Math, asked by Mihir5158, 8 months ago

Integration of (3+2cosx)/(2+3cosx)^2
Answer is sinx/2+3cosx

Answers

Answered by knjroopa
1

Step-by-step explanation:

Given Integration of (3+2cosx)/(2+3cosx)^2

  • ∫ (3+2cosx)/(2+3cosx)^2 dx  x cosec^2 x / cosec^2 x
  •           Now cos x / sin x sin x = cot x cosec x
  •   ∫ (3cosec^2 x + 2 cot x cosec x) dx / (2 cosec x + 3 cot x)^2
  •  = -  ∫ -( 3 cosec^2 x – 2 cot x cosec x ) dx / (2 cosec x + 3 cot x)^2
  •                Let 2 cosec x + 3 cot x = t
  •                    Or (– 2 cot x cosec x – 3 cosec^2 x dx) dt
  •                I = -  ∫ dt / t^2
  •                    = 1/t + c
  •                   = 1/2 cosec x + 3 cot x + c
  •                    = 1 / 2 / sin x + 3 cos x / sin x + c
  •                    = 1 / 2 + 3 cos x / sin x
  •                     = sin x  / 2 + 3 cos x

Reference link will be

https://brainly.in/question/5598489

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