43.42 Problem number 6096

\[ \int \frac {e^{\frac {1}{2} \left (5 e^{\frac {1}{x^2}} x-5 x^2-5 x^3\right )} \left (2 x+10 x^3+15 x^4+e^{\frac {1}{x^2}} \left (10-5 x^2\right )\right )}{2 e^{5 e^{\frac {1}{x^2}} x-5 x^2-5 x^3} x-4 e^{\frac {1}{2} \left (5 e^{\frac {1}{x^2}} x-5 x^2-5 x^3\right )} x^2+2 x^3} \, dx \]

Optimal antiderivative \[ \frac {x}{{\mathrm e}^{\frac {5 x \,{\mathrm e}^{\frac {1}{x^{2}}}}{2}-\frac {5 x^{3}}{2}-\frac {5 x^{2}}{2}}-x} \]

command

integrate(((-5*x^2+10)*exp(1/x^2)+15*x^4+10*x^3+2*x)*exp(5/2*x*exp(1/x^2)-5/2*x^3-5/2*x^2)/(2*x*exp(5/2*x*exp(1/x^2)-5/2*x^3-5/2*x^2)^2-4*x^2*exp(5/2*x*exp(1/x^2)-5/2*x^3-5/2*x^2)+2*x^3),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

\[ -\frac {x}{x - e^{\left (-\frac {5}{2} \, x^{3} - \frac {5}{2} \, x^{2} + \frac {5}{2} \, x e^{\left (\frac {1}{x^{2}}\right )}\right )}} \]