Let $\{W_t,t \geq 0\}$ be a standard Brownian motion under $\mathbb P$. Let $T_a$ be the hitting time of level $a$, that is: $$T_a= \text{inf}\{t \geq 0:W_t=a\}.$$ From a proposition, we know that $$\mathbb E[\exp(-\theta T_a)] = \exp(-a \sqrt{2\theta}).$$
How do we make use of the above preposition to calculate $\mathbb E[T_a]$?
I am supposed to obtain $\infty$ as the expectation.