Multiply and divide by 2. 

 I= dx/root(3) sinx+cosx

  then 2I= dx/(root(3)/2 *sinx + (cosx)/2 ) 

 then root(3)/2=cos30 1/2 = sin 30

then root(3)sinx+ cosx becomes  2sin(30+x) .  then the integration becomes integration of cosec(x+30) multiplied by 1/2. 

 which equals  [log(tan(x+30)/2))] . 1/2+constant.

HOPE I HAVE NOT CONFUSED U! 

(√3)i=∫(sinx+cosx)dx

(√3)i=(-cosx+sinx) + c

no complexity now convet into anythin u wantt