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PIYUSH AGRAWAL Grade: 12
        

find ∫{(3+4cosx)/(4+3cosx)2}dx.


plz give solution in detail.

7 years ago

Answers : (2)

Sukhendra Reddy Rompally B.Tech Mining Machinery Engg, ISM Dhanbad
93 Points
										

Cos2x= 1-Tan^2 x/ 1+Tan^2 x { Cosx= 1-Tan square x whole divided by 1+ Tan square x}


using this formula,the function will reduce to f(t)= 2(7-t^2)/(7+t^2)^2, where t= Tanx/2


Now u can use simple algebraic operations to solve it


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7 years ago
vikas askiitian expert
510 Points
										

       f(x)= 3+4cosx/(4+3cosx)^2


 


      putting cosx=1-tan^2(x/2) /1+tan^2(x/2)       


                                                                                               [from cos2x=1-tan^2(x)/1+tan^2(x)]


 f(x) becomes 7-tan^2(x/2) .sex^2(x/2)/7+tan^2(x/2)


 


       I=  int [7-tan^2(x/2) . sex^2(x/2)/7+tan^2(x/2)]


        put tanx/2 =t


     after differentiating we get


               sex^2(x/2)dx=dt


       putting in previous eq we get


     I=  int 7-t^2/7+t^2 or -(t^2-7)/(t^2+7)


      =  int  t^2+7-14/t^2+7


       =int {  (1)  -(14/t^2+7)  }   after separating                                                      int 1/x^2+a^2 =1/ataninverse(x/a)


        =       t  -  14/root7taninverse(t/root7) + c


     again substituting value of t we get


    I =tanx/2  -  2root7(taninverse{tan(x/2))/root7} +c


 

7 years ago
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