Answer
$\dfrac{-1}{\pi} \cot (\pi s)+c$
Work Step by Step
Calculate the anti-derivative .
Since, we know $\int \csc^2 x =-\cot t+C$
Substitute $k=\pi s \implies du=\pi ds$
$\int \csc^2 k (1/\pi) dk=\dfrac{1}{\pi} \int \csc^2 k dk$
or, $=\dfrac{-1}{\pi} \cot k+c$
Back substitution: $k=\pi s$
$=\dfrac{-1}{\pi} \cot (\pi s)+c$
