# Energy of continious charge distribution

In the book of Griffith intro to electrodynamics, on page 94, the energy of continuous charge distribution is derived in the following way:

W(total energy) = $$\frac{1}{2} \int\rho V d\tau$$, where $$\rho$$ is volume charge density, V is potential at that point and $$d\tau$$ is infinitesimal volume element.

Then, using $$\rho = \epsilon_0 \nabla \cdot E$$, one gets:

\begin{align} W = \frac{\epsilon_0}{2} (-\int (\nabla\cdot E)V d\tau \qquad.......(1)\end{align}

After which, he uses integration by parts to get:

\begin{align} W = \frac{\epsilon_0}{2} (-\int (\nabla V)\cdot \,E\ d\tau\quad + \oint V\,E \cdot da ) \qquad.........(2)\end{align}

I am unable to understand how one goes from equation 1 to 2. Please provide me detailed process rather than hints.

$$\overrightarrow{\nabla }\centerdot (V\overrightarrow{E})=V(\overrightarrow{\nabla }\centerdot \overrightarrow{E})+(\overrightarrow{\nabla }V)\centerdot \overrightarrow{E}$$
And then use the Green formula for $$\overrightarrow{\nabla }\centerdot (V\overrightarrow{E})$$