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∫ 1/ (cos3x – cosx ) dx , please say how to simplyfy, thank you.

∫ 1/ (cos3x – cosx ) dx , please say how to simplyfy, thank you.

Grade:12

1 Answers

Arun
25763 Points
4 years ago
 

dx/cos3x-cosx =dx/4cos^3x-4cosx   by using identity   cos3x =4cos^3x - 3cosx

 

=  dx/4.cosx(cos^2x-1)

 

=cosxdx/4cos^x(cos^x-1)

 

=-cosxdx/4sin^2x(1-sin^x)

 

 now putting sinx=t,cosxdx=dt

 

  =-dt/4(1-t^2)t^2

 

  =1/4 {-dt/t^2  -dt/1-t^2 }

 

  =1/4 .{1/t + log1-t/1+t } +c

 

 =1/4 .(cosecx + log1-sinx/1+sinx } +c

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