Answer
a) $-\csc x+C$
b) $\dfrac{1}{5} \csc 5x+C$
c) $2\csc\dfrac{\pi x}{2}+C $
Work Step by Step
a) The anti-derivative for $\csc x \cot x$ is $-\csc x+C$
b) The anti-derivative is:
$-\csc 5x \cot 5x= \dfrac{1}{5} \csc 5x+C$
c) The anti-derivative is:
$-\pi \csc \dfrac{2}{\pi} \cot \dfrac{\pi x}{2}+C =2\csc\dfrac{\pi x}{2}+C $
