मूल्यांकन कीजिएः
`int_(0)^(4) (dx)/(sqrt(x^2+2x+3))dx`

Explanation

`underset(0)overset(4)int (dx)/(sqrt(x^2+2x+3))dx`
`=underset(0)overset(4)int (1)/(sqrt((x^(2)+2x+1)+2))dx`
`=underset(0)overset(4)int (1)/(sqrt((x+1)^(2)+(sqrt2)^2))dx`
`=[log|(x+1)+sqrt((x+1)^(2)+(sqrt2)^(2)|)]_(0)^(4)`
`=[log|(x+1)+sqrt(x^(2)+2x+3)|]_(0)^(4)`
`=log|5+sqrt(16+8+3)|-log|1+sqrt3|`
`=log(5+3sqrt3)-log(1+sqrt3)`
`=log((5+3sqrt3)/(1+sqrt3))`