## anonymous 5 years ago Could someone please explain how to find the indefinite integral of csc(x) ?

1. Owlfred

Hoot! You just asked your first question! Hang tight while I find people to answer it for you. You can thank people who give you good answers by clicking the 'Good Answer' button on the right!

2. watchmath

$$\csc x=\frac{\csc x(-\csc x+\cot x)}{(-\csc x+\cot x)}$$ Now use substitution $$u=-\csc x+\cot x$$. Then the integral become $$\int du/u=\ln |u|+C=\ln|-\csc x+\cot x|+C$$

3. anonymous

so you have to multiply by a factor of the derivative of csc(x) divided by itself, or 1, to solve?

4. watchmath

Well, first yes we multiply by 1 so it won't change anything. But $$-\csc x+\cot x$$ is not the derivative of $$\csc x$$. What I can say that we multiply that weird expression just to make it work. How the first person come up with this trick I have no idea :D.

5. anonymous

oops i did not take notice of the plus sign between them, now i see, thanks for the explanation