Could someone please explain how to find the indefinite integral of csc(x) ?

Question

owlfred · Answer

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!

watchmath · Answer

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

anonymous · Answer

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

watchmath · Answer

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.

anonymous · Answer

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