I am having a bit of difficulty with the following practice problem that involves multidimensional brownian motion.
With $B_t = (B_t^{(1)},B_t^{(2)})$ apply ito to the following process:
$$X_t = \exp\left(1+\int_0^t{B_s^{(1)}\, dB_s^{(2)}}\right)$$
I have tried proceeding with the differential form with the following function of $y$:
Let $Y_t = \int_0^t{B_s^{(1)}\, dB_s^{(2)}} $, $dY_t = B_t^{(1)}\, dB_t^{(2)} $, $\langle Y\rangle_t = \left(B_t^{(1)}\right)^2 \,dt $
But I am not too sure where to proceed from here or if I am on the right track when it comes to multidimensional Ito.