Evaluate: `int(sinx)/(2+sin2x)dx`

Explanation

`int(sinx)/(2+sin2x)dx`
`=(1)/(2)int(sinx+cosx-(cosx-sinx))/(2+sin2x)dx`
`=(1)/(2)int(sinx+cosx)/(2+sin2x)dx-(1)/(2)int(cosx-sinx)/(2+sin2x)dx`
`=(1)/(2)int(sinx+cosx)/(3-(sinx-cosx)^(2))dx-(1)/(2)int(cosx-sinx)/(1+(sinx+cosx)^(2))dx`
`=(1)/(2)int(dt)/(3-t^(2))-(1)/(2)int(du)/(1+u^(2)) " "{:((" where " t=sinx-cosx),(" and " u=sinx+cosx)):}`
`=(1)/(2)(1)/(2sqrt(3))log|(sqrt(3)-t)/(sqrt(3)+t)|-(1)/(2)"tan"^(-1)u+c`
`=(1)/(4sqrt(3))log|(sqrt(3)-(sinx-cosx))/(sqrt(3)+(sinx-cosx))|-(1)/(2)"tan"^(-1)(sinx+cosx)+c`