Evaluate the following definite integral: `int_(-1)^1 1/(x^2+2x+5)dx`

Explanation

`I=int_{-1}^{1} frac{1}{x^{2}+2 x+5} d x`
`
I=int_{-1}^{1} frac{1}{(x+1)^{2}+2^{2}} d x`
`
I=frac{1}{2}[tan ^{-1} frac{x+1}{2}]_{-1}^{1}`
`
I=frac{1}{2}(tan ^{-1} 1-tan ^{-1} 0) `
`
I=frac{pi}{8}`
`