# Dynkin formula and expectation

I have a question about the use of Dynkin's formula. Suppose I have a stochastic process $$X_t$$, from an SDE that I cannot solve analytically. I want to find the expectation $$\mathbb{E}X_t$$. By Dynkin with initial condition $$X_0=x$$,

$$\mathbb{E}X_t=x+\mathbb{E}^x\int_0^t L(X_s)ds$$

,here $$L$$ is the generator of the diffusion, found from the SDE. How would one find an expression for the expectation of the integral?