# Trouble With Applying Ito's Lemma

I am having trouble applying Ito's Formula to the following:

Let $$Z_t = W_{1t}^2 e^{W_{1t}+ \int_0^t W_{3s}dW_{2s}}$$. Find $$dZ_t$$. $$W_1,W_2,W_3$$ are independent Brownian motions.

I know the formula but I am having trouble differentiating the integral with respect to $$W_2$$ and $$W_3$$.

But, if you write, for example $$Z_t = W_{1t}^2 e^{Y_t}$$, where $$Y_t = W_{1t} + \int_0^t W_{3s}dW_{2s}$$, you should be able to see how to do it.
• Ok thanks! I think it is better to define $Y_t$without $W_{1,t}$ Dec 25 '20 at 18:28