\[ \int \frac {e^{-7 x/3} \left (\left (192+e^{7 x/3} \left (-36-12 x+12 x^2\right )\right ) \log ^3(x)+\left (-112 x+e^{7 x/3} \left (-3 x+6 x^2\right )\right ) \log ^4(x)\right )}{3 x} \, dx \]
Optimal antiderivative \[ \ln \left (x \right )^{4} \left (x^{2}-3+16 \,{\mathrm e}^{-\frac {7 x}{3}}-x \right ) \]
command
integrate(1/3*(((6*x^2-3*x)*exp(7/3*x)-112*x)*log(x)^4+((12*x^2-12*x-36)*exp(7/3*x)+192)*log(x)^3)/x/exp(7/3*x),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ x^{2} \log \left (3\right )^{4} + 4 \, x^{2} \log \left (3\right )^{3} \log \left (\frac {1}{3} \, x\right ) + 6 \, x^{2} \log \left (3\right )^{2} \log \left (\frac {1}{3} \, x\right )^{2} + 4 \, x^{2} \log \left (3\right ) \log \left (\frac {1}{3} \, x\right )^{3} + x^{2} \log \left (\frac {1}{3} \, x\right )^{4} - x \log \left (3\right )^{4} + 16 \, e^{\left (-\frac {7}{3} \, x\right )} \log \left (3\right )^{4} - 4 \, x \log \left (3\right )^{3} \log \left (\frac {1}{3} \, x\right ) + 64 \, e^{\left (-\frac {7}{3} \, x\right )} \log \left (3\right )^{3} \log \left (\frac {1}{3} \, x\right ) - 6 \, x \log \left (3\right )^{2} \log \left (\frac {1}{3} \, x\right )^{2} + 96 \, e^{\left (-\frac {7}{3} \, x\right )} \log \left (3\right )^{2} \log \left (\frac {1}{3} \, x\right )^{2} - 4 \, x \log \left (3\right ) \log \left (\frac {1}{3} \, x\right )^{3} + 64 \, e^{\left (-\frac {7}{3} \, x\right )} \log \left (3\right ) \log \left (\frac {1}{3} \, x\right )^{3} - x \log \left (\frac {1}{3} \, x\right )^{4} + 16 \, e^{\left (-\frac {7}{3} \, x\right )} \log \left (\frac {1}{3} \, x\right )^{4} - 12 \, \log \left (3\right )^{3} \log \left (\frac {1}{3} \, x\right ) - 18 \, \log \left (3\right )^{2} \log \left (\frac {1}{3} \, x\right )^{2} - 12 \, \log \left (3\right ) \log \left (\frac {1}{3} \, x\right )^{3} - 3 \, \log \left (\frac {1}{3} \, x\right )^{4} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \int \frac {{\left ({\left (3 \, {\left (2 \, x^{2} - x\right )} e^{\left (\frac {7}{3} \, x\right )} - 112 \, x\right )} \log \left (x\right )^{4} + 12 \, {\left ({\left (x^{2} - x - 3\right )} e^{\left (\frac {7}{3} \, x\right )} + 16\right )} \log \left (x\right )^{3}\right )} e^{\left (-\frac {7}{3} \, x\right )}}{3 \, x}\,{d x} \]________________________________________________________________________________________