100.184 Problem number 7960

\[ \int -\frac {1}{e^{10}+2 e^5 x+x^2} \, dx \]

Optimal antiderivative \[ \frac {1}{{\mathrm e}^{5}+x} \]

command

integrate(-1/(exp(5)^2+2*x*exp(5)+x^2),x, algorithm="giac")

Giac 1.9.0-11 via sagemath 9.6 output

\[ \frac {1}{x + e^{5}} \]

Giac 1.7.0 via sagemath 9.3 output

\[ \text {Exception raised: NotImplementedError} \]________________________________________________________________________________________