Question Number 90023 by Rio Michael last updated on 20/Apr/20
$$\:\int\:{e}^{\mid{x}\mid} \:{dx}\:=\:??? \\ $$
Answered by MJS last updated on 21/Apr/20
$$\mathrm{e}^{\mid{x}\mid} =\begin{cases}{\mathrm{e}^{−{x}} ;\:{x}<\mathrm{0}}\\{\mathrm{e}^{{x}} ;\:{x}\geqslant\mathrm{0}}\end{cases}\:\Rightarrow\:\int\mathrm{e}^{\mid{x}\mid} {dx}=\begin{cases}{−\mathrm{e}^{−{x}} +{C};\:{x}<\mathrm{0}}\\{\mathrm{e}^{{x}} +{C};\:{x}\geqslant\mathrm{0}}\end{cases} \\ $$