Variance of Exponential Distribution/Proof 1

Proof
From Variance as Expectation of Square minus Square of Expectation:
 * $\var X = \expect {X^2} - \paren {\expect X}^2$

From Expectation of Exponential Distribution:
 * $\expect X = \beta$

The expectation of $X^2$ is:

Thus the variance of $X$ is: