`(1)/(9x^(2)+6x+5)`

Explanation

`int(1)/(9x^(2)+6x+5)dx`
`=(1)/(9)int(1)/(x^(2)+(2)/(3)x+(5)/(9))dx`
`=(1)/(9)int(1)/(x^(2)+(2x)/(3)+(1)/(9)+(5)/(9)-(1)/(9))dx`
`=(1)/(9)int(1)/((x+(1)/(3))^(2)+((2)/(3))^(2))dx`
`=(1)/(9).(1)/(2//3)tan^(-1)(x+(1)/(3))/((2)/(3))+c`
`=(1)/(6)tan^(-1)((3x+1)/(2))+c`