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) Since, the anti-derivative for $(\csc x \cot x)$ is: $-\csc x+C$
b) The anti-derivative is:
Thus, $(-\csc 5x \cot 5x)= (\dfrac{1}{5}) \csc 5x+C$
c) The anti-derivative is:
Thus, $(-\pi) \csc (\dfrac{2}{\pi}) \cot (\dfrac{\pi x}{2})+C =2\csc(\dfrac{\pi x}{2})+C $
