Computing closed-form solutions for stochastic integrals

I am new to stochastic calculus. I would like to compute the closed-form solution for $$ \int_0^t \exp \left( \alpha s - \sigma W_s \right) \; {\rm d}s \tag{1}$$ $$ \int_0^t \exp \left( \alpha s - \sigma W_s \right) \; {\rm d} W_s \tag{2} $$ which I encountered when trying to solve the following stochastic differential equation (SDE) $$ dX_t = \theta(\mu - X_t)\; dt + \sigma X_t \; dW_t $$ How to compute these closed-form solutions?