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