Integrate the function

Sin(x-a)/sinx+a) with respect to x

I={sinx-a/sinx+a }dx

put x+a=t

  so    dx=dt

 I={sin(t-2a) /sint }dt                     (sina-b=sinacosb-cosasinb)

 I ={sintcos2a -costsin2a/sint }dt

 I ={cos2a - cottsin2a}dt

 I={tcos2a -sin2alogsint} +c

 I={(x+a)cos2a-sin2a.logsin(x+a)} + c

Regards

Arun (askIITians forum expert)