Latex Version of Equations

Eq. (1)

$$\sigma_{\rm BEB} = \frac{S}{t+(u+1)/n} \left[ 
  \frac{Q \ln t}{2} \left( 1 - \frac{1}{t^2} \right) + (2-Q)
  \left( 1 - \frac{1}{t} - \frac{\ln t}{t+1} \right) \right]~ ,$$


Eq. (2)

$Q = \frac{2}{N} \int \frac{B}{B+W} ~ 
  \frac{{\rm d}f}{{\rm d}W} ~ {\rm d}W ~. $


Eq. (3)

\begin{eqnarray*}\frac{{\rm d}\sigma(W,T)}{{\rm d}W}&=&\frac{S}{B[t+(u+1)/n]} 
   \left\{ \frac{(N_i/N)-2}{t+1} 
   \left( \frac{1}{w+1} + \frac{1}{t-w}
    \right) \right. \\
   &+& \left. [2 - (N_i/N)] ~ \left[ \frac{1}{(w+1)^2} + \frac{1}{(t-w)^2} 
   \right] + \frac{\ln t}{N(w+1)} ~ \frac{{\rm d}f(w)}{{\rm d}w}
   \right\} ~, \end{eqnarray*}


Eq. (4)

${\rm d}f/{\rm d}w = ay^2 + by^3 + cy^4 + dy^5 + ey^6 ~ , $


Eq. (5)

$\sigma_{BE}(T)=\sigma_{\rm PWB}[T/(T+B+E)] ~ ,$


Eq. (6)

$\sigma_E(T)=\sigma_{\rm CB}[T/(T+E)] ~ .$