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Evaluate int sqrt(x^(2)+4x+8)dx...

Evaluate `int sqrt(x^(2)+4x+8)dx`

Text Solution

Verified by Experts

The correct Answer is:
`(1)/(2)(x+1)sqrt(x^(2)+2x+5)+2log|(x+1)+sqrt(x^(2)+2x+5)|+C`
`int sqrt(x^(2)+2x+5)dx`
`=int sqrt((x+1)^(2)+4)dx`
`=(1)/(2)(x+1)sqrt((x+1)^(2)+2^(2)) +(1)/(2)*(2)^(2)log|(x+1)+sqrt((x+1)^(2)+2^(2))|+C`
`=(1)/(2)(x+1)sqrt(x^(2)+2x+5)+2log|(x+1)+sqrt(x^(2)+2x+5)|+C`
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