Integrate (cos^2(x))/(sin^6(x))

1. Mar 27, 2008

n77ler

[SOLVED] ff

1. The problem statement, all variables and given/known data

integrate (cos^2(x))/(sin^6(x))

2. Relevant equations

Double angles?
u-sub?

3. The attempt at a solution

I tried using double angles but im really not sure what to do I havnt seen any like this... I have only done stuff without fraction like integrating cos^3x sin^5x can anyone just start me off please

Last edited: Mar 27, 2008
2. Mar 27, 2008

tiny-tim

Hi n77ler!

Hint: it's cosec^6(x) - cosec^4(x).

Does that help … ?

3. Mar 27, 2008

n77ler

hmm kind of Im not sure where you got that though. The division in an integral can be changed to subtration i guess... but im not sure how you are getting the two csc's. I know it is 1/sin but not sure other than that

4. Mar 27, 2008

tiny-tim

cos^2(x)/sin^6(x)

= (1 - sin^2(x))/sin^6(x) = 1/sin^6(x) - 1/sin^4(x)

= cosec^6(x) - cosec^4(x).

5. Mar 27, 2008

n77ler

right, god lol I'm not functioning well right now.

6. Mar 27, 2008

n77ler

ok so i seperate those into two different integrals and then integrate right

7. Mar 27, 2008