| utf20-003 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*} |