\[ \int \frac {-2+8 e^{4-60 x+225 x^2}-12 e^{8-120 x+450 x^2}+8 e^{12-180 x+675 x^2}-2 e^{16-240 x+900 x^2}+\left (10+e^{12-180 x+675 x^2} \left (720 x-5400 x^2\right )+e^{4-60 x+225 x^2} \left (-20+240 x-1800 x^2\right )+e^{16-240 x+900 x^2} \left (-240 x+1800 x^2\right )+e^{8-120 x+450 x^2} \left (10-720 x+5400 x^2\right )\right ) \log (x)+\left (e^{8-120 x+450 x^2} \left (1200 x-9000 x^2\right )+e^{4-60 x+225 x^2} \left (-1200 x+9000 x^2\right )\right ) \log ^2(x)-\log ^3(x)}{x \log ^3(x)} \, dx \]
Optimal antiderivative \[ \ln \left (\frac {{\mathrm e}^{{\left (5-\frac {\left ({\mathrm e}^{\left (2-15 x \right )^{2}}-1\right )^{2}}{\ln \left (x \right )}\right )}^{2}}}{x}\right ) \]
command
Int[(-2 + 8*E^(4 - 60*x + 225*x^2) - 12*E^(8 - 120*x + 450*x^2) + 8*E^(12 - 180*x + 675*x^2) - 2*E^(16 - 240*x + 900*x^2) + (10 + E^(12 - 180*x + 675*x^2)*(720*x - 5400*x^2) + E^(4 - 60*x + 225*x^2)*(-20 + 240*x - 1800*x^2) + E^(16 - 240*x + 900*x^2)*(-240*x + 1800*x^2) + E^(8 - 120*x + 450*x^2)*(10 - 720*x + 5400*x^2))*Log[x] + (E^(8 - 120*x + 450*x^2)*(1200*x - 9000*x^2) + E^(4 - 60*x + 225*x^2)*(-1200*x + 9000*x^2))*Log[x]^2 - Log[x]^3)/(x*Log[x]^3),x]
Rubi 4.17.3 under Mathematica 13.3.1 output
\[ -\frac {4 e^{3 (2-15 x)^2} \left (2 x \log (x)-15 x^2 \log (x)\right )}{(2-15 x) x \log ^3(x)}+\frac {e^{4 (2-15 x)^2} \left (2 x \log (x)-15 x^2 \log (x)\right )}{(2-15 x) x \log ^3(x)}+\frac {2 e^{2 (2-15 x)^2} \left (75 x^2 \log ^2(x)-45 x^2 \log (x)-10 x \log ^2(x)+6 x \log (x)\right )}{(2-15 x) x \log ^3(x)}-\frac {4 e^{225 x^2-60 x+4} \left (75 x^2 \log ^2(x)-15 x^2 \log (x)-10 x \log ^2(x)+2 x \log (x)\right )}{(2-15 x) x \log ^3(x)}+\frac {1}{\log ^2(x)}-\log (x)-\frac {10}{\log (x)} \]
Rubi 4.16.1 under Mathematica 13.3.1 output
\[ \text {\$Aborted} \]________________________________________________________________________________________