Solution
= Solution
Completing the square gives
$$
\boxed{M_X(t)=\frac1{\sqrt{2\pi}}\int_{-\infty}^{\infty}
e^{tx-x^2/2}dx
=e^{t^2/2}\frac1{\sqrt{2\pi}}
\int_{-\infty}^{\infty}e^{-(x-t)^2/2}dx
=e^{t^2/2}.}
$$
= Solution
Completing the square gives
$$
\boxed{M_X(t)=\frac1{\sqrt{2\pi}}\int_{-\infty}^{\infty}
e^{tx-x^2/2}dx
=e^{t^2/2}\frac1{\sqrt{2\pi}}
\int_{-\infty}^{\infty}e^{-(x-t)^2/2}dx
=e^{t^2/2}.}
$$