Evaluate `int(dx)/(sinx+cosx).`

Explanation

`I=int(dx)/(2+sinx+cosx)`
`=int(dx)/(2+(2tanx//2)/(1+tan^(2)x//2)+(1-tan^(2)x//2)/(1+tan^(2)x//2))`
`=int(1+tan^(2)x//2)/(tan^(2)x//2+2tanx//2+3)dx`
`=int(sec^(2)x//2)/(tan^(2)x//2+2tanx//2+3)dx`
`" put " "tan"(x)/(2)=t . :. (1)/(2)"sec"^(2)(x)/(2)dx=dt`
`:. I=int(2dt)/(t^(2)+2t+3)`
`=2int(dt)/((t+1)^(2)+2)`
`=2int(1)/(sqrt(2))"tan"(t+1)/(sqrt(2))+c`
`=sqrt(2)"tan"("tan"(x)/(2)+2)/(sqrt(2))+c`