\[ \int \frac {-6 x^3+28 x^5-22 x^7+16 x \log (3)+\left (2 x^3-4 x^5+2 x^7+16 x \log (3)\right ) \log \left (\frac {1}{64} \left (x^4-4 x^6+6 x^8-4 x^{10}+x^{12}+\left (16 x^2-32 x^4+16 x^6\right ) \log (3)+64 \log ^2(3)\right )\right )}{x^2-2 x^4+x^6+8 \log (3)+\left (3 x^2-6 x^4+3 x^6+24 \log (3)\right ) \log \left (\frac {1}{64} \left (x^4-4 x^6+6 x^8-4 x^{10}+x^{12}+\left (16 x^2-32 x^4+16 x^6\right ) \log (3)+64 \log ^2(3)\right )\right )+\left (3 x^2-6 x^4+3 x^6+24 \log (3)\right ) \log ^2\left (\frac {1}{64} \left (x^4-4 x^6+6 x^8-4 x^{10}+x^{12}+\left (16 x^2-32 x^4+16 x^6\right ) \log (3)+64 \log ^2(3)\right )\right )+\left (x^2-2 x^4+x^6+8 \log (3)\right ) \log ^3\left (\frac {1}{64} \left (x^4-4 x^6+6 x^8-4 x^{10}+x^{12}+\left (16 x^2-32 x^4+16 x^6\right ) \log (3)+64 \log ^2(3)\right )\right )} \, dx \]
Optimal antiderivative \[ \frac {x^{2}}{\left (\ln \left (\left (\ln \left (3\right )+\frac {\left (-x^{3}+x \right )^{2}}{8}\right )^{2}\right )+1\right )^{2}} \]
command
integrate(((16*x*log(3)+2*x^7-4*x^5+2*x^3)*log(log(3)^2+1/64*(16*x^6-32*x^4+16*x^2)*log(3)+1/64*x^12-1/16*x^10+3/32*x^8-1/16*x^6+1/64*x^4)+16*x*log(3)-22*x^7+28*x^5-6*x^3)/((8*log(3)+x^6-2*x^4+x^2)*log(log(3)^2+1/64*(16*x^6-32*x^4+16*x^2)*log(3)+1/64*x^12-1/16*x^10+3/32*x^8-1/16*x^6+1/64*x^4)^3+(24*log(3)+3*x^6-6*x^4+3*x^2)*log(log(3)^2+1/64*(16*x^6-32*x^4+16*x^2)*log(3)+1/64*x^12-1/16*x^10+3/32*x^8-1/16*x^6+1/64*x^4)^2+(24*log(3)+3*x^6-6*x^4+3*x^2)*log(log(3)^2+1/64*(16*x^6-32*x^4+16*x^2)*log(3)+1/64*x^12-1/16*x^10+3/32*x^8-1/16*x^6+1/64*x^4)+8*log(3)+x^6-2*x^4+x^2),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ \frac {3 \, x^{7} - 4 \, x^{5} + x^{3}}{108 \, x^{5} \log \left (2\right )^{2} - 36 \, x^{5} \log \left (2\right ) \log \left (x^{12} - 4 \, x^{10} + 6 \, x^{8} + 16 \, x^{6} \log \left (3\right ) - 4 \, x^{6} - 32 \, x^{4} \log \left (3\right ) + x^{4} + 16 \, x^{2} \log \left (3\right ) + 64 \, \log \left (3\right )^{2}\right ) + 3 \, x^{5} \log \left (x^{12} - 4 \, x^{10} + 6 \, x^{8} + 16 \, x^{6} \log \left (3\right ) - 4 \, x^{6} - 32 \, x^{4} \log \left (3\right ) + x^{4} + 16 \, x^{2} \log \left (3\right ) + 64 \, \log \left (3\right )^{2}\right )^{2} - 36 \, x^{5} \log \left (2\right ) + 6 \, x^{5} \log \left (x^{12} - 4 \, x^{10} + 6 \, x^{8} + 16 \, x^{6} \log \left (3\right ) - 4 \, x^{6} - 32 \, x^{4} \log \left (3\right ) + x^{4} + 16 \, x^{2} \log \left (3\right ) + 64 \, \log \left (3\right )^{2}\right ) + 3 \, x^{5} - 144 \, x^{3} \log \left (2\right )^{2} + 48 \, x^{3} \log \left (2\right ) \log \left (x^{12} - 4 \, x^{10} + 6 \, x^{8} + 16 \, x^{6} \log \left (3\right ) - 4 \, x^{6} - 32 \, x^{4} \log \left (3\right ) + x^{4} + 16 \, x^{2} \log \left (3\right ) + 64 \, \log \left (3\right )^{2}\right ) - 4 \, x^{3} \log \left (x^{12} - 4 \, x^{10} + 6 \, x^{8} + 16 \, x^{6} \log \left (3\right ) - 4 \, x^{6} - 32 \, x^{4} \log \left (3\right ) + x^{4} + 16 \, x^{2} \log \left (3\right ) + 64 \, \log \left (3\right )^{2}\right )^{2} + 48 \, x^{3} \log \left (2\right ) - 8 \, x^{3} \log \left (x^{12} - 4 \, x^{10} + 6 \, x^{8} + 16 \, x^{6} \log \left (3\right ) - 4 \, x^{6} - 32 \, x^{4} \log \left (3\right ) + x^{4} + 16 \, x^{2} \log \left (3\right ) + 64 \, \log \left (3\right )^{2}\right ) - 4 \, x^{3} + 36 \, x \log \left (2\right )^{2} - 12 \, x \log \left (2\right ) \log \left (x^{12} - 4 \, x^{10} + 6 \, x^{8} + 16 \, x^{6} \log \left (3\right ) - 4 \, x^{6} - 32 \, x^{4} \log \left (3\right ) + x^{4} + 16 \, x^{2} \log \left (3\right ) + 64 \, \log \left (3\right )^{2}\right ) + x \log \left (x^{12} - 4 \, x^{10} + 6 \, x^{8} + 16 \, x^{6} \log \left (3\right ) - 4 \, x^{6} - 32 \, x^{4} \log \left (3\right ) + x^{4} + 16 \, x^{2} \log \left (3\right ) + 64 \, \log \left (3\right )^{2}\right )^{2} - 12 \, x \log \left (2\right ) + 2 \, x \log \left (x^{12} - 4 \, x^{10} + 6 \, x^{8} + 16 \, x^{6} \log \left (3\right ) - 4 \, x^{6} - 32 \, x^{4} \log \left (3\right ) + x^{4} + 16 \, x^{2} \log \left (3\right ) + 64 \, \log \left (3\right )^{2}\right ) + x} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \text {Exception raised: TypeError} \]________________________________________________________________________________________