pleeeeeeas help meeee

Question

i used an online integral calculator and got an answer which says -1/2cot(x^2) but i don't know how to get there. the problem is "integral{xcsc^2(x^2)}

Answer 1

Recall that (cot u)' = -csc² u
Let u = 2x

Then you have ∫-½du = -½u = -½cot u = -½cot x²

Answer 2

Oops u = x²

Answer 3

mumble mumble. Bad notation, but you see the steps.