proof of inequality $e^x\le x+e^{x^2}$ Does anybody have a simple proof this inequality 
$$e^x\le x+e^{x^2}.$$
Thanks.

Consider $f(x) = x+e^{x^2}-e^x$. Then $f'(x) = 1+ 2xe^{x^2}-e^x$. Find the critical points. So the minimum of $f(x)$ is $0$ which implies that $e^x \leq x+e^{x^2}$. 
