#### Answer

a) $-\cot x+C$
b) $\cot (\dfrac{3x}{2})+C$
c) $x+4 \cot 2x+C$

#### Work Step by Step

a) The anti-derivative for $csc^2 x$ is $-\cot x+C$
b) The anti-derivative is:
$\dfrac{-3}{2}(-\dfrac{1}{3/2} cot (\dfrac{3x}{2}))= \cot (\dfrac{3x}{2})+C$
c) The anti-derivative is:
$x-8(\dfrac{-1}{2} \cot 2x)=x+4 \cot 2x+C$