\[ \int \frac {e^{a+b x+c x^2} (b+2 c x)}{a+b x+c x^2} \, dx \]
Optimal antiderivative \[ \expIntegral \left (c \,x^{2}+b x +a \right ) \]
command
integrate(exp(c*x^2+b*x+a)*(2*c*x+b)/(c*x^2+b*x+a),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ {\rm Ei}\left (c x^{2} + b x + a\right ) \]
Giac 1.7.0 via sagemath 9.3 output
\[ \int \frac {{\left (2 \, c x + b\right )} e^{\left (c x^{2} + b x + a\right )}}{c x^{2} + b x + a}\,{d x} \]________________________________________________________________________________________