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Plzzz integrate x-sin x / 1- cos x .........plzz ....... How to do it?

Plzzz integrate x-sin x / 1- cos x .........plzz ....... How to do it?

Grade:12

1 Answers

Arun
25763 Points
4 years ago
∫(x –sinx)/(1 –cosx)dx
 => write sinx and cosx in half angle formulaes:
 
 
 
 
 
 
 
 
 
 
 
=> (x –2sinx/2cosx/2)/(2sin^2x/2)dx => 0.5xcosec^2x/2 dx + cotx/2 dx …..........................(1)

 
 
 
 
let cotx/2 = u
 – 0.5cosec^2x/2 dx = du
and x = vv
dx = dv
substittue in the eqn. (1)
and after integrating we get,
=> – cot(x/2) + c

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