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Falling in Love With Love Chatroulette Camming Not Just for Fun But for Real Chats For Real People The Look   .Q:
How does $\frac{e^{x^2}}{\sqrt{2\pi}}$ = $1-\frac{e^{ -x^2}}{\sqrt{2\pi}}$ hold?
How does
$$ \frac{e^{x^2}}{\sqrt{2\pi}} = 1-\frac{e^{ -x^2}}{\sqrt{2\pi}}$$
hold?
A:
By using the change-of-variables $u=x^2$, one gets:
$$
\frac{e^{u}}{\sqrt{2\pi}} = \frac{1}{\sqrt{2\pi}}\cdot e^u.
$$
By partial fractions, it also holds that:
$$
\frac{1}{\sqrt{2\pi}} = \frac{1}{\sqrt{2\pi}}\cdot\frac{\sqrt{2\pi}}{2} + \frac{1}{2\sqrt{2\pi}}\cdot 1 = \frac{1}{2\sqrt{2\pi}}.
$$
Combining:
$$
\frac{e^{u}}{\sqrt{2\pi}} = \frac{1}{2\sqrt{2\pi}}\cdot e^u,
$$
or, as you wanted:
$$
e^{u/2} = 1-\frac{e^{ -u}}{\sqrt{2\pi}}.
$$
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