integrate cosec^2 x (1 Viewer)

[foram]

how do i intergrate cosec^2 x ?
This is NOT ^2x but (cosec x)^2

cosec^2 x = 1/sin^2 x.
1/sin^2 x = 2/ (1 - cos2x) ?

Now how do i integrate this?

 

[Aerath]

how do i intergrate cosec^2 x ?
This is NOT ^2x but (cosec x)^2

Isn't cosec^2 (x) and (cosec x)^2 the same thing?

 

[foram]

they are. but cosec^2x cosec ^2 x are different. i was afraid people wouldn't notice the space between the 2 and teh x.

 

[Aerath]

what is cosec^2x? Cosec to the power of 2x? Then what's the 'body' of the trigonometric thingo?

By the way, I have no idea how to do it. All I can think of is double angle formula, but that sorta doesn't get us anywhere. That being said, whenever I see 1/(something) in an integration, I think log.

 

[cwag]

i would do it differently....

int: cosec²x dx
= int: sec²(pi/2 - x)

= -tan (pi/2 - x) + C

 

[independantz]

I(cosecx)^2
=I(sec(n/2-x))^2, using complimentary angles
=-I-(sec(n/2-x))^2
=-tan(n/2-x)+C
=-cotx+C

 

[foram]

thats pretty smart. thankyou.