln \relax (2)^{6}-35232153600000 \ln \relax (2)^{5}[phone] \ln \relax (2)^{4}-1973000601600000 \ln \relax (2)^{3}+4650644275200000 \ln \relax (2)^{2}-5374077829120000 \ln \relax (2)+2442762649600000\right ) x^{12}+\left (3758096384000 \ln \relax (2)^{6}-75161927680000 \ln \relax (2)^{5}[phone] \ln \relax (2)^{4}-1803886264320000 \ln \relax (2)^{3}+3307124817920000 \ln \relax (2)^{2}-3126736191488000 \ln \relax (2)+1202590842880000\right ) x^{13}+\left (-214748364800 \ln \relax (2)^{7}[phone] \ln \relax (2)^{6}-90194313216000 \ln \relax (2)^{5}[phone] \ln \relax (2)^{4}-1082331758592000 \ln \relax (2)^{3}+1587419912601600 \ln \relax (2)^{2}-1250694476595200 \ln \relax (2)[phone]\right ) x^{14}}{134217728 x^{32}}\)	\(455\)
default	\(-\frac {3865470566400 \ln \relax (2)^{7}-162349763788800 \ln \relax (2)^{6}+1623497637888000 \ln \relax (2)^{5}-7576322310144000 \ln \relax (2)^{4}+19481971654656000 \ln \relax (2)^{3}-28573558426828800 \ln \relax (2)^{2}+22512500578713600 \ln \relax (2)-7421703487488000}{2415919104 x^{18}}-\frac {14560000000000 \ln \relax (2)^{3}-960960000000000 \ln \relax (2)^{2}+8328320000000000 \ln \relax (2)-16656640000000000}{3489660928 x^{26}}-\frac {-549755813888 \ln \relax (2)^{8}[phone] \ln \relax (2)^{7}-61572651155456 \ln \relax (2)^{6}[phone] \ln \relax (2)^{5}-615726511554560 \ln \relax (2)^{4}[phone] \ln \relax (2)^{3}-985162418487296 \ln \relax (2)^{2}[phone] \ln \relax (2)-140737488355328}{2147483648 x^{16}}-\frac {31718750000000 \ln \relax (2)-317187500000000}{3892314112 x^{29}}-\frac {224000000000000 \ln \relax (2)^{3}-4928000000000000 \ln \relax (2)^{2}+25625600000000000 \ln \relax (2)-36608000000000000}{3355443200 x^{25}}-\frac {1464843750000 \ln \relax (2)-43945312500000}{4026531840 x^{30}}-\frac {-21504000000000 \ln \relax (2)^{4}+1548288000000000 \ln \relax (2)^{3}-17031168000000000 \ln \relax (2)^{2}+59041382400000000 \ln \relax (2)-63258624000000000}{3221225472 x^{24}}-\frac {184968806400000 \ln \relax (2)^{5}-4315938816000000 \ln \relax (2)^{4}+31074759475200000 \ln \relax (2)^{3}-97663529779200000 \ln \relax (2)^{2}+141069543014400000 \ln \relax (2)-76947023462400000}{2818572288 x^{21}}-\frac {-11744051200000 \ln \relax (2)^{6}[phone] \ln \relax (2)^{5}-8220835840000000 \ln \relax (2)^{4}+39460012032000000 \ln \relax (2)^{3}-93012885504000000 \ln \relax (2)^{2}+107481556582400000 \ln \relax (2)-48855252992000000}{2684354560 x^{20}}-\frac {-263782400000000 \ln \relax (2)^{4}+6330777600000000 \ln \relax (2)^{3}-41783132160000000 \ln \relax (2)^{2}+103462993920000000 \ln \relax (2)-86219161600000000}{3087007744 x^{23}}-\frac {20185088000000 \ln \relax (2)^{5}-1412956160000000 \ln \relax (2)^{4}+16955473920000000 \ln \relax (2)^{3}-74604085248000000 \ln \relax (2)^{2}+138550444032000000 \ln \relax (2)-92366962688000000}{2952790016 x^{22}}-\frac {11682311045120 \ln \relax (2)^{7}-163552354631680 \ln \relax (2)^{6}[phone] \ln \relax (2)^{5}-3271047092633600 \ln \relax (2)^{4}+6542094185267200 \ln \relax (2)^{3}-7850513022320640 \ln \relax (2)^{2}+5233675348213760 \ln \relax (2)-1495335813775360}{2281701376 x^{17}}-\frac {-71403831296000 \ln \relax (2)^{6}+1428076625920000 \ln \relax (2)^{5}-9996536381440000 \ln \relax (2)^{4}+34273839022080000 \ln \relax (2)^{3}-62835371540480000 \ln \relax (2)^{2}+59407987638272000 \ln \relax (2)-22849226014720000}{2550136832 x^{19}}-\frac {-113400000000000 \ln \relax (2)^{2}+1965600000000000 \ln \relax (2)-5896800000000000}{3623878656 x^{27}}-\frac {-6125000000000 \ln \relax (2)^{2}[phone] \ln \relax (2)-1592500000000000}{3758096384 x^{28}}+\frac {152587890625}{4294967296 x^{32}}+\frac {30517578125}{33554432 x^{31}}\)	\(471\)
gosper	\(\frac {152587890625+3906250000000 x -17592186044416 \ln \relax (2)^{7} x^{16}-21990232555520 \ln \relax (2)^{7} x^{15}[phone] \ln \relax (2)^{6} x^{16}-6871947673600 \ln \relax (2)^{7} x^{14}[phone] \ln \relax (2)^{6} x^{15}-492581209243648 \ln \relax (2)^{5} x^{16}[phone] \ln \relax (2)^{6} x^{14}-1847179534663680 \ln \relax (2)^{5} x^{15}+1231453023109120 \ln \relax (2)^{4} x^{16}[phone] \ln \relax (2)^{6} x^{13}-2886218022912000 \ln \relax (2)^{5} x^{14}+6157265115545600 \ln \relax (2)^{4} x^{15}-1970324836974592 \ln \relax (2)^{3} x^{16}[phone] \ln \relax (2)^{6} x^{12}-2405181685760000 \ln \relax (2)^{5} x^{13}+13469017440256000 \ln \relax (2)^{4} x^{14}-12314530231091200 \ln \relax (2)^{3} x^{15}+1970324836974592 \ln \relax (2)^{2} x^{16}-1127428915200000 \ln \relax (2)^{5} x^{12}+16836271800320000 \ln \relax (2)^{4} x^{13}-34634616274944000 \ln \relax (2)^{3} x^{14}+14777436277309440 \ln \relax (2)^{2} x^{15}-1125899906842624 \ln \relax (2) x^{16}-281857228800000 \ln \relax (2)^{5} x^{11}-57724360458240000 \ln \relax (2)^{3} x^{13}+50797437203251200 \ln \relax (2)^{2} x^{14}-9851624184872960 \ln \relax (2) x^{15}+6576668672000000 \ln \relax (2)^{4} x^{11}-63136019251200000 \ln \relax (2)^{3} x^{12}+105827994173440000 \ln \relax (2)^{2} x^{13}-40022223251046400 \ln \relax (2) x^{14}+2055208960000000 \ln \relax (2)^{4} x^{10}-47352014438400000 \ln \relax (2)^{3} x^{11}+148820616806400000 \ln \relax (2)^{2} x^{12}-100055558127616000 \ln \relax (2) x^{13}-24662507520000000 \ln \relax (2)^{3} x^{10}+148820616806400000 \ln \relax (2)^{2} x^{11}-171970490531840000 \ln \relax (2) x^{12}-8808038400000000 \ln \relax (2)^{3} x^{9}+108515033088000000 \ln \relax (2)^{2} x^{10}-214963113164800000 \ln \relax (2) x^{11}+58133053440000000 \ln \relax (2)^{2} x^{9}-201527918592000000 \ln \relax (2) x^{10}+22708224000000000 \ln \relax (2)^{2} x^{8}-143948513280000000 \ln \relax (2) x^{9}-17920000000000 x^{6} \ln \relax (2)^{3}+1182720000000000 x^{6} \ln \relax (2)^{2}-29360128000000 x^{10} \ln \relax (2)^{5}[phone] x^{9} \ln \relax (2)^{4}-2064384000000000 x^{8} \ln \relax (2)^{3}+117252607180800000 x^{11}+78168404787200000 x^{12}+38482906972160000 x^{13}+13194139533312000 x^{14}[phone] x^{16}+2814749767106560 x^{15}+46858240000000000 x^{7}+84344832000000000 x^{8}+134351945728000000 x^{10}+119957094400000000 x^{9}+20500480000000000 x^{6}+6988800000000000 x^{5}+1820000000000000 x^{4}[phone] x^{3}[phone] x^{2}[phone] x^{16} \ln \relax (2)^{8}-78721843200000000 x^{8} \ln \relax (2)+13153337344000000 x^{12} \ln \relax (2)^{4}[phone] x^{5} \ln \relax (2)^{2}+6307840000000000 x^{7} \ln \relax (2)^{2}-32800768000000000 x^{7} \ln \relax (2)-286720000000000 x^{7} \ln \relax (2)^{3}[phone] x^{4} \ln \relax (2)^{2}-364000000000000 x^{4} \ln \relax (2)-2329600000000000 x^{5} \ln \relax (2)-10250240000000000 x^{6} \ln \relax (2)-1562500000000 x^{2} \ln \relax (2)-35000000000000 x^{3} \ln \relax (2)[phone] x^{8} \ln \relax (2)^{4}}{4294967296 x^{32}}\)	\(632\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/134217728*(-152587890625-3784179687500*x-76947023462400000*x^11-48855252992000000*x^12-22849226014720000
*x^13-7421703487488000*x^14-140737488355328*x^16-1495335813775360*x^15-36608000000000000*x^7-63258624000000000
*x^8-92366962688000000*x^10-86219161600000000*x^9-16656640000000000*x^6-5896800000000000*x^5-1592500000000000*
x^4-317187500000000*x^3-43945312500000*x^2-549755813888*x^16*ln(2)^8+128*(68719476736*x^16+91268055040*x^15+30
198988800*x^14)*ln(2)^7+64*(-962072674304*x^16-2555505541120*x^15-2536715059200*x^14-1115684864000*x^13-183500
800000*x^12)*ln(2)^6+32*(7696581394432*x^16+30666066493440*x^15+50734301184000*x^14+44627394560000*x^13+220200
96000000*x^12+5780275200000*x^11+630784000000*x^10)*ln(2)^5+16*(-38482906972160*x^16-204440443289600*x^15-4735
20144384000*x^14-624783523840000*x^13-513802240000000*x^12-269746176000000*x^11-88309760000000*x^10-1648640000
0000*x^9-1344000000000*x^8)*ln(2)^4+8*(123145302310912*x^16+817761773158400*x^15+2435246456832000*x^14+4284229
877760000*x^13+4932501504000000*x^12+3884344934400000*x^11+2119434240000000*x^10+791347200000000*x^9+193536000
000000*x^8+28000000000000*x^7+1820000000000*x^6)*ln(2)^3+4*(-246290604621824*x^16-1962628255580160*x^15-714338
9606707200*x^14-15708842885120000*x^13-23253221376000000*x^12-24415882444800000*x^11-18651021312000000*x^10-10
445783040000000*x^9-4257792000000000*x^8-1232000000000000*x^7-240240000000000*x^6-28350000000000*x^5-153125000
0000*x^4)*ln(2)^2+2*(281474976710656*x^16+2616837674106880*x^15+11256250289356800*x^14+29703993819136000*x^13+
53740778291200000*x^12+70534771507200000*x^11+69275222016000000*x^10+51731496960000000*x^9+29520691200000000*x
^8+12812800000000000*x^7+4164160000000000*x^6+982800000000000*x^5+159250000000000*x^4+15859375000000*x^3+73242
1875000*x^2)*ln(2))/x^33,x,method=_RETURNVERBOSE)

[Out]

(152587890625/4294967296+(-8544921875/1048576*ln(2)[phone]/524288)*x^3+(-6103515625/16777216*ln(2)+915527
34375/8388608)*x^2+(1025390625/32768*ln(2)^2-4443359375/8192*ln(2)[phone]/8192)*x^5+(1708984375/1048576*l
n(2)^2-22216796875/262144*ln(2)[phone]/262144)*x^4+(-68359375/1024*ln(2)^3+751953125/512*ln(2)^2-1955078
125/256*ln(2)[phone]/128)*x^7+(-68359375/16384*ln(2)^3+2255859375/8192*ln(2)^2-9775390625/4096*ln(2)+97753
90625/2048)*x^6+(2734375/32*ln(2)^4-8203125/4*ln(2)^3+54140625/4*ln(2)^2-33515625*ln(2)[phone]/2)*x^9+(13671
875/2048*ln(2)^4-123046875/256*ln(2)^3+1353515625/256*ln(2)^2-1173046875/64*ln(2)[phone]/128)*x^8+(-65625*
ln(2)^5+1531250*ln(2)^4-11025000*ln(2)^3+34650000*ln(2)^2-50050000*ln(2)[phone])*x^11+(-109375/16*ln(2)^5+38
28125/8*ln(2)^4-11484375/2*ln(2)^3+25265625*ln(2)^2-46921875*ln(2)[phone])*x^10+(4375*ln(2)^6-262500*ln(2)^5
+3062500*ln(2)^4-14700000*ln(2)^3+34650000*ln(2)^2-40040000*ln(2)[phone])*x^12+(28000*ln(2)^6-560000*ln(2)^5
+3920000*ln(2)^4-13440000*ln(2)^3+24640000*ln(2)^2-23296000*ln(2)+8960000)*x^13+(-5120*ln(2)^7+71680*ln(2)^6-4
30080*ln(2)^5+1433600*ln(2)^4-2867200*ln(2)^3+3440640*ln(2)^2-2293760*ln(2)+655360)*x^15+(-1600*ln(2)^7+67200*
ln(2)^6-672000*ln(2)^5+3136000*ln(2)^4-8064000*ln(2)^3+11827200*ln(2)^2-9318400*ln(2)+3072000)*x^14+(256*ln(2)
^8-4096*ln(2)^7+28672*ln(2)^6-114688*ln(2)^5+286720*ln(2)^4-458752*ln(2)^3+458752*ln(2)^2-262144*ln(2)+65536)*
x^16+30517578125/33554432*x)/x^32

________________________________________________________________________________________

maxima [B]  time = 0.40, size = 449, normalized size = 20.41 \begin {gather*} \frac {1099511627776 \, {\left (\log \relax (2)^{8} - 16 \, \log \relax (2)^{7} + 112 \, \log \relax (2)^{6} - 448 \, \log \relax (2)^{5} + 1120 \, \log \relax (2)^{4} - 1792 \, \log \relax (2)^{3} + 1792 \, \log \relax (2)^{2} - 1024 \, \log \relax (2) + 256\right )} x^{16} - 21990232555520 \, {\left (\log \relax (2)^{7} - 14 \, \log \relax (2)^{6} + 84 \, \log \relax (2)^{5} - 280 \, \log \relax (2)^{4} + 560 \, \log \relax (2)^{3} - 672 \, \log \relax (2)^{2} + 448 \, \log \relax (2) - 128\right )} x^{15} - 6871947673600 \, {\left (\log \relax (2)^{7} - 42 \, \log \relax (2)^{6} + 420 \, \log \relax (2)^{5} - 1960 \, \log \relax (2)^{4} + 5040 \, \log \relax (2)^{3} - 7392 \, \log \relax (2)^{2} + 5824 \, \log \relax (2) - 1920\right )} x^{14} + 120259084288000 \, {\left (\log \relax (2)^{6} - 20 \, \log \relax (2)^{5} + 140 \, \log \relax (2)^{4} - 480 \, \log \relax (2)^{3} + 880 \, \log \relax (2)^{2} - 832 \, \log \relax (2) + 320\right )} x^{13} + 18790481920000 \, {\left (\log \relax (2)^{6} - 60 \, \log \relax (2)^{5} + 700 \, \log \relax (2)^{4} - 3360 \, \log \relax (2)^{3} + 7920 \, \log \relax (2)^{2} - 9152 \, \log \relax (2) + 4160\right )} x^{12} - 93952409600000 \, {\left (3 \, \log \relax (2)^{5} - 70 \, \log \relax (2)^{4} + 504 \, \log \relax (2)^{3} - 1584 \, \log \relax (2)^{2} + 2288 \, \log \relax (2) - 1248\right )} x^{11} - 29360128000000 \, {\left (\log \relax (2)^{5} - 70 \, \log \relax (2)^{4} + 840 \, \log \relax (2)^{3} - 3696 \, \log \relax (2)^{2} + 6864 \, \log \relax (2) - 4576\right )} x^{10} + 10485760000000 \, {\left (35 \, \log \relax (2)^{4} - 840 \, \log \relax (2)^{3} + 5544 \, \log \relax (2)^{2} - 13728 \, \log \relax (2) + 11440\right )} x^{9} + 819200000000 \, {\left (35 \, \log \relax (2)^{4} - 2520 \, \log \relax (2)^{3} + 27720 \, \log \relax (2)^{2} - 96096 \, \log \relax (2) + 102960\right )} x^{8} - 8192000000000 \, {\left (35 \, \log \relax (2)^{3} - 770 \, \log \relax (2)^{2} + 4004 \, \log \relax (2) - 5720\right )} x^{7} - 17920000000000 \, {\left (\log \relax (2)^{3} - 66 \, \log \relax (2)^{2} + 572 \, \log \relax (2) - 1144\right )} x^{6} + 44800000000000 \, {\left (3 \, \log \relax (2)^{2} - 52 \, \log \relax (2) + 156\right )} x^{5} + 7000000000000 \, {\left (\log \relax (2)^{2} - 52 \, \log \relax (2) + 260\right )} x^{4} - 35000000000000 \, x^{3} {\left (\log \relax (2) - 10\right )} - 1562500000000 \, x^{2} {\left (\log \relax (2) - 30\right )} + 3906250000000 \, x + 152587890625}{4294967296 \, x^{32}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/134217728*(-152587890625-3784179687500*x-549755813888*x^16*log(2)^8+128*(68719476736*x^16+91268055
040*x^15+30198988800*x^14)*log(2)^7+64*(-962072674304*x^16-2555505541120*x^15-2536715059200*x^14-1115684864000
*x^13-183500800000*x^12)*log(2)^6+32*(7696581394432*x^16+30666066493440*x^15+50734301184000*x^14+4462739456000
0*x^13+22020096000000*x^12+5780275200000*x^11+630784000000*x^10)*log(2)^5+16*(-38482906972160*x^16-20444044328
9600*x^15-473520144384000*x^14-624783523840000*x^13-513802240000000*x^12-269746176000000*x^11-88309760000000*x
^10-16486400000000*x^9-1344000000000*x^8)*log(2)^4+8*(123145302310912*x^16+817761773158400*x^15+24352464568320
00*x^14+4284229877760000*x^13+4932501504000000*x^12+3884344934400000*x^11+2119434240000000*x^10+79134720000000
0*x^9+193536000000000*x^8+28000000000000*x^7+1820000000000*x^6)*log(2)^3+4*(-246290604621824*x^16-196262825558
0160*x^15-7143389606707200*x^14-15708842885120000*x^13-23253221376000000*x^12-24415882444800000*x^11-186510213
12000000*x^10-10445783040000000*x^9-4257792000000000*x^8-1232000000000000*x^7-240240000000000*x^6-283500000000
00*x^5-1531250000000*x^4)*log(2)^2+2*(281474976710656*x^16+2616837674106880*x^15+11256250289356800*x^14+297039
93819136000*x^13+53740778291200000*x^12+70534771507200000*x^11+69275222016000000*x^10+51731496960000000*x^9+29
520691200000000*x^8+12812800000000000*x^7+4164160000000000*x^6+982800000000000*x^5+159250000000000*x^4+1585937
5000000*x^3+732421875000*x^2)*log(2)-1592500000000000*x^4-317187500000000*x^3-43945312500000*x^2-1665664000000
0000*x^6-5896800000000000*x^5-36608000000000000*x^7-63258624000000000*x^8-92366962688000000*x^10-8621916160000
0000*x^9-1495335813775360*x^15-140737488355328*x^16-76947023462400000*x^11-48855252992000000*x^12-228492260147
20000*x^13-7421703487488000*x^14)/x^33,x, algorithm="maxima")

[Out]

1/4294967296*(1099511627776*(log(2)^8 - 16*log(2)^7 + 112*log(2)^6 - 448*log(2)^5 + 1120*log(2)^4 - 1792*log(2
)^3 + 1792*log(2)^2 - 1024*log(2) + 256)*x^16 - 21990232555520*(log(2)^7 - 14*log(2)^6 + 84*log(2)^5 - 280*log
(2)^4 + 560*log(2)^3 - 672*log(2)^2 + 448*log(2) - 128)*x^15 - 6871947673600*(log(2)^7 - 42*log(2)^6 + 420*log
(2)^5 - 1960*log(2)^4 + 5040*log(2)^3 - 7392*log(2)^2 + 5824*log(2) - 1920)*x^14 + 120259084288000*(log(2)^6 -
20*log(2)^5 + 140*log(2)^4 - 480*log(2)^3 + 880*log(2)^2 - 832*log(2) + 320)*x^13 + 18790481920000*(log(2)^6
- 60*log(2)^5 + 700*log(2)^4 - 3360*log(2)^3 + 7920*log(2)^2 - 9152*log(2) + 4160)*x^12 - 93952409600000*(3*lo
g(2)^5 - 70*log(2)^4 + 504*log(2)^3 - 1584*log(2)^2 + 2288*log(2) - 1248)*x^11 - 29360128000000*(log(2)^5 - 70
*log(2)^4 + 840*log(2)^3 - 3696*log(2)^2 + 6864*log(2) - 4576)*x^10 + 10485760000000*(35*log(2)^4 - 840*log(2)
^3 + 5544*log(2)^2 - 13728*log(2) + 11440)*x^9 + 819200000000*(35*log(2)^4 - 2520*log(2)^3 + 27720*log(2)^2 -
96096*log(2) + 102960)*x^8 - 8192000000000*(35*log(2)^3 - 770*log(2)^2 + 4004*log(2) - 5720)*x^7 - 17920000000
000*(log(2)^3 - 66*log(2)^2 + 572*log(2) - 1144)*x^6 + 44800000000000*(3*log(2)^2 - 52*log(2) + 156)*x^5 + 700
0000000000*(log(2)^2 - 52*log(2) + 260)*x^4 - 35000000000000*x^3*(log(2) - 10) - 1562500000000*x^2*(log(2) - 3
0) + 3906250000000*x + 152587890625)/x^32

________________________________________________________________________________________

mupad [B]  time = 4.77, size = 461, normalized size = 20.95 \begin {gather*} \frac {\left (458752\,{\ln \relax (2)}^2-262144\,\ln \relax (2)-458752\,{\ln \relax (2)}^3+286720\,{\ln \relax (2)}^4-114688\,{\ln \relax (2)}^5+28672\,{\ln \relax (2)}^6-4096\,{\ln \relax (2)}^7+256\,{\ln \relax (2)}^8+65536\right )\,x^{16}+\left (3440640\,{\ln \relax (2)}^2-2293760\,\ln \relax (2)-2867200\,{\ln \relax (2)}^3+1433600\,{\ln \relax (2)}^4-430080\,{\ln \relax (2)}^5+71680\,{\ln \relax (2)}^6-5120\,{\ln \relax (2)}^7+655360\right )\,x^{15}+\left (11827200\,{\ln \relax (2)}^2-9318400\,\ln \relax (2)-8064000\,{\ln \relax (2)}^3+3136000\,{\ln \relax (2)}^4-672000\,{\ln \relax (2)}^5+67200\,{\ln \relax (2)}^6-1600\,{\ln \relax (2)}^7+3072000\right )\,x^{14}+\left (24640000\,{\ln \relax (2)}^2-23296000\,\ln \relax (2)-13440000\,{\ln \relax (2)}^3+3920000\,{\ln \relax (2)}^4-560000\,{\ln \relax (2)}^5+28000\,{\ln \relax (2)}^6+8960000\right )\,x^{13}+\left (34650000\,{\ln \relax (2)}^2-40040000\,\ln \relax (2)-14700000\,{\ln \relax (2)}^3+3062500\,{\ln \relax (2)}^4-262500\,{\ln \relax (2)}^5+4375\,{\ln \relax (2)}^6+18200000\right )\,x^{12}+\left (34650000\,{\ln \relax (2)}^2-50050000\,\ln \relax (2)-11025000\,{\ln \relax (2)}^3+1531250\,{\ln \relax (2)}^4-65625\,{\ln \relax (2)}^5+27300000\right )\,x^{11}+\left (25265625\,{\ln \relax (2)}^2-46921875\,\ln \relax (2)-\frac {11484375\,{\ln \relax (2)}^3}{2}+\frac {3828125\,{\ln \relax (2)}^4}{8}-\frac {109375\,{\ln \relax (2)}^5}{16}[phone]\right )\,x^{10}+\left (\frac {54140625\,{\ln \relax (2)}^2}{4}-33515625\,\ln \relax (2)-\frac {8203125\,{\ln \relax (2)}^3}{4}+\frac {2734375\,{\ln \relax (2)}^4}{32}+\frac {55859375}{2}\right )\,x^9+\left (\frac {1353515625\,{\ln \relax (2)}^2}{256}-\frac {1173046875\,\ln \relax (2)}{64}-\frac {123046875\,{\ln \relax (2)}^3}{256}+\frac {13671875\,{\ln \relax (2)}^4}{2048}+\frac {2513671875}{128}\right )\,x^8+\left (\frac {751953125\,{\ln \relax (2)}^2}{512}-\frac {1955078125\,\ln \relax (2)}{256}-\frac {68359375\,{\ln \relax (2)}^3}{1024}+\frac {1396484375}{128}\right )\,x^7+\left (\frac {2255859375\,{\ln \relax (2)}^2}{8192}-\frac {9775390625\,\ln \relax (2)}{4096}-\frac {68359375\,{\ln \relax (2)}^3}{16384}+\frac {9775390625}{2048}\right )\,x^6+\left (\frac {1025390625\,{\ln \relax (2)}^2}{32768}-\frac {4443359375\,\ln \relax (2)}{8192}+\frac {13330078125}{8192}\right )\,x^5+\left (\frac {1708984375\,{\ln \relax (2)}^2}{1048576}-\frac {22216796875\,\ln \relax (2)}{262144}+\frac {111083984375}{262144}\right )\,x^4+\left (\frac {42724609375}{524288}-\frac {8544921875\,\ln \relax (2)}{1048576}\right )\,x^3+\left (\frac {91552734375}{8388608}-\frac {6103515625\,\ln \relax (2)}{16777216}\right )\,x^2+\frac {30517578125\,x}{33554432}+\frac {152587890625}{4294967296}}{x^{32}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-((946044921875*x)/33554432 + 4096*x^16*log(2)^8 - (log(2)^3*(1820000000000*x^6 + 28000000000000*x^7 + 193
536000000000*x^8 + 791347200000000*x^9 + 2119434240000000*x^10 + 3884344934400000*x^11 + 4932501504000000*x^12
+ 4284229877760000*x^13 + 2435246456832000*x^14 + 817761773158400*x^15 + 123145302310912*x^16))/16777216 - (l
og(2)*(732421875000*x^2 + 15859375000000*x^3 + 159250000000000*x^4 + 982800000000000*x^5 + 4164160000000000*x^
6 + 12812800000000000*x^7 + 29520691200000000*x^8 + 51731496960000000*x^9 + 69275222016000000*x^10 + 705347715
07200000*x^11 + 53740778291200000*x^12 + 29703993819136000*x^13 + 11256250289356800*x^14 + 2616837674106880*x^
15 + 281474976710656*x^16))/67108864 + (log(2)^2*(1531250000000*x^4 + 28350000000000*x^5 + 240240000000000*x^6
+ 1232000000000000*x^7 + 4257792000000000*x^8 + 10445783040000000*x^9 + 18651021312000000*x^10 + 244158824448
00000*x^11 + 23253221376000000*x^12 + 15708842885120000*x^13 + 7143389606707200*x^14 + 1962628255580160*x^15 +
246290604621824*x^16))/33554432 - (log(2)^7*(30198988800*x^14 + 91268055040*x^15 + 68719476736*x^16))/1048576
+ (log(2)^6*(183500800000*x^12 + 1115684864000*x^13 + 2536715059200*x^14 + 2555505541120*x^15 + 962072674304*
x^16))/2097152 - (log(2)^5*(630784000000*x^10 + 5780275200000*x^11 + 22020096000000*x^12 + 44627394560000*x^13
+ 50734301184000*x^14 + 30666066493440*x^15 + 7696581394432*x^16))/4194304 + (1373291015625*x^2)/4194304 + (1
239013671875*x^3)/524288 + (777587890625*x^4)/65536 + (359912109375*x^5)/8192 + (127080078125*x^6)/1024 + (349
12109375*x^7)/128 + (7541015625*x^8)/16 + (1284765625*x^9)/2 + 688187500*x^10 + 573300000*x^11 + 364000000*x^1
2 + 170240000*x^13 + 55296000*x^14 + 11141120*x^15 + 1048576*x^16 + (log(2)^4*(1344000000000*x^8 + 16486400000
000*x^9 + 88309760000000*x^10 + 269746176000000*x^11 + 513802240000000*x^12 + 624783523840000*x^13 + 473520144
384000*x^14 + 204440443289600*x^15 + 38482906972160*x^16))/8388608 + 152587890625/134217728)/x^33,x)

[Out]

((30517578125*x)/33554432 - x^10*(46921875*log(2) - 25265625*log(2)^2 + (11484375*log(2)^3)/2 - (3828125*log(2
)^4)/8 + (109375*log(2)^5)/16 - 31281250) - x^11*(50050000*log(2) - 34650000*log(2)^2 + 11025000*log(2)^3 - 15
31250*log(2)^4 + 65625*log(2)^5 - 27300000) + x^8*((1353515625*log(2)^2)/256 - (1173046875*log(2))/64 - (12304
6875*log(2)^3)/256 + (13671875*log(2)^4)/2048 + 2513671875/128) - x^2*((6103515625*log(2))/16777216 - 91552734
375/8388608) + x^13*(24640000*log(2)^2 - 23296000*log(2) - 13440000*log(2)^3 + 3920000*log(2)^4 - 560000*log(2
)^5 + 28000*log(2)^6 + 8960000) + x^12*(34650000*log(2)^2 - 40040000*log(2) - 14700000*log(2)^3 + 3062500*log(
2)^4 - 262500*log(2)^5 + 4375*log(2)^6 + 18200000) - x^3*((8544921875*log(2))/1048576 - 42724609375/524288) -
x^15*(2293760*log(2) - 3440640*log(2)^2 + 2867200*log(2)^3 - 1433600*log(2)^4 + 430080*log(2)^5 - 71680*log(2)
^6 + 5120*log(2)^7 - 655360) - x^14*(9318400*log(2) - 11827200*log(2)^2 + 8064000*log(2)^3 - 3136000*log(2)^4
+ 672000*log(2)^5 - 67200*log(2)^6 + 1600*log(2)^7 - 3072000) + x^16*(458752*log(2)^2 - 262144*log(2) - 458752
*log(2)^3 + 286720*log(2)^4 - 114688*log(2)^5 + 28672*log(2)^6 - 4096*log(2)^7 + 256*log(2)^8 + 65536) - x^7*(
(1955078125*log(2))/256 - (751953125*log(2)^2)/512 + (68359375*log(2)^3)/1024 - 1396484375/128) - x^6*((977539
0625*log(2))/4096 - (2255859375*log(2)^2)/8192 + (68359375*log(2)^3)/16384 - 9775390625/2048) + x^9*((54140625
*log(2)^2)/4 - 33515625*log(2) - (8203125*log(2)^3)/4 + (2734375*log(2)^4)/32 + 55859375/2) + x^5*((1025390625
*log(2)^2)/32768 - (4443359375*log(2))/8192 + 13330078125/8192) + x^4*((1708984375*log(2)^2)/1048576 - (222167
96875*log(2))/262144 + 111083984375/262144) + 152587890625/4294967296)/x^32

________________________________________________________________________________________

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/134217728*(-152587890625-3784179687500*x-1592500000000000*x**4-317187500000000*x**3-43945312500000
*x**2-16656640000000000*x**6-5896800000000000*x**5-36608000000000000*x**7-63258624000000000*x**8-9236696268800
0000*x**10-86219161600000000*x**9-549755813888*x**16*ln(2)**8+128*(68719476736*x**16+91268055040*x**15+3019898
8800*x**14)*ln(2)**7+64*(-962072674304*x**16-2555505541120*x**15-2536715059200*x**14-1115684864000*x**13-18350
0800000*x**12)*ln(2)**6+32*(7696581394432*x**16+30666066493440*x**15+50734301184000*x**14+44627394560000*x**13
[phone]*x**12+5780275200000*x**11+630784000000*x**10)*ln(2)**5+16*(-38482906972160*x**16-2044404432896
00*x**15-473520144384000*x**14-624783523840000*x**13-513802240000000*x**12-269746176000000*x**11-8830976000000
0*x**10-16486400000000*x**9-1344000000000*x**8)*ln(2)**4+8*(123145302310912*x**16+817761773158400*x**15+243524
6456832000*x**14+4284229877760000*x**13+4932501504000000*x**12+3884344934400000*x**11+2119434240000000*x**10+7
91347200000000*x**9+193536000000000*x**8+28000000000000*x**7+1820000000000*x**6)*ln(2)**3+4*(-246290604621824*
x**16-1962628255580160*x**15-7143389606707200*x**14-15708842885120000*x**13-23253221376000000*x**12-2441588244
4800000*x**11-18651021312000000*x**10-10445783040000000*x**9-4257792000000000*x**8-1232000000000000*x**7-24024
0000000000*x**6-28350000000000*x**5-1531250000000*x**4)*ln(2)**2+2*(281474976710656*x**16+2616837674106880*x**
15+11256250289356800*x**14+29703993819136000*x**13+53740778291200000*x**12+70534771507200000*x**11+69275222016
000000*x**10+51731496960000000*x**9+29520691200000000*x**8+12812800000000000*x**7+4164160000000000*x**6+982800
000000000*x**5+159250000000000*x**4+15859375000000*x**3+732421875000*x**2)*ln(2)-1495335813775360*x**15-140737
488355328*x**16-76947023462400000*x**11-48855252992000000*x**12-22849226014720000*x**13-7421703487488000*x**14
)/x**33,x)

[Out]

Timed out

________________________________________________________________________________________