Integrand size = 451, antiderivative size = 22 \[ \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}+\left (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}+281474976710656 x^{16}\right ) \log (4)+\left (-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}\right ) \log ^2(4)+\left (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}+817761773158400 x^{15}+123145302310912 x^{16}\right ) \log ^3(4)+\left (-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}\right ) \log ^4(4)+\left (630784000000 x^{10}+5780275200000 x^{11}+22020096000000 x^{12}+44627394560000 x^{13}+50734301184000 x^{14}+30666066493440 x^{15}+7696581394432 x^{16}\right ) \log ^5(4)+\left (-183500800000 x^{12}-1115684864000 x^{13}-2536715059200 x^{14}-2555505541120 x^{15}-962072674304 x^{16}\right ) \log ^6(4)+\left (30198988800 x^{14}+91268055040 x^{15}+68719476736 x^{16}\right ) \log ^7(4)-2147483648 x^{16} \log ^8(4)}{134217728 x^{33}} \, dx=\frac {\left (\left (2+\frac {5}{4 x}\right )^2-\log (4)\right )^8}{x^{16}} \]
Time = 0.06 (sec) , antiderivative size = 23, normalized size of antiderivative = 1.05 \[ \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}+\left (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}+281474976710656 x^{16}\right ) \log (4)+\left (-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}\right ) \log ^2(4)+\left (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}+817761773158400 x^{15}+123145302310912 x^{16}\right ) \log ^3(4)+\left (-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}\right ) \log ^4(4)+\left (630784000000 x^{10}+5780275200000 x^{11}+22020096000000 x^{12}+44627394560000 x^{13}+50734301184000 x^{14}+30666066493440 x^{15}+7696581394432 x^{16}\right ) \log ^5(4)+\left (-183500800000 x^{12}-1115684864000 x^{13}-2536715059200 x^{14}-2555505541120 x^{15}-962072674304 x^{16}\right ) \log ^6(4)+\left (30198988800 x^{14}+91268055040 x^{15}+68719476736 x^{16}\right ) \log ^7(4)-2147483648 x^{16} \log ^8(4)}{134217728 x^{33}} \, dx=\frac {\left (25+80 x-16 x^2 (-4+\log (4))\right )^8}{4294967296 x^{32}} \]
Integrate[(-152587890625 - 3784179687500*x - 43945312500000*x^2 - 31718750 0000000*x^3 - 1592500000000000*x^4 - 5896800000000000*x^5 - 16656640000000 000*x^6 - 36608000000000000*x^7 - 63258624000000000*x^8 - 8621916160000000 0*x^9 - 92366962688000000*x^10 - 76947023462400000*x^11 - 4885525299200000 0*x^12 - 22849226014720000*x^13 - 7421703487488000*x^14 - 1495335813775360 *x^15 - 140737488355328*x^16 + (732421875000*x^2 + 15859375000000*x^3 + 15 9250000000000*x^4 + 982800000000000*x^5 + 4164160000000000*x^6 + 128128000 00000000*x^7 + 29520691200000000*x^8 + 51731496960000000*x^9 + 69275222016 000000*x^10 + 70534771507200000*x^11 + 53740778291200000*x^12 + 2970399381 9136000*x^13 + 11256250289356800*x^14 + 2616837674106880*x^15 + 2814749767 10656*x^16)*Log[4] + (-1531250000000*x^4 - 28350000000000*x^5 - 2402400000 00000*x^6 - 1232000000000000*x^7 - 4257792000000000*x^8 - 1044578304000000 0*x^9 - 18651021312000000*x^10 - 24415882444800000*x^11 - 2325322137600000 0*x^12 - 15708842885120000*x^13 - 7143389606707200*x^14 - 1962628255580160 *x^15 - 246290604621824*x^16)*Log[4]^2 + (1820000000000*x^6 + 280000000000 00*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 + 123145302310912*x^16)*Log[ 4]^3 + (-1344000000000*x^8 - 16486400000000*x^9 - 88309760000000*x^10 - 26 9746176000000*x^11 - 513802240000000*x^12 - 624783523840000*x^13 - 4735201 44384000*x^14 - 204440443289600*x^15 - 38482906972160*x^16)*Log[4]^4 + (63 0784000000*x^10 + 5780275200000*x^11 + 22020096000000*x^12 + 4462739456000 0*x^13 + 50734301184000*x^14 + 30666066493440*x^15 + 7696581394432*x^16)*L og[4]^5 + (-183500800000*x^12 - 1115684864000*x^13 - 2536715059200*x^14 - 2555505541120*x^15 - 962072674304*x^16)*Log[4]^6 + (30198988800*x^14 + 912 68055040*x^15 + 68719476736*x^16)*Log[4]^7 - 2147483648*x^16*Log[4]^8)/(13 4217728*x^33),x]
Leaf count is larger than twice the leaf count of optimal. \(318\) vs. \(2(22)=44\).
Time = 1.65 (sec) , antiderivative size = 318, normalized size of antiderivative = 14.45, number of steps used = 5, number of rules used = 5, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.011, Rules used = {6, 27, 25, 2010, 2009}
Below are the steps used by Rubi to obtain the solution. The rule number used for the transformation is given above next to the arrow. The rules definitions used are listed below.
| \(\displaystyle \int \frac {-140737488355328 x^{16}-2147483648 x^{16} \log ^8(4)-1495335813775360 x^{15}-7421703487488000 x^{14}-22849226014720000 x^{13}-48855252992000000 x^{12}-76947023462400000 x^{11}-92366962688000000 x^{10}-86219161600000000 x^9-63258624000000000 x^8-36608000000000000 x^7-16656640000000000 x^6-5896800000000000 x^5-1592500000000000 x^4-317187500000000 x^3-43945312500000 x^2+\left (68719476736 x^{16}+91268055040 x^{15}+30198988800 x^{14}\right ) \log ^7(4)+\left (-962072674304 x^{16}-2555505541120 x^{15}-2536715059200 x^{14}-1115684864000 x^{13}-183500800000 x^{12}\right ) \log ^6(4)+\left (7696581394432 x^{16}+30666066493440 x^{15}+50734301184000 x^{14}+44627394560000 x^{13}+22020096000000 x^{12}+5780275200000 x^{11}+630784000000 x^{10}\right ) \log ^5(4)+\left (-38482906972160 x^{16}-204440443289600 x^{15}-473520144384000 x^{14}-624783523840000 x^{13}-513802240000000 x^{12}-269746176000000 x^{11}-88309760000000 x^{10}-16486400000000 x^9-1344000000000 x^8\right ) \log ^4(4)-3784179687500 x+\left (123145302310912 x^{16}+817761773158400 x^{15}+2435246456832000 x^{14}+4284229877760000 x^{13}+4932501504000000 x^{12}+3884344934400000 x^{11}+2119434240000000 x^{10}+791347200000000 x^9+193536000000000 x^8+28000000000000 x^7+1820000000000 x^6\right ) \log ^3(4)+\left (-246290604621824 x^{16}-1962628255580160 x^{15}-7143389606707200 x^{14}-15708842885120000 x^{13}-23253221376000000 x^{12}-24415882444800000 x^{11}-18651021312000000 x^{10}-10445783040000000 x^9-4257792000000000 x^8-1232000000000000 x^7-240240000000000 x^6-28350000000000 x^5-1531250000000 x^4\right ) \log ^2(4)+\left (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+732421875000 x^2\right ) \log (4)-152587890625}{134217728 x^{33}} \, dx\) |
| \(\Big \downarrow \) 6 |
| \(\displaystyle \int \frac {x^{16} \left (-140737488355328-2147483648 \log ^8(4)\right )-1495335813775360 x^{15}-7421703487488000 x^{14}-22849226014720000 x^{13}-48855252992000000 x^{12}-76947023462400000 x^{11}-92366962688000000 x^{10}-86219161600000000 x^9-63258624000000000 x^8-36608000000000000 x^7-16656640000000000 x^6-5896800000000000 x^5-1592500000000000 x^4-317187500000000 x^3-43945312500000 x^2+\left (68719476736 x^{16}+91268055040 x^{15}+30198988800 x^{14}\right ) \log ^7(4)+\left (-962072674304 x^{16}-2555505541120 x^{15}-2536715059200 x^{14}-1115684864000 x^{13}-183500800000 x^{12}\right ) \log ^6(4)+\left (7696581394432 x^{16}+30666066493440 x^{15}+50734301184000 x^{14}+44627394560000 x^{13}+22020096000000 x^{12}+5780275200000 x^{11}+630784000000 x^{10}\right ) \log ^5(4)+\left (-38482906972160 x^{16}-204440443289600 x^{15}-473520144384000 x^{14}-624783523840000 x^{13}-513802240000000 x^{12}-269746176000000 x^{11}-88309760000000 x^{10}-16486400000000 x^9-1344000000000 x^8\right ) \log ^4(4)-3784179687500 x+\left (123145302310912 x^{16}+817761773158400 x^{15}+2435246456832000 x^{14}+4284229877760000 x^{13}+4932501504000000 x^{12}+3884344934400000 x^{11}+2119434240000000 x^{10}+791347200000000 x^9+193536000000000 x^8+28000000000000 x^7+1820000000000 x^6\right ) \log ^3(4)+\left (-246290604621824 x^{16}-1962628255580160 x^{15}-7143389606707200 x^{14}-15708842885120000 x^{13}-23253221376000000 x^{12}-24415882444800000 x^{11}-18651021312000000 x^{10}-10445783040000000 x^9-4257792000000000 x^8-1232000000000000 x^7-240240000000000 x^6-28350000000000 x^5-1531250000000 x^4\right ) \log ^2(4)+\left (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+732421875000 x^2\right ) \log (4)-152587890625}{134217728 x^{33}}dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle \frac {\int -\frac {2147483648 \left (65536+\log ^8(4)\right ) x^{16}+1495335813775360 x^{15}+7421703487488000 x^{14}+22849226014720000 x^{13}+48855252992000000 x^{12}+76947023462400000 x^{11}+92366962688000000 x^{10}+86219161600000000 x^9+63258624000000000 x^8+36608000000000000 x^7+16656640000000000 x^6+5896800000000000 x^5+1592500000000000 x^4+317187500000000 x^3+43945312500000 x^2+3784179687500 x-134217728 \left (512 x^{16}+680 x^{15}+225 x^{14}\right ) \log ^7(4)+58720256 \left (16384 x^{16}+43520 x^{15}+43200 x^{14}+19000 x^{13}+3125 x^{12}\right ) \log ^6(4)-3670016 \left (2097152 x^{16}+8355840 x^{15}+13824000 x^{14}+12160000 x^{13}+6000000 x^{12}+1575000 x^{11}+171875 x^{10}\right ) \log ^5(4)+1146880 \left (33554432 x^{16}+178257920 x^{15}+412876800 x^{14}+544768000 x^{13}+448000000 x^{12}+235200000 x^{11}+77000000 x^{10}+14375000 x^9+1171875 x^8\right ) \log ^4(4)-14336 \left (8589934592 x^{16}+57042534400 x^{15}+169869312000 x^{14}+298844160000 x^{13}+344064000000 x^{12}+270950400000 x^{11}+147840000000 x^{10}+55200000000 x^9+13500000000 x^8+1953125000 x^7+126953125 x^6\right ) \log ^3(4)+896 \left (274877906944 x^{16}+2190433320960 x^{15}+7972533043200 x^{14}+17532190720000 x^{13}+25952256000000 x^{12}+27249868800000 x^{11}+20815872000000 x^{10}+11658240000000 x^9+4752000000000 x^8+1375000000000 x^7+268125000000 x^6+31640625000 x^5+1708984375 x^4\right ) \log ^2(4)-8 \left (35184372088832 x^{16}+327104709263360 x^{15}+1407031286169600 x^{14}+3712999227392000 x^{13}+6717597286400000 x^{12}+8816846438400000 x^{11}+8659402752000000 x^{10}+6466437120000000 x^9+3690086400000000 x^8+1601600000000000 x^7+520520000000000 x^6+122850000000000 x^5+19906250000000 x^4+1982421875000 x^3+91552734375 x^2\right ) \log (4)+152587890625}{x^{33}}dx}{134217728}\) |
| \(\Big \downarrow \) 25 |
| \(\displaystyle -\frac {\int \frac {2147483648 \left (65536+\log ^8(4)\right ) x^{16}+1495335813775360 x^{15}+7421703487488000 x^{14}+22849226014720000 x^{13}+48855252992000000 x^{12}+76947023462400000 x^{11}+92366962688000000 x^{10}+86219161600000000 x^9+63258624000000000 x^8+36608000000000000 x^7+16656640000000000 x^6+5896800000000000 x^5+1592500000000000 x^4+317187500000000 x^3+43945312500000 x^2+3784179687500 x-134217728 \left (512 x^{16}+680 x^{15}+225 x^{14}\right ) \log ^7(4)+58720256 \left (16384 x^{16}+43520 x^{15}+43200 x^{14}+19000 x^{13}+3125 x^{12}\right ) \log ^6(4)-3670016 \left (2097152 x^{16}+8355840 x^{15}+13824000 x^{14}+12160000 x^{13}+6000000 x^{12}+1575000 x^{11}+171875 x^{10}\right ) \log ^5(4)+1146880 \left (33554432 x^{16}+178257920 x^{15}+412876800 x^{14}+544768000 x^{13}+448000000 x^{12}+235200000 x^{11}+77000000 x^{10}+14375000 x^9+1171875 x^8\right ) \log ^4(4)-14336 \left (8589934592 x^{16}+57042534400 x^{15}+169869312000 x^{14}+298844160000 x^{13}+344064000000 x^{12}+270950400000 x^{11}+147840000000 x^{10}+55200000000 x^9+13500000000 x^8+1953125000 x^7+126953125 x^6\right ) \log ^3(4)+896 \left (274877906944 x^{16}+2190433320960 x^{15}+7972533043200 x^{14}+17532190720000 x^{13}+25952256000000 x^{12}+27249868800000 x^{11}+20815872000000 x^{10}+11658240000000 x^9+4752000000000 x^8+1375000000000 x^7+268125000000 x^6+31640625000 x^5+1708984375 x^4\right ) \log ^2(4)-8 \left (35184372088832 x^{16}+327104709263360 x^{15}+1407031286169600 x^{14}+3712999227392000 x^{13}+6717597286400000 x^{12}+8816846438400000 x^{11}+8659402752000000 x^{10}+6466437120000000 x^9+3690086400000000 x^8+1601600000000000 x^7+520520000000000 x^6+122850000000000 x^5+19906250000000 x^4+1982421875000 x^3+91552734375 x^2\right ) \log (4)+152587890625}{x^{33}}dx}{134217728}\) |
| \(\Big \downarrow \) 2010 |
| \(\displaystyle -\frac {\int \left (\frac {2147483648 (-4+\log (4))^8}{x^{17}}-\frac {91268055040 (-4+\log (4))^7}{x^{18}}-\frac {30198988800 (-60+\log (4)) (-4+\log (4))^6}{x^{19}}+\frac {1115684864000 (-20+\log (4)) (-4+\log (4))^5}{x^{20}}+\frac {183500800000 (-4+\log (4))^4 \left (1040-104 \log (4)+\log ^2(4)\right )}{x^{21}}-\frac {1926758400000 (-4+\log (4))^3 \left (624-104 \log (4)+3 \log ^2(4)\right )}{x^{22}}-\frac {630784000000 (-4+\log (4))^2 \left (-9152+2288 \log (4)-132 \log ^2(4)+\log ^3(4)\right )}{x^{23}}+\frac {471040000000 (4-\log (4)) \left (45760-16016 \log (4)+1540 \log ^2(4)-35 \log ^3(4)\right )}{x^{24}}+\frac {38400000000 \left (1647360-768768 \log (4)+110880 \log ^2(4)-5040 \log ^3(4)+35 \log ^4(4)\right )}{x^{25}}-\frac {800000000000 \left (-45760+16016 \log (4)-1540 \log ^2(4)+35 \log ^3(4)\right )}{x^{26}}-\frac {1820000000000 \left (-9152+2288 \log (4)-132 \log ^2(4)+\log ^3(4)\right )}{x^{27}}+\frac {9450000000000 \left (624-104 \log (4)+3 \log ^2(4)\right )}{x^{28}}+\frac {1531250000000 \left (1040-104 \log (4)+\log ^2(4)\right )}{x^{29}}-\frac {15859375000000 (-20+\log (4))}{x^{30}}-\frac {732421875000 (-60+\log (4))}{x^{31}}+\frac {3784179687500}{x^{32}}+\frac {152587890625}{x^{33}}\right )dx}{134217728}\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle \frac {\frac {152587890625}{32 x^{32}}+\frac {122070312500}{x^{31}}+\frac {24414062500 (60-\log (4))}{x^{30}}+\frac {546875000000 (20-\log (4))}{x^{29}}+\frac {54687500000 \left (1040+\log ^2(4)-104 \log (4)\right )}{x^{28}}+\frac {350000000000 \left (624+3 \log ^2(4)-104 \log (4)\right )}{x^{27}}+\frac {70000000000 \left (9152-\log ^3(4)+132 \log ^2(4)-2288 \log (4)\right )}{x^{26}}+\frac {32000000000 \left (45760-35 \log ^3(4)+1540 \log ^2(4)-16016 \log (4)\right )}{x^{25}}+\frac {1600000000 \left (1647360+35 \log ^4(4)-5040 \log ^3(4)+110880 \log ^2(4)-768768 \log (4)\right )}{x^{24}}+\frac {20480000000 (4-\log (4)) \left (45760-35 \log ^3(4)+1540 \log ^2(4)-16016 \log (4)\right )}{x^{23}}+\frac {28672000000 (4-\log (4))^2 \left (9152-\log ^3(4)+132 \log ^2(4)-2288 \log (4)\right )}{x^{22}}+\frac {91750400000 (4-\log (4))^3 \left (624+3 \log ^2(4)-104 \log (4)\right )}{x^{21}}+\frac {9175040000 (4-\log (4))^4 \left (1040+\log ^2(4)-104 \log (4)\right )}{x^{20}}+\frac {58720256000 (4-\log (4))^5 (20-\log (4))}{x^{19}}+\frac {1677721600 (4-\log (4))^6 (60-\log (4))}{x^{18}}+\frac {5368709120 (4-\log (4))^7}{x^{17}}+\frac {134217728 (4-\log (4))^8}{x^{16}}}{134217728}\) |
Int[(-152587890625 - 3784179687500*x - 43945312500000*x^2 - 31718750000000 0*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 + 15925000 0000000*x^4 + 982800000000000*x^5 + 4164160000000000*x^6 + 128128000000000 00*x^7 + 29520691200000000*x^8 + 51731496960000000*x^9 + 69275222016000000 *x^10 + 70534771507200000*x^11 + 53740778291200000*x^12 + 2970399381913600 0*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 - 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[4]^2 + (1820000000000*x^6 + 28000000000000*x^7 + 193536000000000*x^8 + 791347200000000*x^9 + 2119434240000000*x^10 + 388 4344934400000*x^11 + 4932501504000000*x^12 + 4284229877760000*x^13 + 24352 46456832000*x^14 + 817761773158400*x^15 + 123145302310912*x^16)*Log[4]^3 + (-1344000000000*x^8 - 16486400000000*x^9 - 88309760000000*x^10 - 26974617 6000000*x^11 - 513802240000000*x^12 - 624783523840000*x^13 - 4735201443840 00*x^14 - 204440443289600*x^15 - 38482906972160*x^16)*Log[4]^4 + (63078400 0000*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 - 2536715059200*x^14 - 255550 5541120*x^15 - 962072674304*x^16)*Log[4]^6 + (30198988800*x^14 + 912680550 40*x^15 + 68719476736*x^16)*Log[4]^7 - 2147483648*x^16*Log[4]^8)/(13421772 8*x^33),x]
(152587890625/(32*x^32) + 122070312500/x^31 + (5368709120*(4 - Log[4])^7)/ x^17 + (134217728*(4 - Log[4])^8)/x^16 + (546875000000*(20 - Log[4]))/x^29 + (58720256000*(4 - Log[4])^5*(20 - Log[4]))/x^19 + (24414062500*(60 - Lo g[4]))/x^30 + (1677721600*(4 - Log[4])^6*(60 - Log[4]))/x^18 + (5468750000 0*(1040 - 104*Log[4] + Log[4]^2))/x^28 + (9175040000*(4 - Log[4])^4*(1040 - 104*Log[4] + Log[4]^2))/x^20 + (350000000000*(624 - 104*Log[4] + 3*Log[4 ]^2))/x^27 + (91750400000*(4 - Log[4])^3*(624 - 104*Log[4] + 3*Log[4]^2))/ x^21 + (32000000000*(45760 - 16016*Log[4] + 1540*Log[4]^2 - 35*Log[4]^3))/ x^25 + (20480000000*(4 - Log[4])*(45760 - 16016*Log[4] + 1540*Log[4]^2 - 3 5*Log[4]^3))/x^23 + (70000000000*(9152 - 2288*Log[4] + 132*Log[4]^2 - Log[ 4]^3))/x^26 + (28672000000*(4 - Log[4])^2*(9152 - 2288*Log[4] + 132*Log[4] ^2 - Log[4]^3))/x^22 + (1600000000*(1647360 - 768768*Log[4] + 110880*Log[4 ]^2 - 5040*Log[4]^3 + 35*Log[4]^4))/x^24)/134217728
3.10.15.3.1 Defintions of rubi rules used
Int[(u_.)*((v_.) + (a_.)*(Fx_) + (b_.)*(Fx_))^(p_.), x_Symbol] :> Int[u*(v + (a + b)*Fx)^p, x] /; FreeQ[{a, b}, x] && !FreeQ[Fx, x]
Int[(a_)*(Fx_), x_Symbol] :> Simp[a Int[Fx, x], x] /; FreeQ[a, x] && !Ma tchQ[Fx, (b_)*(Gx_) /; FreeQ[b, x]]
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]]
Leaf count of result is larger than twice the leaf count of optimal. \(453\) vs. \(2(20)=40\).
Time = 0.60 (sec) , antiderivative size = 454, normalized size of antiderivative = 20.64
| method | result | size |
| norman | \(\frac {\frac {152587890625}{4294967296}+\left (-\frac {8544921875 \ln \left (2\right )}{1048576}+\frac {42724609375}{524288}\right ) x^{3}+\left (-\frac {6103515625 \ln \left (2\right )}{16777216}+\frac {91552734375}{8388608}\right ) x^{2}+\left (\frac {1025390625 \ln \left (2\right )^{2}}{32768}-\frac {4443359375 \ln \left (2\right )}{8192}+\frac {13330078125}{8192}\right ) x^{5}+\left (\frac {1708984375 \ln \left (2\right )^{2}}{1048576}-\frac {22216796875 \ln \left (2\right )}{262144}+\frac {111083984375}{262144}\right ) x^{4}+\left (-\frac {68359375 \ln \left (2\right )^{3}}{1024}+\frac {751953125 \ln \left (2\right )^{2}}{512}-\frac {1955078125 \ln \left (2\right )}{256}+\frac {1396484375}{128}\right ) x^{7}+\left (-\frac {68359375 \ln \left (2\right )^{3}}{16384}+\frac {2255859375 \ln \left (2\right )^{2}}{8192}-\frac {9775390625 \ln \left (2\right )}{4096}+\frac {9775390625}{2048}\right ) x^{6}+\left (\frac {2734375 \ln \left (2\right )^{4}}{32}-\frac {8203125 \ln \left (2\right )^{3}}{4}+\frac {54140625 \ln \left (2\right )^{2}}{4}-33515625 \ln \left (2\right )+\frac {55859375}{2}\right ) x^{9}+\left (\frac {13671875 \ln \left (2\right )^{4}}{2048}-\frac {123046875 \ln \left (2\right )^{3}}{256}+\frac {1353515625 \ln \left (2\right )^{2}}{256}-\frac {1173046875 \ln \left (2\right )}{64}+\frac {2513671875}{128}\right ) x^{8}+\left (-65625 \ln \left (2\right )^{5}+1531250 \ln \left (2\right )^{4}-11025000 \ln \left (2\right )^{3}+34650000 \ln \left (2\right )^{2}-50050000 \ln \left (2\right )+27300000\right ) x^{11}+\left (-\frac {109375 \ln \left (2\right )^{5}}{16}+\frac {3828125 \ln \left (2\right )^{4}}{8}-\frac {11484375 \ln \left (2\right )^{3}}{2}+25265625 \ln \left (2\right )^{2}-46921875 \ln \left (2\right )+31281250\right ) x^{10}+\left (4375 \ln \left (2\right )^{6}-262500 \ln \left (2\right )^{5}+3062500 \ln \left (2\right )^{4}-14700000 \ln \left (2\right )^{3}+34650000 \ln \left (2\right )^{2}-40040000 \ln \left (2\right )+18200000\right ) x^{12}+\left (28000 \ln \left (2\right )^{6}-560000 \ln \left (2\right )^{5}+3920000 \ln \left (2\right )^{4}-13440000 \ln \left (2\right )^{3}+24640000 \ln \left (2\right )^{2}-23296000 \ln \left (2\right )+8960000\right ) x^{13}+\left (-5120 \ln \left (2\right )^{7}+71680 \ln \left (2\right )^{6}-430080 \ln \left (2\right )^{5}+1433600 \ln \left (2\right )^{4}-2867200 \ln \left (2\right )^{3}+3440640 \ln \left (2\right )^{2}-2293760 \ln \left (2\right )+655360\right ) x^{15}+\left (-1600 \ln \left (2\right )^{7}+67200 \ln \left (2\right )^{6}-672000 \ln \left (2\right )^{5}+3136000 \ln \left (2\right )^{4}-8064000 \ln \left (2\right )^{3}+11827200 \ln \left (2\right )^{2}-9318400 \ln \left (2\right )+3072000\right ) x^{14}+\left (256 \ln \left (2\right )^{8}-4096 \ln \left (2\right )^{7}+28672 \ln \left (2\right )^{6}-114688 \ln \left (2\right )^{5}+286720 \ln \left (2\right )^{4}-458752 \ln \left (2\right )^{3}+458752 \ln \left (2\right )^{2}-262144 \ln \left (2\right )+65536\right ) x^{16}+\frac {30517578125 x}{33554432}}{x^{32}}\) | \(454\) |
| risch | \(\frac {122070312500 x +\left (-48828125000 \ln \left (2\right )+1464843750000\right ) x^{2}+\left (-1093750000000 \ln \left (2\right )+10937500000000\right ) x^{3}+\left (218750000000 \ln \left (2\right )^{2}-11375000000000 \ln \left (2\right )+56875000000000\right ) x^{4}+\left (4200000000000 \ln \left (2\right )^{2}-72800000000000 \ln \left (2\right )+218400000000000\right ) x^{5}+\left (-560000000000 \ln \left (2\right )^{3}+36960000000000 \ln \left (2\right )^{2}-320320000000000 \ln \left (2\right )+640640000000000\right ) x^{6}+\left (-8960000000000 \ln \left (2\right )^{3}+197120000000000 \ln \left (2\right )^{2}-1025024000000000 \ln \left (2\right )+1464320000000000\right ) x^{7}+\left (896000000000 \ln \left (2\right )^{4}-64512000000000 \ln \left (2\right )^{3}+709632000000000 \ln \left (2\right )^{2}-2460057600000000 \ln \left (2\right )+2635776000000000\right ) x^{8}+\left (11468800000000 \ln \left (2\right )^{4}-275251200000000 \ln \left (2\right )^{3}+1816657920000000 \ln \left (2\right )^{2}-4498391040000000 \ln \left (2\right )+3748659200000000\right ) x^{9}+\left (-917504000000 \ln \left (2\right )^{5}+64225280000000 \ln \left (2\right )^{4}-770703360000000 \ln \left (2\right )^{3}+3391094784000000 \ln \left (2\right )^{2}-6297747456000000 \ln \left (2\right )+4198498304000000\right ) x^{10}+\left (-8808038400000 \ln \left (2\right )^{5}+205520896000000 \ln \left (2\right )^{4}-1479750451200000 \ln \left (2\right )^{3}+4650644275200000 \ln \left (2\right )^{2}-6717597286400000 \ln \left (2\right )+3664143974400000\right ) x^{11}+\left (587202560000 \ln \left (2\right )^{6}-35232153600000 \ln \left (2\right )^{5}+411041792000000 \ln \left (2\right )^{4}-1973000601600000 \ln \left (2\right )^{3}+4650644275200000 \ln \left (2\right )^{2}-5374077829120000 \ln \left (2\right )+2442762649600000\right ) x^{12}+\left (3758096384000 \ln \left (2\right )^{6}-75161927680000 \ln \left (2\right )^{5}+526133493760000 \ln \left (2\right )^{4}-1803886264320000 \ln \left (2\right )^{3}+3307124817920000 \ln \left (2\right )^{2}-3126736191488000 \ln \left (2\right )+1202590842880000\right ) x^{13}+\left (-214748364800 \ln \left (2\right )^{7}+9019431321600 \ln \left (2\right )^{6}-90194313216000 \ln \left (2\right )^{5}+420906795008000 \ln \left (2\right )^{4}-1082331758592000 \ln \left (2\right )^{3}+1587419912601600 \ln \left (2\right )^{2}-1250694476595200 \ln \left (2\right )+412316860416000\right ) x^{14}+\left (-687194767360 \ln \left (2\right )^{7}+9620726743040 \ln \left (2\right )^{6}-57724360458240 \ln \left (2\right )^{5}+192414534860800 \ln \left (2\right )^{4}-384829069721600 \ln \left (2\right )^{3}+461794883665920 \ln \left (2\right )^{2}-307863255777280 \ln \left (2\right )+87960930222080\right ) x^{15}+\left (34359738368 \ln \left (2\right )^{8}-549755813888 \ln \left (2\right )^{7}+3848290697216 \ln \left (2\right )^{6}-15393162788864 \ln \left (2\right )^{5}+38482906972160 \ln \left (2\right )^{4}-61572651155456 \ln \left (2\right )^{3}+61572651155456 \ln \left (2\right )^{2}-35184372088832 \ln \left (2\right )+8796093022208\right ) x^{16}+\frac {152587890625}{32}}{134217728 x^{32}}\) | \(455\) |
| default | \(\text {Expression too large to display}\) | \(471\) |
| gosper | \(\text {Expression too large to display}\) | \(632\) |
| parallelrisch | \(\text {Expression too large to display}\) | \(632\) |
int(1/134217728*(-152587890625-3784179687500*x-76947023462400000*x^11-4885 5252992000000*x^12-22849226014720000*x^13-7421703487488000*x^14-1407374883 55328*x^16-1495335813775360*x^15-36608000000000000*x^7-63258624000000000*x ^8-92366962688000000*x^10-86219161600000000*x^9-16656640000000000*x^6-5896 800000000000*x^5-1592500000000000*x^4-317187500000000*x^3-43945312500000*x ^2-549755813888*x^16*ln(2)^8+128*(68719476736*x^16+91268055040*x^15+301989 88800*x^14)*ln(2)^7+64*(-962072674304*x^16-2555505541120*x^15-253671505920 0*x^14-1115684864000*x^13-183500800000*x^12)*ln(2)^6+32*(7696581394432*x^1 6+30666066493440*x^15+50734301184000*x^14+44627394560000*x^13+220200960000 00*x^12+5780275200000*x^11+630784000000*x^10)*ln(2)^5+16*(-38482906972160* x^16-204440443289600*x^15-473520144384000*x^14-624783523840000*x^13-513802 240000000*x^12-269746176000000*x^11-88309760000000*x^10-16486400000000*x^9 -1344000000000*x^8)*ln(2)^4+8*(123145302310912*x^16+817761773158400*x^15+2 435246456832000*x^14+4284229877760000*x^13+4932501504000000*x^12+388434493 4400000*x^11+2119434240000000*x^10+791347200000000*x^9+193536000000000*x^8 +28000000000000*x^7+1820000000000*x^6)*ln(2)^3+4*(-246290604621824*x^16-19 62628255580160*x^15-7143389606707200*x^14-15708842885120000*x^13-232532213 76000000*x^12-24415882444800000*x^11-18651021312000000*x^10-10445783040000 000*x^9-4257792000000000*x^8-1232000000000000*x^7-240240000000000*x^6-2835 0000000000*x^5-1531250000000*x^4)*ln(2)^2+2*(281474976710656*x^16+26168376 74106880*x^15+11256250289356800*x^14+29703993819136000*x^13+53740778291200 000*x^12+70534771507200000*x^11+69275222016000000*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))/x^33,x,method=_RETURNVERBOSE)
(152587890625/4294967296+(-8544921875/1048576*ln(2)+42724609375/524288)*x^ 3+(-6103515625/16777216*ln(2)+91552734375/8388608)*x^2+(1025390625/32768*l n(2)^2-4443359375/8192*ln(2)+13330078125/8192)*x^5+(1708984375/1048576*ln( 2)^2-22216796875/262144*ln(2)+111083984375/262144)*x^4+(-68359375/1024*ln( 2)^3+751953125/512*ln(2)^2-1955078125/256*ln(2)+1396484375/128)*x^7+(-6835 9375/16384*ln(2)^3+2255859375/8192*ln(2)^2-9775390625/4096*ln(2)+977539062 5/2048)*x^6+(2734375/32*ln(2)^4-8203125/4*ln(2)^3+54140625/4*ln(2)^2-33515 625*ln(2)+55859375/2)*x^9+(13671875/2048*ln(2)^4-123046875/256*ln(2)^3+135 3515625/256*ln(2)^2-1173046875/64*ln(2)+2513671875/128)*x^8+(-65625*ln(2)^ 5+1531250*ln(2)^4-11025000*ln(2)^3+34650000*ln(2)^2-50050000*ln(2)+2730000 0)*x^11+(-109375/16*ln(2)^5+3828125/8*ln(2)^4-11484375/2*ln(2)^3+25265625* ln(2)^2-46921875*ln(2)+31281250)*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)+18200000)*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)^6-430080*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*l n(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
Leaf count of result is larger than twice the leaf count of optimal. 456 vs. \(2 (21) = 42\).
Time = 0.24 (sec) , antiderivative size = 456, normalized size of antiderivative = 20.73 \[ \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}+\left (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}+281474976710656 x^{16}\right ) \log (4)+\left (-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}\right ) \log ^2(4)+\left (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}+817761773158400 x^{15}+123145302310912 x^{16}\right ) \log ^3(4)+\left (-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}\right ) \log ^4(4)+\left (630784000000 x^{10}+5780275200000 x^{11}+22020096000000 x^{12}+44627394560000 x^{13}+50734301184000 x^{14}+30666066493440 x^{15}+7696581394432 x^{16}\right ) \log ^5(4)+\left (-183500800000 x^{12}-1115684864000 x^{13}-2536715059200 x^{14}-2555505541120 x^{15}-962072674304 x^{16}\right ) \log ^6(4)+\left (30198988800 x^{14}+91268055040 x^{15}+68719476736 x^{16}\right ) \log ^7(4)-2147483648 x^{16} \log ^8(4)}{134217728 x^{33}} \, dx =\text {Too large to display} \]
integrate(1/134217728*(-152587890625-3784179687500*x-5896800000000000*x^5- 1592500000000000*x^4-43945312500000*x^2-549755813888*x^16*log(2)^8+128*(68 719476736*x^16+91268055040*x^15+30198988800*x^14)*log(2)^7+64*(-9620726743 04*x^16-2555505541120*x^15-2536715059200*x^14-1115684864000*x^13-183500800 000*x^12)*log(2)^6+32*(7696581394432*x^16+30666066493440*x^15+507343011840 00*x^14+44627394560000*x^13+22020096000000*x^12+5780275200000*x^11+6307840 00000*x^10)*log(2)^5+16*(-38482906972160*x^16-204440443289600*x^15-4735201 44384000*x^14-624783523840000*x^13-513802240000000*x^12-269746176000000*x^ 11-88309760000000*x^10-16486400000000*x^9-1344000000000*x^8)*log(2)^4+8*(1 23145302310912*x^16+817761773158400*x^15+2435246456832000*x^14+42842298777 60000*x^13+4932501504000000*x^12+3884344934400000*x^11+2119434240000000*x^ 10+791347200000000*x^9+193536000000000*x^8+28000000000000*x^7+182000000000 0*x^6)*log(2)^3+4*(-246290604621824*x^16-1962628255580160*x^15-71433896067 07200*x^14-15708842885120000*x^13-23253221376000000*x^12-24415882444800000 *x^11-18651021312000000*x^10-10445783040000000*x^9-4257792000000000*x^8-12 32000000000000*x^7-240240000000000*x^6-28350000000000*x^5-1531250000000*x^ 4)*log(2)^2+2*(281474976710656*x^16+2616837674106880*x^15+1125625028935680 0*x^14+29703993819136000*x^13+53740778291200000*x^12+70534771507200000*x^1 1+69275222016000000*x^10+51731496960000000*x^9+29520691200000000*x^8+12812 800000000000*x^7+4164160000000000*x^6+982800000000000*x^5+159250000000000* x^4+15859375000000*x^3+732421875000*x^2)*log(2)-48855252992000000*x^12-140 737488355328*x^16-16656640000000000*x^6-317187500000000*x^3-86219161600000 000*x^9-92366962688000000*x^10-36608000000000000*x^7-63258624000000000*x^8 -1495335813775360*x^15-7421703487488000*x^14-22849226014720000*x^13-769470 23462400000*x^11)/x^33,x, algorithm=\
1/4294967296*(1099511627776*x^16*log(2)^8 + 281474976710656*x^16 + 2814749 767106560*x^15 + 13194139533312000*x^14 + 38482906972160000*x^13 + 7816840 4787200000*x^12 + 117252607180800000*x^11 + 134351945728000000*x^10 + 1199 57094400000000*x^9 + 84344832000000000*x^8 - 274877906944*(64*x^16 + 80*x^ 15 + 25*x^14)*log(2)^7 + 46858240000000000*x^7 + 30064771072*(4096*x^16 + 10240*x^15 + 9600*x^14 + 4000*x^13 + 625*x^12)*log(2)^6 + 2050048000000000 0*x^6 - 1879048192*(262144*x^16 + 983040*x^15 + 1536000*x^14 + 1280000*x^1 3 + 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 + 229376000*x ^13 + 179200000*x^12 + 89600000*x^11 + 28000000*x^10 + 5000000*x^9 + 39062 5*x^8)*log(2)^4 + 1820000000000000*x^4 - 1835008*(1073741824*x^16 + 671088 6400*x^15 + 18874368000*x^14 + 31457280000*x^13 + 34406400000*x^12 + 25804 800000*x^11 + 13440000000*x^10 + 4800000000*x^9 + 1125000000*x^8 + 1562500 00*x^7 + 9765625*x^6)*log(2)^3 + 350000000000000*x^3 + 28672*(68719476736* x^16 + 515396075520*x^15 + 1771674009600*x^14 + 3690987520000*x^13 + 51904 51200000*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)*log(2)^2 + 46875000000000*x^2 - 256*(4398046511104*x^16 + 38482906972160*x^15 + 156336809574400*x^14 + 390842023936000*x^13 + 6717 59728640000*x^12 + 839699660800000*x^11 + 787218432000000*x^10 + 562298...
Timed out. \[ \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}+\left (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}+281474976710656 x^{16}\right ) \log (4)+\left (-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}\right ) \log ^2(4)+\left (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}+817761773158400 x^{15}+123145302310912 x^{16}\right ) \log ^3(4)+\left (-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}\right ) \log ^4(4)+\left (630784000000 x^{10}+5780275200000 x^{11}+22020096000000 x^{12}+44627394560000 x^{13}+50734301184000 x^{14}+30666066493440 x^{15}+7696581394432 x^{16}\right ) \log ^5(4)+\left (-183500800000 x^{12}-1115684864000 x^{13}-2536715059200 x^{14}-2555505541120 x^{15}-962072674304 x^{16}\right ) \log ^6(4)+\left (30198988800 x^{14}+91268055040 x^{15}+68719476736 x^{16}\right ) \log ^7(4)-2147483648 x^{16} \log ^8(4)}{134217728 x^{33}} \, dx=\text {Timed out} \]
integrate(1/134217728*(-152587890625-3784179687500*x-43945312500000*x**2-1 592500000000000*x**4-86219161600000000*x**9-5896800000000000*x**5-16656640 000000000*x**6-1495335813775360*x**15-7421703487488000*x**14-2284922601472 0000*x**13-76947023462400000*x**11-48855252992000000*x**12-140737488355328 *x**16-317187500000000*x**3-549755813888*x**16*ln(2)**8+128*(68719476736*x **16+91268055040*x**15+30198988800*x**14)*ln(2)**7+64*(-962072674304*x**16 -2555505541120*x**15-2536715059200*x**14-1115684864000*x**13-183500800000* x**12)*ln(2)**6+32*(7696581394432*x**16+30666066493440*x**15+5073430118400 0*x**14+44627394560000*x**13+22020096000000*x**12+5780275200000*x**11+6307 84000000*x**10)*ln(2)**5+16*(-38482906972160*x**16-204440443289600*x**15-4 73520144384000*x**14-624783523840000*x**13-513802240000000*x**12-269746176 000000*x**11-88309760000000*x**10-16486400000000*x**9-1344000000000*x**8)* ln(2)**4+8*(123145302310912*x**16+817761773158400*x**15+2435246456832000*x **14+4284229877760000*x**13+4932501504000000*x**12+3884344934400000*x**11+ 2119434240000000*x**10+791347200000000*x**9+193536000000000*x**8+280000000 00000*x**7+1820000000000*x**6)*ln(2)**3+4*(-246290604621824*x**16-19626282 55580160*x**15-7143389606707200*x**14-15708842885120000*x**13-232532213760 00000*x**12-24415882444800000*x**11-18651021312000000*x**10-10445783040000 000*x**9-4257792000000000*x**8-1232000000000000*x**7-240240000000000*x**6- 28350000000000*x**5-1531250000000*x**4)*ln(2)**2+2*(281474976710656*x**16+ 2616837674106880*x**15+11256250289356800*x**14+29703993819136000*x**13+537 40778291200000*x**12+70534771507200000*x**11+69275222016000000*x**10+51731 496960000000*x**9+29520691200000000*x**8+12812800000000000*x**7+4164160000 000000*x**6+982800000000000*x**5+159250000000000*x**4+15859375000000*x**3+ 732421875000*x**2)*ln(2)-36608000000000000*x**7-63258624000000000*x**8-923 66962688000000*x**10)/x**33,x)
Leaf count of result is larger than twice the leaf count of optimal. 449 vs. \(2 (21) = 42\).
Time = 0.20 (sec) , antiderivative size = 449, normalized size of antiderivative = 20.41 \[ \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}+\left (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}+281474976710656 x^{16}\right ) \log (4)+\left (-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}\right ) \log ^2(4)+\left (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}+817761773158400 x^{15}+123145302310912 x^{16}\right ) \log ^3(4)+\left (-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}\right ) \log ^4(4)+\left (630784000000 x^{10}+5780275200000 x^{11}+22020096000000 x^{12}+44627394560000 x^{13}+50734301184000 x^{14}+30666066493440 x^{15}+7696581394432 x^{16}\right ) \log ^5(4)+\left (-183500800000 x^{12}-1115684864000 x^{13}-2536715059200 x^{14}-2555505541120 x^{15}-962072674304 x^{16}\right ) \log ^6(4)+\left (30198988800 x^{14}+91268055040 x^{15}+68719476736 x^{16}\right ) \log ^7(4)-2147483648 x^{16} \log ^8(4)}{134217728 x^{33}} \, dx =\text {Too large to display} \]
integrate(1/134217728*(-152587890625-3784179687500*x-5896800000000000*x^5- 1592500000000000*x^4-43945312500000*x^2-549755813888*x^16*log(2)^8+128*(68 719476736*x^16+91268055040*x^15+30198988800*x^14)*log(2)^7+64*(-9620726743 04*x^16-2555505541120*x^15-2536715059200*x^14-1115684864000*x^13-183500800 000*x^12)*log(2)^6+32*(7696581394432*x^16+30666066493440*x^15+507343011840 00*x^14+44627394560000*x^13+22020096000000*x^12+5780275200000*x^11+6307840 00000*x^10)*log(2)^5+16*(-38482906972160*x^16-204440443289600*x^15-4735201 44384000*x^14-624783523840000*x^13-513802240000000*x^12-269746176000000*x^ 11-88309760000000*x^10-16486400000000*x^9-1344000000000*x^8)*log(2)^4+8*(1 23145302310912*x^16+817761773158400*x^15+2435246456832000*x^14+42842298777 60000*x^13+4932501504000000*x^12+3884344934400000*x^11+2119434240000000*x^ 10+791347200000000*x^9+193536000000000*x^8+28000000000000*x^7+182000000000 0*x^6)*log(2)^3+4*(-246290604621824*x^16-1962628255580160*x^15-71433896067 07200*x^14-15708842885120000*x^13-23253221376000000*x^12-24415882444800000 *x^11-18651021312000000*x^10-10445783040000000*x^9-4257792000000000*x^8-12 32000000000000*x^7-240240000000000*x^6-28350000000000*x^5-1531250000000*x^ 4)*log(2)^2+2*(281474976710656*x^16+2616837674106880*x^15+1125625028935680 0*x^14+29703993819136000*x^13+53740778291200000*x^12+70534771507200000*x^1 1+69275222016000000*x^10+51731496960000000*x^9+29520691200000000*x^8+12812 800000000000*x^7+4164160000000000*x^6+982800000000000*x^5+159250000000000* x^4+15859375000000*x^3+732421875000*x^2)*log(2)-48855252992000000*x^12-140 737488355328*x^16-16656640000000000*x^6-317187500000000*x^3-86219161600000 000*x^9-92366962688000000*x^10-36608000000000000*x^7-63258624000000000*x^8 -1495335813775360*x^15-7421703487488000*x^14-22849226014720000*x^13-769470 23462400000*x^11)/x^33,x, algorithm=\
1/4294967296*(1099511627776*(log(2)^8 - 16*log(2)^7 + 112*log(2)^6 - 448*l og(2)^5 + 1120*log(2)^4 - 1792*log(2)^3 + 1792*log(2)^2 - 1024*log(2) + 25 6)*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*log(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 + 6 864*log(2) - 4576)*x^10 + 10485760000000*(35*log(2)^4 - 840*log(2)^3 + 554 4*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 - 17920000000000*(log(2 )^3 - 66*log(2)^2 + 572*log(2) - 1144)*x^6 + 44800000000000*(3*log(2)^2 - 52*log(2) + 156)*x^5 + 7000000000000*(log(2)^2 - 52*log(2) + 260)*x^4 - 35 000000000000*x^3*(log(2) - 10) - 1562500000000*x^2*(log(2) - 30) + 3906250 000000*x + 152587890625)/x^32
Leaf count of result is larger than twice the leaf count of optimal. 631 vs. \(2 (21) = 42\).
Time = 0.28 (sec) , antiderivative size = 631, normalized size of antiderivative = 28.68 \[ \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}+\left (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}+281474976710656 x^{16}\right ) \log (4)+\left (-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}\right ) \log ^2(4)+\left (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}+817761773158400 x^{15}+123145302310912 x^{16}\right ) \log ^3(4)+\left (-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}\right ) \log ^4(4)+\left (630784000000 x^{10}+5780275200000 x^{11}+22020096000000 x^{12}+44627394560000 x^{13}+50734301184000 x^{14}+30666066493440 x^{15}+7696581394432 x^{16}\right ) \log ^5(4)+\left (-183500800000 x^{12}-1115684864000 x^{13}-2536715059200 x^{14}-2555505541120 x^{15}-962072674304 x^{16}\right ) \log ^6(4)+\left (30198988800 x^{14}+91268055040 x^{15}+68719476736 x^{16}\right ) \log ^7(4)-2147483648 x^{16} \log ^8(4)}{134217728 x^{33}} \, dx=\text {Too large to display} \]
integrate(1/134217728*(-152587890625-3784179687500*x-5896800000000000*x^5- 1592500000000000*x^4-43945312500000*x^2-549755813888*x^16*log(2)^8+128*(68 719476736*x^16+91268055040*x^15+30198988800*x^14)*log(2)^7+64*(-9620726743 04*x^16-2555505541120*x^15-2536715059200*x^14-1115684864000*x^13-183500800 000*x^12)*log(2)^6+32*(7696581394432*x^16+30666066493440*x^15+507343011840 00*x^14+44627394560000*x^13+22020096000000*x^12+5780275200000*x^11+6307840 00000*x^10)*log(2)^5+16*(-38482906972160*x^16-204440443289600*x^15-4735201 44384000*x^14-624783523840000*x^13-513802240000000*x^12-269746176000000*x^ 11-88309760000000*x^10-16486400000000*x^9-1344000000000*x^8)*log(2)^4+8*(1 23145302310912*x^16+817761773158400*x^15+2435246456832000*x^14+42842298777 60000*x^13+4932501504000000*x^12+3884344934400000*x^11+2119434240000000*x^ 10+791347200000000*x^9+193536000000000*x^8+28000000000000*x^7+182000000000 0*x^6)*log(2)^3+4*(-246290604621824*x^16-1962628255580160*x^15-71433896067 07200*x^14-15708842885120000*x^13-23253221376000000*x^12-24415882444800000 *x^11-18651021312000000*x^10-10445783040000000*x^9-4257792000000000*x^8-12 32000000000000*x^7-240240000000000*x^6-28350000000000*x^5-1531250000000*x^ 4)*log(2)^2+2*(281474976710656*x^16+2616837674106880*x^15+1125625028935680 0*x^14+29703993819136000*x^13+53740778291200000*x^12+70534771507200000*x^1 1+69275222016000000*x^10+51731496960000000*x^9+29520691200000000*x^8+12812 800000000000*x^7+4164160000000000*x^6+982800000000000*x^5+159250000000000* x^4+15859375000000*x^3+732421875000*x^2)*log(2)-48855252992000000*x^12-140 737488355328*x^16-16656640000000000*x^6-317187500000000*x^3-86219161600000 000*x^9-92366962688000000*x^10-36608000000000000*x^7-63258624000000000*x^8 -1495335813775360*x^15-7421703487488000*x^14-22849226014720000*x^13-769470 23462400000*x^11)/x^33,x, algorithm=\
1/4294967296*(1099511627776*x^16*log(2)^8 - 17592186044416*x^16*log(2)^7 + 123145302310912*x^16*log(2)^6 - 21990232555520*x^15*log(2)^7 - 4925812092 43648*x^16*log(2)^5 + 307863255777280*x^15*log(2)^6 - 6871947673600*x^14*l og(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 + 6157265 115545600*x^15*log(2)^4 - 2886218022912000*x^14*log(2)^5 + 120259084288000 *x^13*log(2)^6 + 1970324836974592*x^16*log(2)^2 - 12314530231091200*x^15*l og(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) + 147774362 77309440*x^15*log(2)^2 - 34634616274944000*x^14*log(2)^3 + 168362718003200 00*x^13*log(2)^4 - 1127428915200000*x^12*log(2)^5 + 281474976710656*x^16 - 9851624184872960*x^15*log(2) + 50797437203251200*x^14*log(2)^2 - 57724360 458240000*x^13*log(2)^3 + 13153337344000000*x^12*log(2)^4 - 28185722880000 0*x^11*log(2)^5 + 2814749767106560*x^15 - 40022223251046400*x^14*log(2) + 105827994173440000*x^13*log(2)^2 - 63136019251200000*x^12*log(2)^3 + 65766 68672000000*x^11*log(2)^4 - 29360128000000*x^10*log(2)^5 + 131941395333120 00*x^14 - 100055558127616000*x^13*log(2) + 148820616806400000*x^12*log(2)^ 2 - 47352014438400000*x^11*log(2)^3 + 2055208960000000*x^10*log(2)^4 + 384 82906972160000*x^13 - 171970490531840000*x^12*log(2) + 148820616806400000* x^11*log(2)^2 - 24662507520000000*x^10*log(2)^3 + 367001600000000*x^9*l...
Time = 12.34 (sec) , antiderivative size = 461, normalized size of antiderivative = 20.95 \[ \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}+\left (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}+281474976710656 x^{16}\right ) \log (4)+\left (-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}\right ) \log ^2(4)+\left (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}+817761773158400 x^{15}+123145302310912 x^{16}\right ) \log ^3(4)+\left (-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}\right ) \log ^4(4)+\left (630784000000 x^{10}+5780275200000 x^{11}+22020096000000 x^{12}+44627394560000 x^{13}+50734301184000 x^{14}+30666066493440 x^{15}+7696581394432 x^{16}\right ) \log ^5(4)+\left (-183500800000 x^{12}-1115684864000 x^{13}-2536715059200 x^{14}-2555505541120 x^{15}-962072674304 x^{16}\right ) \log ^6(4)+\left (30198988800 x^{14}+91268055040 x^{15}+68719476736 x^{16}\right ) \log ^7(4)-2147483648 x^{16} \log ^8(4)}{134217728 x^{33}} \, dx =\text {Too large to display} \]
int(-((946044921875*x)/33554432 + 4096*x^16*log(2)^8 - (log(2)^3*(18200000 00000*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 + 817761773158400*x^15 + 12 3145302310912*x^16))/16777216 - (log(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 + 69 275222016000000*x^10 + 70534771507200000*x^11 + 53740778291200000*x^12 + 2 9703993819136000*x^13 + 11256250289356800*x^14 + 2616837674106880*x^15 + 2 81474976710656*x^16))/67108864 + (log(2)^2*(1531250000000*x^4 + 2835000000 0000*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))/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 + 25555055 41120*x^15 + 962072674304*x^16))/2097152 - (log(2)^5*(630784000000*x^10 + 5780275200000*x^11 + 22020096000000*x^12 + 44627394560000*x^13 + 507343011 84000*x^14 + 30666066493440*x^15 + 7696581394432*x^16))/4194304 + (1373291 015625*x^2)/4194304 + (1239013671875*x^3)/524288 + (777587890625*x^4)/6553 6 + (359912109375*x^5)/8192 + (127080078125*x^6)/1024 + (34912109375*x^7)/ 128 + (7541015625*x^8)/16 + (1284765625*x^9)/2 + 688187500*x^10 + 57330000 0*x^11 + 364000000*x^12 + 170240000*x^13 + 55296000*x^14 + 11141120*x^15 + 1048576*x^16 + (log(2)^4*(1344000000000*x^8 + 16486400000000*x^9 + 883097 60000000*x^10 + 269746176000000*x^11 + 513802240000000*x^12 + 624783523840 000*x^13 + 473520144384000*x^14 + 204440443289600*x^15 + 38482906972160*x^ 16))/8388608 + 152587890625/134217728)/x^33,x)
((30517578125*x)/33554432 - x^10*(46921875*log(2) - 25265625*log(2)^2 + (1 1484375*log(2)^3)/2 - (3828125*log(2)^4)/8 + (109375*log(2)^5)/16 - 312812 50) - x^11*(50050000*log(2) - 34650000*log(2)^2 + 11025000*log(2)^3 - 1531 250*log(2)^4 + 65625*log(2)^5 - 27300000) + x^8*((1353515625*log(2)^2)/256 - (1173046875*log(2))/64 - (123046875*log(2)^3)/256 + (13671875*log(2)^4) /2048 + 2513671875/128) - x^2*((6103515625*log(2))/16777216 - 91552734375/ 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*(34 650000*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))/10 48576 - 42724609375/524288) - x^15*(2293760*log(2) - 3440640*log(2)^2 + 28 67200*log(2)^3 - 1433600*log(2)^4 + 430080*log(2)^5 - 71680*log(2)^6 + 512 0*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)/5 12 + (68359375*log(2)^3)/1024 - 1396484375/128) - x^6*((9775390625*log(2)) /4096 - (2255859375*log(2)^2)/8192 + (68359375*log(2)^3)/16384 - 977539062 5/2048) + x^9*((54140625*log(2)^2)/4 - 33515625*log(2) - (8203125*log(2...