\[ \int \frac {e^{2 x} \left (e^4 (48-96 x)-168 x+168 x^2+e^{\frac {1}{3} (2-2 x)} (-48+128 x)\right )}{48 e^8 x^2+48 e^{\frac {2}{3} (2-2 x)} x^2-168 e^4 x^3+147 x^4+e^{\frac {1}{3} (2-2 x)} \left (-96 e^4 x^2+168 x^3\right )} \, dx \]
Optimal antiderivative \[ \frac {{\mathrm e}^{2 x}}{\left (\frac {7 x}{4}+{\mathrm e}^{-\frac {2 x}{3}+\frac {2}{3}}-{\mathrm e}^{4}\right ) x} \]
command
integrate(((128*x-48)*exp(-2/3*x+2/3)+(-96*x+48)*exp(4)+168*x^2-168*x)*exp(x)^2/(48*x^2*exp(-2/3*x+2/3)^2+(-96*x^2*exp(4)+168*x^3)*exp(-2/3*x+2/3)+48*x^2*exp(4)^2-168*x^3*exp(4)+147*x^4),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ \text {could not integrate} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \frac {4 \, {\left (33614 \, x^{6} e^{\left (\frac {8}{3} \, x\right )} + 50421 \, x^{5} e^{\left (\frac {8}{3} \, x\right )} - 96040 \, x^{5} e^{\left (\frac {8}{3} \, x + 4\right )} + 19208 \, x^{5} e^{\left (2 \, x + \frac {2}{3}\right )} + 109760 \, x^{4} e^{\left (\frac {8}{3} \, x + 8\right )} - 115248 \, x^{4} e^{\left (\frac {8}{3} \, x + 4\right )} - 43904 \, x^{4} e^{\left (2 \, x + \frac {14}{3}\right )} + 28812 \, x^{4} e^{\left (2 \, x + \frac {2}{3}\right )} - 62720 \, x^{3} e^{\left (\frac {8}{3} \, x + 12\right )} + 98784 \, x^{3} e^{\left (\frac {8}{3} \, x + 8\right )} + 37632 \, x^{3} e^{\left (2 \, x + \frac {26}{3}\right )} - 49392 \, x^{3} e^{\left (2 \, x + \frac {14}{3}\right )} + 17920 \, x^{2} e^{\left (\frac {8}{3} \, x + 16\right )} - 37632 \, x^{2} e^{\left (\frac {8}{3} \, x + 12\right )} - 14336 \, x^{2} e^{\left (2 \, x + \frac {38}{3}\right )} + 28224 \, x^{2} e^{\left (2 \, x + \frac {26}{3}\right )} - 2048 \, x e^{\left (\frac {8}{3} \, x + 20\right )} + 5376 \, x e^{\left (\frac {8}{3} \, x + 16\right )} + 2048 \, x e^{\left (2 \, x + \frac {50}{3}\right )} - 5376 \, x e^{\left (2 \, x + \frac {38}{3}\right )}\right )}}{235298 \, x^{8} e^{\left (\frac {2}{3} \, x\right )} + 268912 \, x^{7} e^{\frac {2}{3}} + 352947 \, x^{7} e^{\left (\frac {2}{3} \, x\right )} - 806736 \, x^{7} e^{\left (\frac {2}{3} \, x + 4\right )} - 768320 \, x^{6} e^{\frac {14}{3}} + 403368 \, x^{6} e^{\frac {2}{3}} + 1152480 \, x^{6} e^{\left (\frac {2}{3} \, x + 8\right )} - 1008420 \, x^{6} e^{\left (\frac {2}{3} \, x + 4\right )} + 76832 \, x^{6} e^{\left (-\frac {2}{3} \, x + \frac {4}{3}\right )} + 878080 \, x^{5} e^{\frac {26}{3}} - 921984 \, x^{5} e^{\frac {14}{3}} - 878080 \, x^{5} e^{\left (\frac {2}{3} \, x + 12\right )} + 1152480 \, x^{5} e^{\left (\frac {2}{3} \, x + 8\right )} - 175616 \, x^{5} e^{\left (-\frac {2}{3} \, x + \frac {16}{3}\right )} + 115248 \, x^{5} e^{\left (-\frac {2}{3} \, x + \frac {4}{3}\right )} - 501760 \, x^{4} e^{\frac {38}{3}} + 790272 \, x^{4} e^{\frac {26}{3}} + 376320 \, x^{4} e^{\left (\frac {2}{3} \, x + 16\right )} - 658560 \, x^{4} e^{\left (\frac {2}{3} \, x + 12\right )} + 150528 \, x^{4} e^{\left (-\frac {2}{3} \, x + \frac {28}{3}\right )} - 197568 \, x^{4} e^{\left (-\frac {2}{3} \, x + \frac {16}{3}\right )} + 143360 \, x^{3} e^{\frac {50}{3}} - 301056 \, x^{3} e^{\frac {38}{3}} - 86016 \, x^{3} e^{\left (\frac {2}{3} \, x + 20\right )} + 188160 \, x^{3} e^{\left (\frac {2}{3} \, x + 16\right )} - 57344 \, x^{3} e^{\left (-\frac {2}{3} \, x + \frac {40}{3}\right )} + 112896 \, x^{3} e^{\left (-\frac {2}{3} \, x + \frac {28}{3}\right )} - 16384 \, x^{2} e^{\frac {62}{3}} + 43008 \, x^{2} e^{\frac {50}{3}} + 8192 \, x^{2} e^{\left (\frac {2}{3} \, x + 24\right )} - 21504 \, x^{2} e^{\left (\frac {2}{3} \, x + 20\right )} + 8192 \, x^{2} e^{\left (-\frac {2}{3} \, x + \frac {52}{3}\right )} - 21504 \, x^{2} e^{\left (-\frac {2}{3} \, x + \frac {40}{3}\right )}} \]