hi!

ok, i know that deriv(cscx) = -cscxcotx
and that
deriv(cos) = -sinx
deriv(cotx) = -((cscx)^2)

my question is:
is this (statements below) correct?

antideriv(cscxcotx) = -(cscx)

antideriv(sinx) = -cosx

antideriv((cscx)^2)= -cotx

were those antiderivatives above correct?

yes.