Solution
= Solution
For $Z_t=e^{B_t+at}$, the <Itô formula> gives
$$
dZ_t=Z_t\,dB_t+\left(a+\frac12\right)Z_t\,dt.
$$
Thus its local-martingale part is $M_t=\int_0^tZ_s,dB_s$, its finite-variation part is $(a+1/2)\int_0^tZ_sds$, and its <quadratic variation> clock is
$$
[M]_t=\int_0^tZ_s^2ds.
$$