Integrand size = 266, antiderivative size = 24 \[ \int \frac {\left (25165824-524288 x^2\right ) \log ^4(4)-524288 x^2 \log ^4(4) \log (x)+\left (-452984832 x+18874368 x^3-196608 x^5\right ) \log ^3(4) \log ^2(x)+\left (75497472 x+6291456 x^3-163840 x^5\right ) \log ^3(4) \log ^3(x)+\left (2717908992 x^2-169869312 x^4+3538944 x^6-24576 x^8\right ) \log ^2(4) \log ^4(x)+\left (-1358954496 x^2+28311552 x^4+589824 x^6-12288 x^8\right ) \log ^2(4) \log ^5(x)+\left (-5435817984 x^3+452984832 x^5-14155776 x^7+196608 x^9-1024 x^{11}\right ) \log (4) \log ^6(x)+\left (8153726976 x^3-566231040 x^5+14155776 x^7-147456 x^9+512 x^{11}\right ) \log (4) \log ^7(x)+\left (-16307453952 x^4+1698693120 x^6-70778880 x^8+1474560 x^{10}-15360 x^{12}+64 x^{14}\right ) \log ^9(x)}{\left (-254803968 x+26542080 x^3-1105920 x^5+23040 x^7-240 x^9+x^{11}\right ) \log ^9(x)} \, dx=\left (2 x+\frac {\log (4)}{\left (-3+\frac {x^2}{16}\right ) \log ^2(x)}\right )^4 \] Output:
(2*x+2*ln(2)/(1/16*x^2-3)/ln(x)^2)^4
Time = 5.04 (sec) , antiderivative size = 31, normalized size of antiderivative = 1.29 \[ \int \frac {\left (25165824-524288 x^2\right ) \log ^4(4)-524288 x^2 \log ^4(4) \log (x)+\left (-452984832 x+18874368 x^3-196608 x^5\right ) \log ^3(4) \log ^2(x)+\left (75497472 x+6291456 x^3-163840 x^5\right ) \log ^3(4) \log ^3(x)+\left (2717908992 x^2-169869312 x^4+3538944 x^6-24576 x^8\right ) \log ^2(4) \log ^4(x)+\left (-1358954496 x^2+28311552 x^4+589824 x^6-12288 x^8\right ) \log ^2(4) \log ^5(x)+\left (-5435817984 x^3+452984832 x^5-14155776 x^7+196608 x^9-1024 x^{11}\right ) \log (4) \log ^6(x)+\left (8153726976 x^3-566231040 x^5+14155776 x^7-147456 x^9+512 x^{11}\right ) \log (4) \log ^7(x)+\left (-16307453952 x^4+1698693120 x^6-70778880 x^8+1474560 x^{10}-15360 x^{12}+64 x^{14}\right ) \log ^9(x)}{\left (-254803968 x+26542080 x^3-1105920 x^5+23040 x^7-240 x^9+x^{11}\right ) \log ^9(x)} \, dx=\frac {16 \left (8 \log (4)+x \left (-48+x^2\right ) \log ^2(x)\right )^4}{\left (-48+x^2\right )^4 \log ^8(x)} \] Input:
Integrate[((25165824 - 524288*x^2)*Log[4]^4 - 524288*x^2*Log[4]^4*Log[x] + (-452984832*x + 18874368*x^3 - 196608*x^5)*Log[4]^3*Log[x]^2 + (75497472* x + 6291456*x^3 - 163840*x^5)*Log[4]^3*Log[x]^3 + (2717908992*x^2 - 169869 312*x^4 + 3538944*x^6 - 24576*x^8)*Log[4]^2*Log[x]^4 + (-1358954496*x^2 + 28311552*x^4 + 589824*x^6 - 12288*x^8)*Log[4]^2*Log[x]^5 + (-5435817984*x^ 3 + 452984832*x^5 - 14155776*x^7 + 196608*x^9 - 1024*x^11)*Log[4]*Log[x]^6 + (8153726976*x^3 - 566231040*x^5 + 14155776*x^7 - 147456*x^9 + 512*x^11) *Log[4]*Log[x]^7 + (-16307453952*x^4 + 1698693120*x^6 - 70778880*x^8 + 147 4560*x^10 - 15360*x^12 + 64*x^14)*Log[x]^9)/((-254803968*x + 26542080*x^3 - 1105920*x^5 + 23040*x^7 - 240*x^9 + x^11)*Log[x]^9),x]
Output:
(16*(8*Log[4] + x*(-48 + x^2)*Log[x]^2)^4)/((-48 + x^2)^4*Log[x]^8)
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.
| \(\displaystyle \int \frac {-524288 x^2 \log ^4(4) \log (x)+\left (25165824-524288 x^2\right ) \log ^4(4)+\left (-163840 x^5+6291456 x^3+75497472 x\right ) \log ^3(4) \log ^3(x)+\left (-196608 x^5+18874368 x^3-452984832 x\right ) \log ^3(4) \log ^2(x)+\left (-12288 x^8+589824 x^6+28311552 x^4-1358954496 x^2\right ) \log ^2(4) \log ^5(x)+\left (-24576 x^8+3538944 x^6-169869312 x^4+2717908992 x^2\right ) \log ^2(4) \log ^4(x)+\left (512 x^{11}-147456 x^9+14155776 x^7-566231040 x^5+8153726976 x^3\right ) \log (4) \log ^7(x)+\left (-1024 x^{11}+196608 x^9-14155776 x^7+452984832 x^5-5435817984 x^3\right ) \log (4) \log ^6(x)+\left (64 x^{14}-15360 x^{12}+1474560 x^{10}-70778880 x^8+1698693120 x^6-16307453952 x^4\right ) \log ^9(x)}{\left (x^{11}-240 x^9+23040 x^7-1105920 x^5+26542080 x^3-254803968 x\right ) \log ^9(x)} \, dx\) |
| \(\Big \downarrow \) 2026 |
| \(\displaystyle \int \frac {-524288 x^2 \log ^4(4) \log (x)+\left (25165824-524288 x^2\right ) \log ^4(4)+\left (-163840 x^5+6291456 x^3+75497472 x\right ) \log ^3(4) \log ^3(x)+\left (-196608 x^5+18874368 x^3-452984832 x\right ) \log ^3(4) \log ^2(x)+\left (-12288 x^8+589824 x^6+28311552 x^4-1358954496 x^2\right ) \log ^2(4) \log ^5(x)+\left (-24576 x^8+3538944 x^6-169869312 x^4+2717908992 x^2\right ) \log ^2(4) \log ^4(x)+\left (512 x^{11}-147456 x^9+14155776 x^7-566231040 x^5+8153726976 x^3\right ) \log (4) \log ^7(x)+\left (-1024 x^{11}+196608 x^9-14155776 x^7+452984832 x^5-5435817984 x^3\right ) \log (4) \log ^6(x)+\left (64 x^{14}-15360 x^{12}+1474560 x^{10}-70778880 x^8+1698693120 x^6-16307453952 x^4\right ) \log ^9(x)}{x \left (x^{10}-240 x^8+23040 x^6-1105920 x^4+26542080 x^2-254803968\right ) \log ^9(x)}dx\) |
| \(\Big \downarrow \) 2070 |
| \(\displaystyle \int \frac {-524288 x^2 \log ^4(4) \log (x)+\left (25165824-524288 x^2\right ) \log ^4(4)+\left (-163840 x^5+6291456 x^3+75497472 x\right ) \log ^3(4) \log ^3(x)+\left (-196608 x^5+18874368 x^3-452984832 x\right ) \log ^3(4) \log ^2(x)+\left (-12288 x^8+589824 x^6+28311552 x^4-1358954496 x^2\right ) \log ^2(4) \log ^5(x)+\left (-24576 x^8+3538944 x^6-169869312 x^4+2717908992 x^2\right ) \log ^2(4) \log ^4(x)+\left (512 x^{11}-147456 x^9+14155776 x^7-566231040 x^5+8153726976 x^3\right ) \log (4) \log ^7(x)+\left (-1024 x^{11}+196608 x^9-14155776 x^7+452984832 x^5-5435817984 x^3\right ) \log (4) \log ^6(x)+\left (64 x^{14}-15360 x^{12}+1474560 x^{10}-70778880 x^8+1698693120 x^6-16307453952 x^4\right ) \log ^9(x)}{x \left (x^2-48\right )^5 \log ^9(x)}dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {64 \left (x \left (x^2-48\right ) \log ^2(x)+8 \log (4)\right )^3 \left (-x \left (x^2-48\right )^2 \log ^3(x)+16 x^2 \log (4) \log (x)+16 \left (x^2-48\right ) \log (4)\right )}{x \left (48-x^2\right )^5 \log ^9(x)}dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle 64 \int -\frac {\left (8 \log (4)-x \left (48-x^2\right ) \log ^2(x)\right )^3 \left (x \left (48-x^2\right )^2 \log ^3(x)-16 x^2 \log (4) \log (x)+16 \left (48-x^2\right ) \log (4)\right )}{x \left (48-x^2\right )^5 \log ^9(x)}dx\) |
| \(\Big \downarrow \) 25 |
| \(\displaystyle -64 \int \frac {\left (8 \log (4)-x \left (48-x^2\right ) \log ^2(x)\right )^3 \left (x \left (48-x^2\right )^2 \log ^3(x)-16 x^2 \log (4) \log (x)+16 \left (48-x^2\right ) \log (4)\right )}{x \left (48-x^2\right )^5 \log ^9(x)}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -64 \int \left (-x^3-\frac {8 \left (x^2-144\right ) \log (4) x^2}{\left (x^2-48\right )^2 \log ^2(x)}+\frac {16 \log (4) x^2}{\left (x^2-48\right ) \log ^3(x)}+\frac {192 \left (x^2+48\right ) \log ^2(4) x}{\left (x^2-48\right )^3 \log ^4(x)}+\frac {384 \log ^2(4) x}{\left (x^2-48\right )^2 \log ^5(x)}+\frac {8192 \log ^4(4) x}{\left (x^2-48\right )^5 \log ^8(x)}+\frac {512 \left (5 x^2+48\right ) \log ^3(4)}{\left (x^2-48\right )^4 \log ^6(x)}+\frac {3072 \log ^3(4)}{\left (x^2-48\right )^3 \log ^7(x)}+\frac {8192 \log ^4(4)}{\left (x^2-48\right )^4 \log ^9(x) x}\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle -64 \left (16 \log (4) \int \frac {x^2}{\left (x^2-48\right ) \log ^3(x)}dx-8 \log (4) \int \frac {x^2 \left (x^2-144\right )}{\left (x^2-48\right )^2 \log ^2(x)}dx+8192 \log ^4(4) \int \frac {1}{x \left (x^2-48\right )^4 \log ^9(x)}dx+8192 \log ^4(4) \int \frac {x}{\left (x^2-48\right )^5 \log ^8(x)}dx+3072 \log ^3(4) \int \frac {1}{\left (x^2-48\right )^3 \log ^7(x)}dx+512 \log ^3(4) \int \frac {5 x^2+48}{\left (x^2-48\right )^4 \log ^6(x)}dx+384 \log ^2(4) \int \frac {x}{\left (x^2-48\right )^2 \log ^5(x)}dx+192 \log ^2(4) \int \frac {x \left (x^2+48\right )}{\left (x^2-48\right )^3 \log ^4(x)}dx-\frac {x^4}{4}\right )\) |
Input:
Int[((25165824 - 524288*x^2)*Log[4]^4 - 524288*x^2*Log[4]^4*Log[x] + (-452 984832*x + 18874368*x^3 - 196608*x^5)*Log[4]^3*Log[x]^2 + (75497472*x + 62 91456*x^3 - 163840*x^5)*Log[4]^3*Log[x]^3 + (2717908992*x^2 - 169869312*x^ 4 + 3538944*x^6 - 24576*x^8)*Log[4]^2*Log[x]^4 + (-1358954496*x^2 + 283115 52*x^4 + 589824*x^6 - 12288*x^8)*Log[4]^2*Log[x]^5 + (-5435817984*x^3 + 45 2984832*x^5 - 14155776*x^7 + 196608*x^9 - 1024*x^11)*Log[4]*Log[x]^6 + (81 53726976*x^3 - 566231040*x^5 + 14155776*x^7 - 147456*x^9 + 512*x^11)*Log[4 ]*Log[x]^7 + (-16307453952*x^4 + 1698693120*x^6 - 70778880*x^8 + 1474560*x ^10 - 15360*x^12 + 64*x^14)*Log[x]^9)/((-254803968*x + 26542080*x^3 - 1105 920*x^5 + 23040*x^7 - 240*x^9 + x^11)*Log[x]^9),x]
Output:
$Aborted
\[\int \frac {\left (64 x^{14}-15360 x^{12}+1474560 x^{10}-70778880 x^{8}+1698693120 x^{6}-16307453952 x^{4}\right ) \ln \left (x \right )^{9}+2 \left (512 x^{11}-147456 x^{9}+14155776 x^{7}-566231040 x^{5}+8153726976 x^{3}\right ) \ln \left (2\right ) \ln \left (x \right )^{7}+2 \left (-1024 x^{11}+196608 x^{9}-14155776 x^{7}+452984832 x^{5}-5435817984 x^{3}\right ) \ln \left (2\right ) \ln \left (x \right )^{6}+4 \left (-12288 x^{8}+589824 x^{6}+28311552 x^{4}-1358954496 x^{2}\right ) \ln \left (2\right )^{2} \ln \left (x \right )^{5}+4 \left (-24576 x^{8}+3538944 x^{6}-169869312 x^{4}+2717908992 x^{2}\right ) \ln \left (2\right )^{2} \ln \left (x \right )^{4}+8 \left (-163840 x^{5}+6291456 x^{3}+75497472 x \right ) \ln \left (2\right )^{3} \ln \left (x \right )^{3}+8 \left (-196608 x^{5}+18874368 x^{3}-452984832 x \right ) \ln \left (2\right )^{3} \ln \left (x \right )^{2}-8388608 x^{2} \ln \left (2\right )^{4} \ln \left (x \right )+16 \left (-524288 x^{2}+25165824\right ) \ln \left (2\right )^{4}}{\left (x^{11}-240 x^{9}+23040 x^{7}-1105920 x^{5}+26542080 x^{3}-254803968 x \right ) \ln \left (x \right )^{9}}d x\]
Input:
int(((64*x^14-15360*x^12+1474560*x^10-70778880*x^8+1698693120*x^6-16307453 952*x^4)*ln(x)^9+2*(512*x^11-147456*x^9+14155776*x^7-566231040*x^5+8153726 976*x^3)*ln(2)*ln(x)^7+2*(-1024*x^11+196608*x^9-14155776*x^7+452984832*x^5 -5435817984*x^3)*ln(2)*ln(x)^6+4*(-12288*x^8+589824*x^6+28311552*x^4-13589 54496*x^2)*ln(2)^2*ln(x)^5+4*(-24576*x^8+3538944*x^6-169869312*x^4+2717908 992*x^2)*ln(2)^2*ln(x)^4+8*(-163840*x^5+6291456*x^3+75497472*x)*ln(2)^3*ln (x)^3+8*(-196608*x^5+18874368*x^3-452984832*x)*ln(2)^3*ln(x)^2-8388608*x^2 *ln(2)^4*ln(x)+16*(-524288*x^2+25165824)*ln(2)^4)/(x^11-240*x^9+23040*x^7- 1105920*x^5+26542080*x^3-254803968*x)/ln(x)^9,x)
Output:
int(((64*x^14-15360*x^12+1474560*x^10-70778880*x^8+1698693120*x^6-16307453 952*x^4)*ln(x)^9+2*(512*x^11-147456*x^9+14155776*x^7-566231040*x^5+8153726 976*x^3)*ln(2)*ln(x)^7+2*(-1024*x^11+196608*x^9-14155776*x^7+452984832*x^5 -5435817984*x^3)*ln(2)*ln(x)^6+4*(-12288*x^8+589824*x^6+28311552*x^4-13589 54496*x^2)*ln(2)^2*ln(x)^5+4*(-24576*x^8+3538944*x^6-169869312*x^4+2717908 992*x^2)*ln(2)^2*ln(x)^4+8*(-163840*x^5+6291456*x^3+75497472*x)*ln(2)^3*ln (x)^3+8*(-196608*x^5+18874368*x^3-452984832*x)*ln(2)^3*ln(x)^2-8388608*x^2 *ln(2)^4*ln(x)+16*(-524288*x^2+25165824)*ln(2)^4)/(x^11-240*x^9+23040*x^7- 1105920*x^5+26542080*x^3-254803968*x)/ln(x)^9,x)
Leaf count of result is larger than twice the leaf count of optimal. 132 vs. \(2 (21) = 42\).
Time = 0.08 (sec) , antiderivative size = 132, normalized size of antiderivative = 5.50 \[ \int \frac {\left (25165824-524288 x^2\right ) \log ^4(4)-524288 x^2 \log ^4(4) \log (x)+\left (-452984832 x+18874368 x^3-196608 x^5\right ) \log ^3(4) \log ^2(x)+\left (75497472 x+6291456 x^3-163840 x^5\right ) \log ^3(4) \log ^3(x)+\left (2717908992 x^2-169869312 x^4+3538944 x^6-24576 x^8\right ) \log ^2(4) \log ^4(x)+\left (-1358954496 x^2+28311552 x^4+589824 x^6-12288 x^8\right ) \log ^2(4) \log ^5(x)+\left (-5435817984 x^3+452984832 x^5-14155776 x^7+196608 x^9-1024 x^{11}\right ) \log (4) \log ^6(x)+\left (8153726976 x^3-566231040 x^5+14155776 x^7-147456 x^9+512 x^{11}\right ) \log (4) \log ^7(x)+\left (-16307453952 x^4+1698693120 x^6-70778880 x^8+1474560 x^{10}-15360 x^{12}+64 x^{14}\right ) \log ^9(x)}{\left (-254803968 x+26542080 x^3-1105920 x^5+23040 x^7-240 x^9+x^{11}\right ) \log ^9(x)} \, dx=\frac {16 \, {\left ({\left (x^{12} - 192 \, x^{10} + 13824 \, x^{8} - 442368 \, x^{6} + 5308416 \, x^{4}\right )} \log \left (x\right )^{8} + 64 \, {\left (x^{9} - 144 \, x^{7} + 6912 \, x^{5} - 110592 \, x^{3}\right )} \log \left (2\right ) \log \left (x\right )^{6} + 1536 \, {\left (x^{6} - 96 \, x^{4} + 2304 \, x^{2}\right )} \log \left (2\right )^{2} \log \left (x\right )^{4} + 16384 \, {\left (x^{3} - 48 \, x\right )} \log \left (2\right )^{3} \log \left (x\right )^{2} + 65536 \, \log \left (2\right )^{4}\right )}}{{\left (x^{8} - 192 \, x^{6} + 13824 \, x^{4} - 442368 \, x^{2} + 5308416\right )} \log \left (x\right )^{8}} \] Input:
integrate(((64*x^14-15360*x^12+1474560*x^10-70778880*x^8+1698693120*x^6-16 307453952*x^4)*log(x)^9+2*(512*x^11-147456*x^9+14155776*x^7-566231040*x^5+ 8153726976*x^3)*log(2)*log(x)^7+2*(-1024*x^11+196608*x^9-14155776*x^7+4529 84832*x^5-5435817984*x^3)*log(2)*log(x)^6+4*(-12288*x^8+589824*x^6+2831155 2*x^4-1358954496*x^2)*log(2)^2*log(x)^5+4*(-24576*x^8+3538944*x^6-16986931 2*x^4+2717908992*x^2)*log(2)^2*log(x)^4+8*(-163840*x^5+6291456*x^3+7549747 2*x)*log(2)^3*log(x)^3+8*(-196608*x^5+18874368*x^3-452984832*x)*log(2)^3*l og(x)^2-8388608*x^2*log(2)^4*log(x)+16*(-524288*x^2+25165824)*log(2)^4)/(x ^11-240*x^9+23040*x^7-1105920*x^5+26542080*x^3-254803968*x)/log(x)^9,x, al gorithm="fricas")
Output:
16*((x^12 - 192*x^10 + 13824*x^8 - 442368*x^6 + 5308416*x^4)*log(x)^8 + 64 *(x^9 - 144*x^7 + 6912*x^5 - 110592*x^3)*log(2)*log(x)^6 + 1536*(x^6 - 96* x^4 + 2304*x^2)*log(2)^2*log(x)^4 + 16384*(x^3 - 48*x)*log(2)^3*log(x)^2 + 65536*log(2)^4)/((x^8 - 192*x^6 + 13824*x^4 - 442368*x^2 + 5308416)*log(x )^8)
Leaf count of result is larger than twice the leaf count of optimal. 134 vs. \(2 (20) = 40\).
Time = 0.27 (sec) , antiderivative size = 134, normalized size of antiderivative = 5.58 \[ \int \frac {\left (25165824-524288 x^2\right ) \log ^4(4)-524288 x^2 \log ^4(4) \log (x)+\left (-452984832 x+18874368 x^3-196608 x^5\right ) \log ^3(4) \log ^2(x)+\left (75497472 x+6291456 x^3-163840 x^5\right ) \log ^3(4) \log ^3(x)+\left (2717908992 x^2-169869312 x^4+3538944 x^6-24576 x^8\right ) \log ^2(4) \log ^4(x)+\left (-1358954496 x^2+28311552 x^4+589824 x^6-12288 x^8\right ) \log ^2(4) \log ^5(x)+\left (-5435817984 x^3+452984832 x^5-14155776 x^7+196608 x^9-1024 x^{11}\right ) \log (4) \log ^6(x)+\left (8153726976 x^3-566231040 x^5+14155776 x^7-147456 x^9+512 x^{11}\right ) \log (4) \log ^7(x)+\left (-16307453952 x^4+1698693120 x^6-70778880 x^8+1474560 x^{10}-15360 x^{12}+64 x^{14}\right ) \log ^9(x)}{\left (-254803968 x+26542080 x^3-1105920 x^5+23040 x^7-240 x^9+x^{11}\right ) \log ^9(x)} \, dx=16 x^{4} + \frac {\left (262144 x^{3} \log {\left (2 \right )}^{3} - 12582912 x \log {\left (2 \right )}^{3}\right ) \log {\left (x \right )}^{2} + \left (24576 x^{6} \log {\left (2 \right )}^{2} - 2359296 x^{4} \log {\left (2 \right )}^{2} + 56623104 x^{2} \log {\left (2 \right )}^{2}\right ) \log {\left (x \right )}^{4} + \left (1024 x^{9} \log {\left (2 \right )} - 147456 x^{7} \log {\left (2 \right )} + 7077888 x^{5} \log {\left (2 \right )} - 113246208 x^{3} \log {\left (2 \right )}\right ) \log {\left (x \right )}^{6} + 1048576 \log {\left (2 \right )}^{4}}{\left (x^{8} - 192 x^{6} + 13824 x^{4} - 442368 x^{2} + 5308416\right ) \log {\left (x \right )}^{8}} \] Input:
integrate(((64*x**14-15360*x**12+1474560*x**10-70778880*x**8+1698693120*x* *6-16307453952*x**4)*ln(x)**9+2*(512*x**11-147456*x**9+14155776*x**7-56623 1040*x**5+8153726976*x**3)*ln(2)*ln(x)**7+2*(-1024*x**11+196608*x**9-14155 776*x**7+452984832*x**5-5435817984*x**3)*ln(2)*ln(x)**6+4*(-12288*x**8+589 824*x**6+28311552*x**4-1358954496*x**2)*ln(2)**2*ln(x)**5+4*(-24576*x**8+3 538944*x**6-169869312*x**4+2717908992*x**2)*ln(2)**2*ln(x)**4+8*(-163840*x **5+6291456*x**3+75497472*x)*ln(2)**3*ln(x)**3+8*(-196608*x**5+18874368*x* *3-452984832*x)*ln(2)**3*ln(x)**2-8388608*x**2*ln(2)**4*ln(x)+16*(-524288* x**2+25165824)*ln(2)**4)/(x**11-240*x**9+23040*x**7-1105920*x**5+26542080* x**3-254803968*x)/ln(x)**9,x)
Output:
16*x**4 + ((262144*x**3*log(2)**3 - 12582912*x*log(2)**3)*log(x)**2 + (245 76*x**6*log(2)**2 - 2359296*x**4*log(2)**2 + 56623104*x**2*log(2)**2)*log( x)**4 + (1024*x**9*log(2) - 147456*x**7*log(2) + 7077888*x**5*log(2) - 113 246208*x**3*log(2))*log(x)**6 + 1048576*log(2)**4)/((x**8 - 192*x**6 + 138 24*x**4 - 442368*x**2 + 5308416)*log(x)**8)
Leaf count of result is larger than twice the leaf count of optimal. 153 vs. \(2 (21) = 42\).
Time = 0.26 (sec) , antiderivative size = 153, normalized size of antiderivative = 6.38 \[ \int \frac {\left (25165824-524288 x^2\right ) \log ^4(4)-524288 x^2 \log ^4(4) \log (x)+\left (-452984832 x+18874368 x^3-196608 x^5\right ) \log ^3(4) \log ^2(x)+\left (75497472 x+6291456 x^3-163840 x^5\right ) \log ^3(4) \log ^3(x)+\left (2717908992 x^2-169869312 x^4+3538944 x^6-24576 x^8\right ) \log ^2(4) \log ^4(x)+\left (-1358954496 x^2+28311552 x^4+589824 x^6-12288 x^8\right ) \log ^2(4) \log ^5(x)+\left (-5435817984 x^3+452984832 x^5-14155776 x^7+196608 x^9-1024 x^{11}\right ) \log (4) \log ^6(x)+\left (8153726976 x^3-566231040 x^5+14155776 x^7-147456 x^9+512 x^{11}\right ) \log (4) \log ^7(x)+\left (-16307453952 x^4+1698693120 x^6-70778880 x^8+1474560 x^{10}-15360 x^{12}+64 x^{14}\right ) \log ^9(x)}{\left (-254803968 x+26542080 x^3-1105920 x^5+23040 x^7-240 x^9+x^{11}\right ) \log ^9(x)} \, dx=\frac {16 \, {\left ({\left (x^{12} - 192 \, x^{10} + 13824 \, x^{8} - 442368 \, x^{6} + 5308416 \, x^{4}\right )} \log \left (x\right )^{8} + 64 \, {\left (x^{9} \log \left (2\right ) - 144 \, x^{7} \log \left (2\right ) + 6912 \, x^{5} \log \left (2\right ) - 110592 \, x^{3} \log \left (2\right )\right )} \log \left (x\right )^{6} + 1536 \, {\left (x^{6} \log \left (2\right )^{2} - 96 \, x^{4} \log \left (2\right )^{2} + 2304 \, x^{2} \log \left (2\right )^{2}\right )} \log \left (x\right )^{4} + 65536 \, \log \left (2\right )^{4} + 16384 \, {\left (x^{3} \log \left (2\right )^{3} - 48 \, x \log \left (2\right )^{3}\right )} \log \left (x\right )^{2}\right )}}{{\left (x^{8} - 192 \, x^{6} + 13824 \, x^{4} - 442368 \, x^{2} + 5308416\right )} \log \left (x\right )^{8}} \] Input:
integrate(((64*x^14-15360*x^12+1474560*x^10-70778880*x^8+1698693120*x^6-16 307453952*x^4)*log(x)^9+2*(512*x^11-147456*x^9+14155776*x^7-566231040*x^5+ 8153726976*x^3)*log(2)*log(x)^7+2*(-1024*x^11+196608*x^9-14155776*x^7+4529 84832*x^5-5435817984*x^3)*log(2)*log(x)^6+4*(-12288*x^8+589824*x^6+2831155 2*x^4-1358954496*x^2)*log(2)^2*log(x)^5+4*(-24576*x^8+3538944*x^6-16986931 2*x^4+2717908992*x^2)*log(2)^2*log(x)^4+8*(-163840*x^5+6291456*x^3+7549747 2*x)*log(2)^3*log(x)^3+8*(-196608*x^5+18874368*x^3-452984832*x)*log(2)^3*l og(x)^2-8388608*x^2*log(2)^4*log(x)+16*(-524288*x^2+25165824)*log(2)^4)/(x ^11-240*x^9+23040*x^7-1105920*x^5+26542080*x^3-254803968*x)/log(x)^9,x, al gorithm="maxima")
Output:
16*((x^12 - 192*x^10 + 13824*x^8 - 442368*x^6 + 5308416*x^4)*log(x)^8 + 64 *(x^9*log(2) - 144*x^7*log(2) + 6912*x^5*log(2) - 110592*x^3*log(2))*log(x )^6 + 1536*(x^6*log(2)^2 - 96*x^4*log(2)^2 + 2304*x^2*log(2)^2)*log(x)^4 + 65536*log(2)^4 + 16384*(x^3*log(2)^3 - 48*x*log(2)^3)*log(x)^2)/((x^8 - 1 92*x^6 + 13824*x^4 - 442368*x^2 + 5308416)*log(x)^8)
Leaf count of result is larger than twice the leaf count of optimal. 165 vs. \(2 (21) = 42\).
Time = 0.17 (sec) , antiderivative size = 165, normalized size of antiderivative = 6.88 \[ \int \frac {\left (25165824-524288 x^2\right ) \log ^4(4)-524288 x^2 \log ^4(4) \log (x)+\left (-452984832 x+18874368 x^3-196608 x^5\right ) \log ^3(4) \log ^2(x)+\left (75497472 x+6291456 x^3-163840 x^5\right ) \log ^3(4) \log ^3(x)+\left (2717908992 x^2-169869312 x^4+3538944 x^6-24576 x^8\right ) \log ^2(4) \log ^4(x)+\left (-1358954496 x^2+28311552 x^4+589824 x^6-12288 x^8\right ) \log ^2(4) \log ^5(x)+\left (-5435817984 x^3+452984832 x^5-14155776 x^7+196608 x^9-1024 x^{11}\right ) \log (4) \log ^6(x)+\left (8153726976 x^3-566231040 x^5+14155776 x^7-147456 x^9+512 x^{11}\right ) \log (4) \log ^7(x)+\left (-16307453952 x^4+1698693120 x^6-70778880 x^8+1474560 x^{10}-15360 x^{12}+64 x^{14}\right ) \log ^9(x)}{\left (-254803968 x+26542080 x^3-1105920 x^5+23040 x^7-240 x^9+x^{11}\right ) \log ^9(x)} \, dx=16 \, x^{4} + \frac {1024 \, {\left (x^{9} \log \left (2\right ) \log \left (x\right )^{6} - 144 \, x^{7} \log \left (2\right ) \log \left (x\right )^{6} + 24 \, x^{6} \log \left (2\right )^{2} \log \left (x\right )^{4} + 6912 \, x^{5} \log \left (2\right ) \log \left (x\right )^{6} - 2304 \, x^{4} \log \left (2\right )^{2} \log \left (x\right )^{4} - 110592 \, x^{3} \log \left (2\right ) \log \left (x\right )^{6} + 256 \, x^{3} \log \left (2\right )^{3} \log \left (x\right )^{2} + 55296 \, x^{2} \log \left (2\right )^{2} \log \left (x\right )^{4} - 12288 \, x \log \left (2\right )^{3} \log \left (x\right )^{2} + 1024 \, \log \left (2\right )^{4}\right )}}{x^{8} \log \left (x\right )^{8} - 192 \, x^{6} \log \left (x\right )^{8} + 13824 \, x^{4} \log \left (x\right )^{8} - 442368 \, x^{2} \log \left (x\right )^{8} + 5308416 \, \log \left (x\right )^{8}} \] Input:
integrate(((64*x^14-15360*x^12+1474560*x^10-70778880*x^8+1698693120*x^6-16 307453952*x^4)*log(x)^9+2*(512*x^11-147456*x^9+14155776*x^7-566231040*x^5+ 8153726976*x^3)*log(2)*log(x)^7+2*(-1024*x^11+196608*x^9-14155776*x^7+4529 84832*x^5-5435817984*x^3)*log(2)*log(x)^6+4*(-12288*x^8+589824*x^6+2831155 2*x^4-1358954496*x^2)*log(2)^2*log(x)^5+4*(-24576*x^8+3538944*x^6-16986931 2*x^4+2717908992*x^2)*log(2)^2*log(x)^4+8*(-163840*x^5+6291456*x^3+7549747 2*x)*log(2)^3*log(x)^3+8*(-196608*x^5+18874368*x^3-452984832*x)*log(2)^3*l og(x)^2-8388608*x^2*log(2)^4*log(x)+16*(-524288*x^2+25165824)*log(2)^4)/(x ^11-240*x^9+23040*x^7-1105920*x^5+26542080*x^3-254803968*x)/log(x)^9,x, al gorithm="giac")
Output:
16*x^4 + 1024*(x^9*log(2)*log(x)^6 - 144*x^7*log(2)*log(x)^6 + 24*x^6*log( 2)^2*log(x)^4 + 6912*x^5*log(2)*log(x)^6 - 2304*x^4*log(2)^2*log(x)^4 - 11 0592*x^3*log(2)*log(x)^6 + 256*x^3*log(2)^3*log(x)^2 + 55296*x^2*log(2)^2* log(x)^4 - 12288*x*log(2)^3*log(x)^2 + 1024*log(2)^4)/(x^8*log(x)^8 - 192* x^6*log(x)^8 + 13824*x^4*log(x)^8 - 442368*x^2*log(x)^8 + 5308416*log(x)^8 )
Time = 9.05 (sec) , antiderivative size = 8404, normalized size of antiderivative = 350.17 \[ \int \frac {\left (25165824-524288 x^2\right ) \log ^4(4)-524288 x^2 \log ^4(4) \log (x)+\left (-452984832 x+18874368 x^3-196608 x^5\right ) \log ^3(4) \log ^2(x)+\left (75497472 x+6291456 x^3-163840 x^5\right ) \log ^3(4) \log ^3(x)+\left (2717908992 x^2-169869312 x^4+3538944 x^6-24576 x^8\right ) \log ^2(4) \log ^4(x)+\left (-1358954496 x^2+28311552 x^4+589824 x^6-12288 x^8\right ) \log ^2(4) \log ^5(x)+\left (-5435817984 x^3+452984832 x^5-14155776 x^7+196608 x^9-1024 x^{11}\right ) \log (4) \log ^6(x)+\left (8153726976 x^3-566231040 x^5+14155776 x^7-147456 x^9+512 x^{11}\right ) \log (4) \log ^7(x)+\left (-16307453952 x^4+1698693120 x^6-70778880 x^8+1474560 x^{10}-15360 x^{12}+64 x^{14}\right ) \log ^9(x)}{\left (-254803968 x+26542080 x^3-1105920 x^5+23040 x^7-240 x^9+x^{11}\right ) \log ^9(x)} \, dx=\text {Too large to display} \] Input:
int((log(x)^9*(16307453952*x^4 - 1698693120*x^6 + 70778880*x^8 - 1474560*x ^10 + 15360*x^12 - 64*x^14) + 16*log(2)^4*(524288*x^2 - 25165824) - 8*log( 2)^3*log(x)^3*(75497472*x + 6291456*x^3 - 163840*x^5) + 8*log(2)^3*log(x)^ 2*(452984832*x - 18874368*x^3 + 196608*x^5) - 4*log(2)^2*log(x)^4*(2717908 992*x^2 - 169869312*x^4 + 3538944*x^6 - 24576*x^8) - 2*log(2)*log(x)^7*(81 53726976*x^3 - 566231040*x^5 + 14155776*x^7 - 147456*x^9 + 512*x^11) + 2*l og(2)*log(x)^6*(5435817984*x^3 - 452984832*x^5 + 14155776*x^7 - 196608*x^9 + 1024*x^11) + 8388608*x^2*log(2)^4*log(x) + 4*log(2)^2*log(x)^5*(1358954 496*x^2 - 28311552*x^4 - 589824*x^6 + 12288*x^8))/(log(x)^9*(254803968*x - 26542080*x^3 + 1105920*x^5 - 23040*x^7 + 240*x^9 - x^11)),x)
Output:
((256*x*(13045963161600*x^3*log(2)^4 - 2536135238615040*x^3*log(2)^2 - 136 7869237493760*x^2*log(2)^3 - 166947559833600*x^4*log(2)^3 - 21134460321792 0*x^5*log(2)^2 + 3786953195520*x^5*log(2)^4 + 6816006144000*x^6*log(2)^3 + 18712803409920*x^7*log(2)^2 + 244234321920*x^7*log(2)^4 + 100063641600*x^ 8*log(2)^3 - 573308928000*x^9*log(2)^2 + 4234936320*x^9*log(2)^4 - 5019770 880*x^10*log(2)^3 + 8121876480*x^11*log(2)^2 + 16777216*x^11*log(2)^4 + 21 957120*x^12*log(2)^3 - 39813120*x^13*log(2)^2 + 300000*x^14*log(2)^3 - 207 360*x^15*log(2)^2 + 2160*x^17*log(2)^2 + 60867245726760960*x*log(2)^2 - 60 867245726760960*x^2*log(2) + 4174708211712*x*log(2)^4 + 11412608573767680* x^4*log(2) - 951050714480640*x^6*log(2) + 46231631953920*x^8*log(2) - 1444 738498560*x^10*log(2) + 30098718720*x^12*log(2) - 418037760*x^14*log(2) + 3732480*x^16*log(2) - 19440*x^18*log(2) + 45*x^20*log(2) - 281792804290560 *log(2)^3))/(315*(x^2 - 48)^10) - (64*x*log(x)^6*(8916100448256*x^2*log(2) + 2681047351296*x^4*log(2) + 125188374528*x^6*log(2) + 1162100736*x^8*log (2) + 1711872*x^10*log(2) - 288*x^12*log(2) + x^14*log(2)))/(63*(x^2 - 48) ^7) - (32*x*log(x)^4*(101758512660480*x^3*log(2)^2 + 21040692461568*x^5*lo g(2)^2 + 889209225216*x^7*log(2)^2 + 9132244992*x^9*log(2)^2 + 19169280*x^ 11*log(2)^2 + 3328*x^13*log(2)^2 + 40703405064192*x*log(2)^2 - 13076947324 108800*x^2*log(2) + 77358484684800*x^4*log(2) + 23193531187200*x^6*log(2) - 462761164800*x^8*log(2) - 1551052800*x^10*log(2) + 63993600*x^12*log(...
Time = 0.20 (sec) , antiderivative size = 186, normalized size of antiderivative = 7.75 \[ \int \frac {\left (25165824-524288 x^2\right ) \log ^4(4)-524288 x^2 \log ^4(4) \log (x)+\left (-452984832 x+18874368 x^3-196608 x^5\right ) \log ^3(4) \log ^2(x)+\left (75497472 x+6291456 x^3-163840 x^5\right ) \log ^3(4) \log ^3(x)+\left (2717908992 x^2-169869312 x^4+3538944 x^6-24576 x^8\right ) \log ^2(4) \log ^4(x)+\left (-1358954496 x^2+28311552 x^4+589824 x^6-12288 x^8\right ) \log ^2(4) \log ^5(x)+\left (-5435817984 x^3+452984832 x^5-14155776 x^7+196608 x^9-1024 x^{11}\right ) \log (4) \log ^6(x)+\left (8153726976 x^3-566231040 x^5+14155776 x^7-147456 x^9+512 x^{11}\right ) \log (4) \log ^7(x)+\left (-16307453952 x^4+1698693120 x^6-70778880 x^8+1474560 x^{10}-15360 x^{12}+64 x^{14}\right ) \log ^9(x)}{\left (-254803968 x+26542080 x^3-1105920 x^5+23040 x^7-240 x^9+x^{11}\right ) \log ^9(x)} \, dx=\frac {16 \mathrm {log}\left (x \right )^{8} x^{12}-3072 \mathrm {log}\left (x \right )^{8} x^{10}+221184 \mathrm {log}\left (x \right )^{8} x^{8}-7077888 \mathrm {log}\left (x \right )^{8} x^{6}+84934656 \mathrm {log}\left (x \right )^{8} x^{4}+1024 \mathrm {log}\left (x \right )^{6} \mathrm {log}\left (2\right ) x^{9}-147456 \mathrm {log}\left (x \right )^{6} \mathrm {log}\left (2\right ) x^{7}+7077888 \mathrm {log}\left (x \right )^{6} \mathrm {log}\left (2\right ) x^{5}-113246208 \mathrm {log}\left (x \right )^{6} \mathrm {log}\left (2\right ) x^{3}+24576 \mathrm {log}\left (x \right )^{4} \mathrm {log}\left (2\right )^{2} x^{6}-2359296 \mathrm {log}\left (x \right )^{4} \mathrm {log}\left (2\right )^{2} x^{4}+56623104 \mathrm {log}\left (x \right )^{4} \mathrm {log}\left (2\right )^{2} x^{2}+262144 \mathrm {log}\left (x \right )^{2} \mathrm {log}\left (2\right )^{3} x^{3}-12582912 \mathrm {log}\left (x \right )^{2} \mathrm {log}\left (2\right )^{3} x +1048576 \mathrm {log}\left (2\right )^{4}}{\mathrm {log}\left (x \right )^{8} \left (x^{8}-192 x^{6}+13824 x^{4}-442368 x^{2}+5308416\right )} \] Input:
int(((64*x^14-15360*x^12+1474560*x^10-70778880*x^8+1698693120*x^6-16307453 952*x^4)*log(x)^9+2*(512*x^11-147456*x^9+14155776*x^7-566231040*x^5+815372 6976*x^3)*log(2)*log(x)^7+2*(-1024*x^11+196608*x^9-14155776*x^7+452984832* x^5-5435817984*x^3)*log(2)*log(x)^6+4*(-12288*x^8+589824*x^6+28311552*x^4- 1358954496*x^2)*log(2)^2*log(x)^5+4*(-24576*x^8+3538944*x^6-169869312*x^4+ 2717908992*x^2)*log(2)^2*log(x)^4+8*(-163840*x^5+6291456*x^3+75497472*x)*l og(2)^3*log(x)^3+8*(-196608*x^5+18874368*x^3-452984832*x)*log(2)^3*log(x)^ 2-8388608*x^2*log(2)^4*log(x)+16*(-524288*x^2+25165824)*log(2)^4)/(x^11-24 0*x^9+23040*x^7-1105920*x^5+26542080*x^3-254803968*x)/log(x)^9,x)
Output:
(16*(log(x)**8*x**12 - 192*log(x)**8*x**10 + 13824*log(x)**8*x**8 - 442368 *log(x)**8*x**6 + 5308416*log(x)**8*x**4 + 64*log(x)**6*log(2)*x**9 - 9216 *log(x)**6*log(2)*x**7 + 442368*log(x)**6*log(2)*x**5 - 7077888*log(x)**6* log(2)*x**3 + 1536*log(x)**4*log(2)**2*x**6 - 147456*log(x)**4*log(2)**2*x **4 + 3538944*log(x)**4*log(2)**2*x**2 + 16384*log(x)**2*log(2)**3*x**3 - 786432*log(x)**2*log(2)**3*x + 65536*log(2)**4))/(log(x)**8*(x**8 - 192*x* *6 + 13824*x**4 - 442368*x**2 + 5308416))