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Please answer my question quickly if you can please.............

Please answer my question quickly if you can please.............
 

Question Image
Grade:12

1 Answers

Arun
25763 Points
2 years ago
Dear Amit
 
∫ 3 + 2 cos x / (2+ 3 cos x)2 dx Let I = 

Multiplying Nr. & Dr. by cosec2x

=> I = int {{(3cosec^{2}x+ 2cot x cosec x) } / (2cosec x +3cot x)^2  }dx


        = - int {{(-3cosec^{2}x- 2cot x cosec x) } / (2cosec x +3cot x)^2  }dx

  Let us consider 2cosec x +3cot x=t

  then    dt = (-3cosec^{2}x- 2cot x cosec x).dx

         =int (dt / t^2)

        integrate it then we get

        ={1} / {(2cosec x +3cot x)} 


        ={sin x}  / {2+3cos x} +c

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