\documentclass[a4paper]{article}
\begin{document}
\begin{eqnarray*}
f (x)
 & = & \frac{1}{x^{2} (x - a)} \\
\end{eqnarray*}
\newpage
\begin{eqnarray*}
F (x)
 & = & \int \frac{1}{x^{2} (x - a)} \, \mbox{d}x \\
& = & - \frac{1}{a} \int \frac{- a}{x^{2} (x - a)} \, \mbox{d}x \\
& = & - \frac{1}{a} \int \frac{x - a - x}{x^{2} (x - a)} \, \mbox{d}x \\
& = & - \frac{1}{a} \int \left ( \frac{x - a}{x^{2} (x - a)} + \frac{- x}{x^{2} (x - a)} \right ) \, \mbox{d}x \\
& = & - \frac{1}{a} \int \left ( \frac{1}{x^{2}} + \frac{- 1}{x (x - a)} \right ) \, \mbox{d}x \\
& = & - \frac{1}{a} \int \left ( x^{-2} + \frac{1}{a} \frac{- a}{x (x - a)} \right ) \, \mbox{d}x \\
& = & - \frac{1}{a} \int \left ( x^{-2} + \frac{1}{a} \frac{x - a - x}{x (x - a)} \right ) \, \mbox{d}x \\
& = & - \frac{1}{a} \int \left ( x^{-2} + \frac{1}{a} \frac{x - a}{x (x - a)} - \frac{1}{a} \frac{x}{x (x - a)} \right ) \, \mbox{d}x \\
& = & - \frac{1}{a} \int \left ( x^{-2} + \frac{1}{a} \frac{1}{x} - \frac{1}{a} \frac{1}{x - a} \right ) \, \mbox{d}x \\
& = & - \frac{1}{a} \left ( - x^{-1} + \frac{1}{a} \ln x - \frac{1}{a} \ln (x - a) \right ) + c \\
& = & \frac{1}{ax} - \frac{1}{a^{2}} \ln x + \frac{1}{a^{2}} \ln (x - a) + c \\
& = & \frac{1}{ax} + \frac{1}{a^{2}} \ln \frac{x - a}{x} + c \\
& = & \frac{1}{ax} + \frac{1}{a^{2}} \ln \left ( 1 - \frac{a}{x} \right ) + c \\
\end{eqnarray*}
\newpage
\begin{eqnarray*}
f (x)
 & = & \frac{\mbox{d}(F (x))}{\mbox{d}x} \\
& = & \frac{\mbox{d}}{\mbox{d}x} \left ( \frac{1}{ax} + \frac{1}{a^{2}} \ln \left ( 1 - \frac{a}{x} \right ) + c \right ) \\
& = & - \frac{1}{ax^{2}} + \frac{1}{a^{2}} \frac{1}{1 - \frac{a}{x}} \frac{a}{x^{2}} + 0 \\
& = & - \frac{1}{ax^{2}} + \frac{1}{ax^{2} - a^{2}x} \\
& = & - \frac{ax^{2} - a^{2}x}{ax^{2} (ax^{2} - a^{2}x)} + \frac{ax^{2}}{ax^{2} (ax^{2} - a^{2}x)} \\
& = & \frac{- ax^{2} + a^{2}x + ax^{2}}{a^{2}x^{3} (x - a)} \\
& = & \frac{a^{2}x}{a^{2}x^{3} (x - a)} \\
& = & \frac{1}{x^{2} (x - a)} \\
\end{eqnarray*}
\newpage
\begin{eqnarray*}
F (x)
 & = & \frac{1}{ax} + \frac{1}{a^{2}} \ln \left | \, 1 - \frac{a}{x} \, \right | + c \\
\end{eqnarray*}
\newpage
\begin{eqnarray*}
F (x)
 & = & \frac{1}{a^{2}} \ln \left | \, 1 - \frac{a}{x} \, \right | + \frac{1}{ax} + c \\
\end{eqnarray*}
\end{document}
