I have a simple question. I will show you four expressions for a certain trigonometric integrals that I THINK are all exactly same but I'm not positive.

The original integral is INTEG: (cot x)^3

After simplifying it, you get INTEG: (csc x)^2 cotx - cotx

Here are the four expressions/results of the integral that I believe are the exactly same -

1. (-1/2)csc^2x - ln (abs(sinx)) + C

2. (-1/2)csc^2x - ln (abs(cscx)) + C

3. (-1/2)cot^2x - ln (abs(sinx)) + C

4. (-1/2)cot^2x - ln (abs(cscx)) + C

They're all the same, right? The integral of cot x isn't just ln (abs(sinx)) + C but also ln (abs(cscx)) + C right?

Right??? I'm not sure.