An Application of Girsanov theorem

Question

I am trying to find the Radon-Nikodym of the path measures $P_X, P_Z$ associated to the following processes \begin{align*} dX_t & = h(X_t)dt + dB_t,\\ dZ_t & = g(Z_t)dt + dB_t. \end{align*} Is the following correct (assuming everything is well defined)? Let us denote by $P_W$ the path measure of the Brownian. Girsanov's theorem says that \begin{equation} \frac{d P_X}{d P_W}(B) = \exp\left( \int_0 ^T h(B_t) dB_t - \frac{1}{2} \int_0 ^T h(B_t)^2 dt \right) \end{equation} and \begin{equation} \frac{dP_W}{dP_Z}(Z) = \exp\left( - \int_0 ^T g(Z_t) d Z_t + \frac{1}{2} \int_0 ^T g(Z_t)^2 dt\right) \end{equation} Thus, \begin{equation} \frac{dP_X}{dP_Z}(Z) = \exp\left( \int_{0}^T \big( h(Z_t) - g(Z_t) \big) dZ_t - \frac{1}{2} \int_{0} ^T \big(h(Z_t)^2 - g(Z_t)^2 \big) dt \right). \end{equation}