\[ \int \frac {7}{20} \sqrt [5]{-2 e^3 x^2+3 e^6 x^2} \, dx \]
Optimal antiderivative \[ \frac {x \left (x \,{\mathrm e}^{3} \left (3 \left ({\mathrm e}^{3}-1\right ) x +x \right )\right )^{\frac {1}{5}}}{4} \]
command
integrate(7/20*(3*x^2*exp(3)^2-2*x^2*exp(3))^(1/5),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ \frac {1}{4} \, {\left (3 \, x^{2} e^{6} - 2 \, x^{2} e^{3}\right )}^{\frac {1}{5}} x \]
Giac 1.7.0 via sagemath 9.3 output
\[ \int \frac {7}{20} \, {\left (3 \, x^{2} e^{6} - 2 \, x^{2} e^{3}\right )}^{\frac {1}{5}}\,{d x} \]________________________________________________________________________________________