Finding the Euler-Lagrange equation of a functional

Question

I have a question about finding the Euler-Lagrange equation. Suppose $\Omega$ is a bound domain in $\mathbb{R}^n$ with smooth boundary $\partial\Omega$. If $u$ is a critical point of the functional: $$F(v)=\int_\Omega (\Delta v)^2$$ where $\Delta$ is the Laplacian, then for all smooth $v$ $$\tag{1}\frac{1}{2}\frac{d}{dt}F(u+tv)\Big|_{t=0}=\int_\Omega \Delta u\Delta v =\int_\Omega v \Delta^2 u +\int_{\partial\Omega}\left(\Delta u\frac{\partial v}{\partial\nu} -v\frac{\partial}{\partial\nu}(\Delta u)\right).$$ To find Euler-Lagrange equation for which $u$ satisfies, we try to put all the derivatives to $u$; something like: $$\frac{1}{2}\frac{d}{dt}F(u+tv)\Big|_{t=0}=\int_\Omega v E_1(u)+\int_{\partial\Omega}v E_2(u)$$ and conclude that $u$ satisfies the Euler-Lagrange equation: $$E_1(u)=0\mbox{ in }\Omega~~\mbox{ and }~~E_2(u)=0\mbox{ on }\partial\Omega.$$ Therefore, I do not know how to deal the the first term in the last integral of $(1)$, since it involves the normal derivative of $v$. I appreciate if someone could give me some ideas. Thank you very much.