Try it out. Take the derivative of . Show us your work that leads you to believe the question is wrong.
A question says this: Show by differentiation that ln(csc x - cot x) is an antiderivative of csc x. I think the integral of csc x is -ln(abs(csc x - cot x)). I don't know why the sign appears to be different.
But, if you still need convincing, consider this:
Let . Taking derivatives of both sides, we get