Evaluate: `int(sinx)/(sin2x)dxdot`

Explanation

`I=int (sinx)/(sin3x)dx=int(sinx)/(3sinx-4sin^(3)x)dx`
`=int(1)/(3-4sin^(2)x)dx`
`=int(sec^(2)x)/(3sec^(2)x-4tan^(2)x)dx`
` " " [ "Dividing " N^(r) and D^(r) " by " cos^(2)x]`
Putting `tanx=t and sec^(2)xdx=dt,` we get
`I=int(dt)/(3(1+t^(2))-4t^(2))=int(dt)/(3-t^(2))=int(1)/((sqrt(3))^(2)-t^(2))dt`
`=(1)/(2sqrt(3))log|(sqrt(3)+t)/(sqrt(3)-t)|+C=(1)/(2sqrt(3))log|(sqrt(3)+tanx)/(sqrt(3)-tanx)|+C`