`int_(-1)^(1)(dx)/(x^(2)+2x+5)`

Explanation

`int_(-1)^(1)(1)/(x^(2)+2x+5)`
`=int_(-1)^(1)(1)/((x^(2)+2x+1)+4)dx`
`=int_(-1)^(1)(1)/((x+1)^(2)+2^(2))Dx=(1)/(2)[tan^(-1).(x+1)/(2)]_(-1)^(1)`
`=(1)/(2)[tan^(-1)((2)/(2))-tan^(-1)((0)/(2))]`
`=(1)/(2)(tan^(-1)1)=(1)/(2)xx(pi)/(4)=(pi)/(8)`