[tex]\displaystyle \int^{1}_0 \left(e^x + e^{-x} \right) dx\\\\=\displaystyle \int^{1}_0 e^x ~~dx+\displaystyle \int^{1}_0 e^{-x} ~ dx\\\\=\left[ e^x\right]^{1}_{0} -\left[e^{-x} \right]^{1}_0~~~~~~~~~~~~~~~~~~~~~~~;\left[\displaystyle \int e^{mx} ~ dx = \dfrac 1m e^{mx} + C \right]\\\\=\left(e^1 - e^0\right) - \left(e^{-1} - e^0\right)\\\\=(e-1)-\left(\dfrac 1 e - 1\right)\\\\=e-1 -\dfrac 1 e+1\\\\=\dfrac{e^2-1}e[/tex]
