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. ∫(cos5x + cos4x)/(1-2cos3x) dx is equal to : how to solve

.      ∫(cos5x + cos4x)/(1-2cos3x) dx  is equal to :    how to solve  

Grade:12

1 Answers

SAGAR SINGH - IIT DELHI
879 Points
11 years ago

Dear student,,

given  integral  


                                 =2(cos9x/2cosx/2)/1-2(2cos23x/2-1)  dx
                           now  multiply and divide  by  cos3x/2
                               
                           =2(cosx/2cos3x/2cos9x/2)/(3cos3x/2-4cos33x/2)dx
                            =2(cosx/2cos3x/2cos9x/2)/-cos9x/2   dx
                           
                            =-2cosx/2cos3x/2  dx
                           
                            = -(cos2x+cosx)dx
                           
                      therefore the answer is  -sin2x/2 - sinx

 

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