\documentclass[a4paper]{article}
\begin{document}
\begin{eqnarray*}
f (x)
 & = & \cot^{6} (ax) \\
& = & \frac{1}{\tan^{6} (ax)} \\
& = & \tan^{-6} (ax) \\
\end{eqnarray*}
\newpage
\begin{eqnarray*}
F (x)
 & = & \int \cot^{6} (ax) \, \mbox{d}x \\
& = & \int \frac{\cos^{6} (ax)}{\sin^{6} (ax)} \, \mbox{d}x \\
& = & \int \frac{\cos^{2} (ax) \cos^{2} (ax) \cos^{2} (ax)}{\sin^{6} (ax)} \, \mbox{d}x \\
& = & \int \frac{(1 - \sin^{2} (ax)) (1 - \sin^{2} (ax)) (1 - \sin^{2} (ax))}{\sin^{6} (ax)} \, \mbox{d}x \\
& = & \int \frac{(1 - 2 \sin^{2} (ax) + \sin^{4} (ax)) (1 - \sin^{2} (ax))}{\sin^{6} (ax)} \, \mbox{d}x \\
& = & \int \frac{1 - 3 \sin^{2} (ax) + 3 \sin^{4} (ax) - \sin^{6} (ax)}{\sin^{6} (ax)} \, \mbox{d}x \\
& = & \int \left ( \frac{1}{\sin^{6} (ax)} - 3 \frac{\sin^{2} (ax)}{\sin^{6} (ax)} + 3 \frac{\sin^{4} (ax)}{\sin^{6} (ax)}
 - \frac{\sin^{6} (ax)}{\sin^{6} (ax)} \right ) \, \mbox{d}x \\
& = & \int \left ( \frac{1}{\sin^{6} (ax)} - 3 \frac{1}{\sin^{4} (ax)} + 3 \frac{1}{\sin^{2} (ax)} - 1 \right ) \, \mbox{d}x \\
\end{eqnarray*}
\newpage
\begin{eqnarray*}
F (x)
 & = & \int \left ( \frac{1}{\sin^{6} (ax)} - 3 \frac{1}{\sin^{4} (ax)} + 3 \frac{1}{\sin^{2} (ax)} - 1 \right ) \, \mbox{d}x \\
& = & - \frac{1}{a} \cot (ax) - \frac{2}{3a} \cot^{3} (ax) - \frac{1}{5a} \cot^{5} (ax)
 - 3 \left ( - \frac{1}{a} \cot (ax) - \frac{1}{3a} \cot^{3} (ax) \right ) - \frac{3}{a} \cot (ax) - x + c \\
& = & - \frac{1}{a} \cot (ax) - \frac{2}{3a} \cot^{3} (ax) - \frac{1}{5a} \cot^{5} (ax)
 + \frac{3}{a} \cot (ax) + \frac{1}{a} \cot^{3} (ax) - \frac{3}{a} \cot (ax) - x + c \\
& = & - \frac{1}{5a} \cot^{5} (ax) + \frac{1}{3a} \cot^{3} (ax) - \frac{1}{a} \cot (ax) - x + 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}{5a} \cot^{5} (ax) + \frac{1}{3a} \cot^{3} (ax) - \frac{1}{a} \cot (ax) - x + c \right ) \\
& = & - \frac{1}{5a} \cdot 5 \cot^{4} (ax) \left ( - \frac{1}{\sin^{2} (ax)} \right ) a
 + \frac{1}{3a} \cdot 3 \cot^{2} (ax) \left ( - \frac{1}{\sin^{2} (ax)} \right ) a
 - \frac{1}{a} \left ( - \frac{1}{\sin^{2} (ax)} \right ) a - 1 + 0 \\
& = & \cot^{4} (ax) \frac{1}{\sin^{2} (ax)} - \cot^{2} (ax) \frac{1}{\sin^{2} (ax)} + \frac{1}{\sin^{2} (ax)} - 1 \\
& = & \frac{\cos^{4} (ax)}{\sin^{4} (ax)} \frac{1}{\sin^{2} (ax)} - \frac{\cos^{2} (ax)}{\sin^{2} (ax)} \frac{\sin^{2} (ax)}{\sin^{4} (ax)}
 + \frac{\sin^{4} (ax)}{\sin^{6} (ax)} - \frac{\sin^{6} (ax)}{\sin^{6} (ax)} \\
& = & \frac{\cos^{4} (ax)}{\sin^{6} (ax)} - \frac{\cos^{2} (ax) \sin^{2} (ax)}{\sin^{6} (ax)}
 + \frac{\sin^{4} (ax)}{\sin^{6} (ax)} - \frac{\sin^{6} (ax)}{\sin^{6} (ax)} \\
& = & \frac{\cos^{4} (ax) - \cos^{2} (ax) \sin^{2} (ax) + \sin^{4} (ax) - \sin^{6} (ax)}{\sin^{6} (ax)} \\
& = & \frac{\cos^{4} (ax) - \cos^{2} (ax) (1 - \cos^{2} (ax)) + (1 - \cos^{2} (ax)) (1 - \cos^{2} (ax))}{\sin^{6} (ax)} \\
 & & \qquad \qquad - \, \frac{(1 - \cos^{2} (ax)) (1 - \cos^{2} (ax)) (1 - \cos^{2} (ax))}{\sin^{6} (ax)} \\
& = & \frac{\cos^{4} (ax) - \cos^{2} (ax) + \cos^{4} (ax) + 1 - 2 \cos^{2} (ax) + \cos^{4} (ax)}{\sin^{6} (ax)} \\
 & & \qquad \qquad - \, \frac{1 - 3 \cos^{2} (ax) + 3 \cos^{4} (ax) - \cos^{6} (ax)}{\sin^{6} (ax)} \\
& = & \frac{\cos^{6} (ax)}{\sin^{6} (ax)} \\
& = & \cot^{6} (ax) \\
\end{eqnarray*}
\newpage
\begin{eqnarray*}
F (x)
 & = & - x - \frac{1}{a} \cot (ax) + \frac{1}{3a} \cot^{3} (ax) \\
 & & \qquad - \, \frac{1}{5a} \cot^{5} (ax) + c \\
\end{eqnarray*}
\end{document}
