\documentclass[a4paper]{article}
\begin{document}
\begin{eqnarray*}
f (x)
 & = & \frac{x}{x - a} \\
\end{eqnarray*}
\newpage
\begin{eqnarray*}
F (x)
 & = & \int \frac{x}{x - a} \, \mbox{d}x \\
& = & \int \frac{x - a + a}{x - a} \, \mbox{d}x \\
& = & \int \left ( \frac{x - a}{x - a} + \frac{a}{x - a} \right ) \, \mbox{d}x \\
& = & \int \left ( 1 + \frac{a}{x - a} \right ) \, \mbox{d}x \\
& = & x + a \ln (x - a) + c \\
\end{eqnarray*}
\newpage
\begin{eqnarray*}
f (x)
 & = & \frac{\mbox{d}(F (x))}{\mbox{d}x} \\
& = & \frac{\mbox{d}}{\mbox{d}x} \left ( x + a \ln (x - a) + c \right ) \\
& = & 1 + a \frac{1}{x - a} + 0 \\
& = & 1 + \frac{a}{x - a} \\
& = & \frac{x - a + a}{x - a} \\
& = & \frac{x}{x - a} \\
\end{eqnarray*}
\newpage
\begin{eqnarray*}
F (x)
 & = & x + a \ln | \, x - a \, | + c \\
\end{eqnarray*}
\newpage
\begin{eqnarray*}
F (x)
 & = & a \ln | \, x - a \, | + x + c \\
\end{eqnarray*}
\end{document}
