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

[n77ler]

[SOLVED] ff

Homework Statement

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

Homework Equations

Double angles?
u-sub?

The Attempt at a Solution

I tried using double angles but I am 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

 

[tiny-tim]

Hi n77ler!

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

Does that help … ?

 

[n77ler]

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

 

[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).

 

[n77ler]

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

 

[n77ler]

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

 

[Bobbadillio]

yup :)

 

[n77ler]

meh gave up cause it was to much parts so i went back to start and found an easier way lol...

(cos^2x/sin^2x ) (1/sin^4x) and then cot^2xcsc^4x and solved...thanks tho :)