Answer
a) $\sec x+C$
b) $\dfrac{4}{3} \sec 3x+C$
c) $\dfrac{2}{\pi} \sec\dfrac{\pi x}{2}+C $
Work Step by Step
a) The anti-derivative for $\sec x \tan x$ is $\sec x+C$
b) The anti-derivative is:
$4(\dfrac{1}{3} \sec 3x)+C=\dfrac{4}{3} \sec 3x+C$
c) The anti-derivative is:
$ \dfrac{1}{\pi/2} \sec \dfrac{\pi x}{2}+C =\dfrac{2}{\pi} \sec\dfrac{\pi x}{2}+C $
