For each of the following solve the indefinite integral,
describe your technique, then write two more integrals which would use the same
technique to solve.
\begin{alignat*}{2}
&a) \int{\frac{1 }{ \sqrt {2x+1}} \sin {( \sqrt {2x+1} )}}
& &b) \int {( \sqrt {\tan x} + ( \tan x )^\frac{1 }{ 3}
) \sec^2 x} \\
&c) \int {\cos^2 {4x}} &
&d) \int {x^{-\frac{2}{ 3}}\cos {x^\frac{1}{ 3}} ( 1+ \sin^2 {x^\frac{1 }{ 3}}
)} \\
&e) \int \frac{( \tan^\frac{1}{ 3} {\sqrt x} ) ( 1+\tan^2 {\sqrt x}) }{\sqrt x}
&
&f) \int {( 1 - \cos^2 x )^{-1}} \\
\end{alignat*}
– James Epperson 1998-08-09