Linear quadratic regulator equivalence of formulations

Question

I don't see why the following three forms of the LQR optimal control problem are equivalent:

For $\begin{cases} x'=Ax+Bu \\ x(t_0)=x_0\end{cases}$ find

1. $$\min_{u\in L^2(t_0,T; \mathbb{R}^m)} J(u)=\frac{1}{2}\left\{\int_{t_0}^T ||Cx||^2+||u||^2 dt + ||Rx(T)||^2\right \}$$ where || || is the euclidean norm, and $C,R$ are arbitrary matrices.

2. $$\min_{u\in L^2(t_0,T; \mathbb{R}^m)} J(u)=\frac{1}{2}\left\{\int_{t_0}^T x^TQx+u^TRu+2x^TNu\ dt + x(T)^TPx(T)\right\}$$

where $Q,P$ are positive semi-definite matrices and $R$ is positive definite.

3. $$\min_{u\in L^2(t_0,T; \mathbb{R}^m)} J(u)=\frac{1}{2}\left\{\int_{t_0}^T x^TQx+u^TRu\ dt + x(T)^TPx(T)\right\}$$

where $Q,P$ are positive semi-definite matrices and $R$ is positive definite.

I found them posed in all 3 versions but I don't see how to pass from one form to another.