$\displaystyle Prob(X \leq x | \theta) = 1 - e^{- \theta x}

$

$\displaystyle

\theta $ is gamma distribution so that the PDF of $\displaystyle \theta$ is $\displaystyle g( \theta ) $

$\displaystyle g( \theta ) = \frac{\beta^{\alpha}}{\Gamma(\alpha)} \theta^{\alpha -1}e^{ - \beta \theta} $

Find the marginal distribution of X.

Stuck on trying to integrate with respect to $\displaystyle \theta$, please could someone give me a hand.

Thanks!