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