The value of ∫π/4π/3dxsinx+tanx is

I=∫π/4π/3cosxsinx(cosx+1)dx=∫π/4π/3cosxsinx1-cos2x(1+cosx)dxPut cosx=t so thatI=∫1/21/2tdt(1+t)2(1-t)=∫1/21/21411+t+11-t-12(1+t)2dt=14log⁡1+t1−t+12(1+t)1/21/2=14log⁡2+12−123+12+2−13