Evaluate the following integral∫1/(2+cosx ) dx
Put z=tan〖x/2〗 , cosx=(1-z^2)/(1+z^2 ) and dz=2dz/(1+z^2 )I=∫dz/(2+(1-z^2)/(1+z^2 ))=∫2dz/(1+z^2 )=2/√3 tan^(-1)(z/√3)+cI=2/√3 tan^(-1)(tan〖x/2〗/√3)+c
total answers (1)
start bookmarking useful questions and collections and save it into your own study-lists, login now to start creating your own collections.
Put z=tan〖x/2〗 , cosx=(1-z^2)/(1+z^2 ) and dz=2dz/(1+z^2 )
need an explanation for this answer? contact us directly to get an explanation for this answerI=∫dz/(2+(1-z^2)/(1+z^2 ))=∫2dz/(1+z^2 )=2/√3 tan^(-1)(z/√3)+c
I=2/√3 tan^(-1)(tan〖x/2〗/√3)+c