1 and 3 appear to be right, but I think 2 and 4 are slightly incorrect. The antiderivative of cot(x) is either ln(abs(sin(x))) + C or -ln(abs(csc(x))) + C. If you use the rules of logarithms you should be able to relate the two: if you consider that A*ln(x) = ln(x^A), you will find that ln(sin(x)) = ln(csc(x)^-1) = -ln(csc(x)). Thus, for 2 and 4, you should have (-1/2)csc^2x + ln (abs(cscx)) + C and (-1/2)cot^2x + ln (abs(cscx)) + C. When you integrate, you can always check by differentiating.