We can solve this integral by using u-substitution with u = csc x and du = -csc x cot x dx:
∫csc x cot x dx = ∫-du/u
Now we can evaluate the integral, remembering to include the constant of integration:
= -ln|csc x + cot x| + C
Therefore, the antiderivative of csc x cot x dx is -ln|csc x + cot x| + C.
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