need help with integration Q! (1 Viewer)

[e7aine]

using the substiution t= tan x/2

how do you integrate this:

cos x
2 - cos x

thnx!

 

[_ShiFTy_]

I "think" u use
cos x = (1 – t^2)/(1 + t^2)

 

[haboozin]

using the substiution t= tan x/2

how do you integrate this:

cos x
2 - cos x

thnx!

x = 2tan^-1 t

x' = 2/(1 + t^2)

cos x= (1 - t^2)/(1 + t^2) (by definition)

can u do it from there?

i need pen and paper to continue.

 

[e7aine]

yep...i did use cos x=
1 - t^2
1 + t^2

using that i came up with this....

2∫ 1 - t^2 dt
(1 + 3t^2)(1+t^2)

kinda stuck wid that at the moment....any hints to continue wid that?

 

[Mountain.Dew]

im using a different method: here goes!

cosx / (2-cosx) = - [-cosx / (2-cosx)]

= -[2-cosx - 2 / (2-cosx)]

= -[1 - 2/(2-cosx)] = 2/(2-cosx) - 1

now hopefully this is much better to integrate...will still have to use the 't' formula ==> will involve partial fractions, eventually lead onto logs.