`int_(0)^(4)(dx)/(sqrt(x^(2)+2x+3))` का मान ज्ञात कीजिए।

Explanation

`int_(0)^(4)(dx)/(sqrt(x^(2)+2x+3))`
`=int_(0)^(4)(1)/(sqrt((x^(2)+2x+1)+2))dx`
`=int_(0)^(4)(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)/(1+sqrt3)|`