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Here's some examples:

1) For the mean-reverting Ornstein-Uhlenbeck (OU) SDE [itex]dX_t = (m-X_t)dt+\sigma X_tdB(t)[/itex], the appropriate integrating factor is [itex]e^t[/itex].

2) For the non-mean-reverting OU SDE [itex]dX_t = uX_tdt + \sigma dB_t[/itex], the integrating factor is [itex]e^{-ut}[/itex].

3) For the SDE [itex]dX_t = udt + \sigma X_t dB_t[/itex], the integrating factor is [itex]e^{-\sigma B_t + \frac12 \sigma^2 t}[/itex].