Evaluate the following integral ∫1/(5+〖2 sin〗x+3 cosx ) dx
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total answers (1)
total answers (1)
Mathematics
Put z=tan〖x/2〗 ,sinx=2z/(1+z^2 ) , cosx=(1-z^2)/(1+z^2 ) and dx=2dz/(1+z^2 )
need an explanation for this answer? contact us directly to get an explanation for this answerI=∫〖1/(5+2(2z/(1+z^2 ))+3((1-z^2)/(1+z^2 )) ) (2dz/(1+z^2 )) 〗
=∫dz/(z^2+2z+1)=∫dz/((z+1)^2+3)=1/√3 tan^(-1)〖((z+1))/√3〗+c
I=1/√3 tan^(-1)〖((tan〖x/2〗+1))/√3〗+c