14.1 Problem number 744

\[ \int \left (\frac {1}{\sqrt {e^x+x}}+\frac {e^x}{\sqrt {e^x+x}}\right ) \, dx \]

Optimal antiderivative \[ 2 \sqrt {x +{\mathrm e}^{x}} \]

command

integrate(exp(x)/(exp(x)+x)^(1/2)+1/(exp(x)+x)^(1/2),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

\[ 2 \, \sqrt {x + e^{x}} \]