`(1)/(sqrt(x^(2)+2x+2))`

Explanation

`int(1)/(sqrt(x^(2)+2x+2))dx`
`=int(1)/(sqrt((x+1)^(2)+(1)^(2)))dx`
`=log|(x+1)+sqrt((x+1)^(2)+1)|+c`
`=log|(x+1)+sqrt(x^(2)+2x+2)|+c`