\[ \int \frac {-12 x^3+60 x^4-108 x^5+84 x^6-24 x^7+\left (-144 x^2+384 x^3-576 x^5+336 x^6\right ) \log (2)+\left (-576 x+2304 x^3-1728 x^5\right ) \log ^2(2)+\left (-768-3072 x+6144 x^3+3840 x^4\right ) \log ^3(2)+\left (-3072-9216 x-9216 x^2-3072 x^3\right ) \log ^4(2)}{1-2 x^4+8 x^5-12 x^6+8 x^7-x^8-8 x^9+28 x^{10}-56 x^{11}+70 x^{12}-56 x^{13}+28 x^{14}-8 x^{15}+x^{16}+\left (-32 x^3+64 x^4-64 x^6+64 x^7-192 x^8+448 x^9-448 x^{10}+448 x^{12}-448 x^{13}+192 x^{14}-32 x^{15}\right ) \log (2)+\left (-192 x^2+384 x^4+256 x^6-1792 x^7+1792 x^8+1792 x^9-4480 x^{10}+1792 x^{11}+1792 x^{12}-1792 x^{13}+448 x^{14}\right ) \log ^2(2)+\left (-512 x-1024 x^2+1024 x^4+4096 x^5-7168 x^6-7168 x^7+21504 x^8-21504 x^{10}+7168 x^{11}+7168 x^{12}-3584 x^{13}\right ) \log ^3(2)+\left (-512-2048 x-3072 x^2-2048 x^3+17408 x^4-71680 x^6+107520 x^8-71680 x^{10}+17920 x^{12}\right ) \log ^4(2)+\left (57344 x^3+114688 x^4-114688 x^5-344064 x^6+344064 x^8+114688 x^9-114688 x^{10}-57344 x^{11}\right ) \log ^5(2)+\left (114688 x^2+458752 x^3+458752 x^4-458752 x^5-1146880 x^6-458752 x^7+458752 x^8+458752 x^9+114688 x^{10}\right ) \log ^6(2)+\left (131072 x+786432 x^2+1835008 x^3+1835008 x^4-1835008 x^6-1835008 x^7-786432 x^8-131072 x^9\right ) \log ^7(2)+\left (65536+524288 x+1835008 x^2+3670016 x^3+4587520 x^4+3670016 x^5+1835008 x^6+524288 x^7+65536 x^8\right ) \log ^8(2)} \, dx \]
Optimal antiderivative \[ \frac {3}{-1+\left (x^{2}-x -\left (4+4 x \right ) \ln \left (2\right )\right )^{4}} \]
command
integrate(((-3072*x^3-9216*x^2-9216*x-3072)*log(2)^4+(3840*x^4+6144*x^3-3072*x-768)*log(2)^3+(-1728*x^5+2304*x^3-576*x)*log(2)^2+(336*x^6-576*x^5+384*x^3-144*x^2)*log(2)-24*x^7+84*x^6-108*x^5+60*x^4-12*x^3)/((65536*x^8+524288*x^7+1835008*x^6+3670016*x^5+4587520*x^4+3670016*x^3+1835008*x^2+524288*x+65536)*log(2)^8+(-131072*x^9-786432*x^8-1835008*x^7-1835008*x^6+1835008*x^4+1835008*x^3+786432*x^2+131072*x)*log(2)^7+(114688*x^10+458752*x^9+458752*x^8-458752*x^7-1146880*x^6-458752*x^5+458752*x^4+458752*x^3+114688*x^2)*log(2)^6+(-57344*x^11-114688*x^10+114688*x^9+344064*x^8-344064*x^6-114688*x^5+114688*x^4+57344*x^3)*log(2)^5+(17920*x^12-71680*x^10+107520*x^8-71680*x^6+17408*x^4-2048*x^3-3072*x^2-2048*x-512)*log(2)^4+(-3584*x^13+7168*x^12+7168*x^11-21504*x^10+21504*x^8-7168*x^7-7168*x^6+4096*x^5+1024*x^4-1024*x^2-512*x)*log(2)^3+(448*x^14-1792*x^13+1792*x^12+1792*x^11-4480*x^10+1792*x^9+1792*x^8-1792*x^7+256*x^6+384*x^4-192*x^2)*log(2)^2+(-32*x^15+192*x^14-448*x^13+448*x^12-448*x^10+448*x^9-192*x^8+64*x^7-64*x^6+64*x^4-32*x^3)*log(2)+x^16-8*x^15+28*x^14-56*x^13+70*x^12-56*x^11+28*x^10-8*x^9-x^8+8*x^7-12*x^6+8*x^5-2*x^4+1),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ \frac {3}{x^{8} - 4 \, x^{7} + 6 \, x^{6} - 4 \, x^{5} + 256 \, {\left (x^{4} + 4 \, x^{3} + 6 \, x^{2} + 4 \, x\right )} \log \left (2\right )^{4} + x^{4} - 256 \, {\left (x^{5} + 2 \, x^{4} - 2 \, x^{2} - x\right )} \log \left (2\right )^{3} + 256 \, \log \left (2\right )^{4} + 96 \, {\left (x^{6} - 2 \, x^{4} + x^{2}\right )} \log \left (2\right )^{2} - 16 \, {\left (x^{7} - 2 \, x^{6} + 2 \, x^{4} - x^{3}\right )} \log \left (2\right ) - 1} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \text {Exception raised: TypeError} \]________________________________________________________________________________________