Expecation of a raised random variable

Question

Let $\alpha>0$ be some scalar and $X$ a random variable. How can I calculate $E[\alpha^X]$?

Answer 1

$$E\left[\alpha^X\right] = \int_{-\infty}^\infty \alpha^x f_X(x) dx, \tag{1}$$ where $f_X(x)$ is the probability density function (pdf) of $X$.