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Evaluate : int(0)^(4) (dx)/(sqrt(x^(2) +...

Evaluate : `int_(0)^(4) (dx)/(sqrt(x^(2) +2x +3)) `

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`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) +(sqrt(2))^(2))) dx`
`=[log |x+1+sqrt((x+1)^(2) +(sqrt(2))^(2))|]_(0)^(4)`
`=[log |x+1+sqrt(x^(2) +2x +3)|]_(0)^(4)`
`=log |5+ sqrt(16 +8+3) |-log |1+sqrt(3)|`l
`log |(5+3sqrt(3))/(1+sqrt(3))|.`
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