Evaluate the integral, `intsqrt(x^(2)+2x+6)dx`.

Explanation

Consider , `l=intsqrt(x^(2)+2x+6)dx`
`:.l=intsqrt((x+1)^(2)+5)dx`, put `x+1=t`
`impliesdx=dt`
`:.l=intsqrt(t^(2)+(sqrt(5))^(2))dt`
Using above formulae,
`l=(1)/(2){tsqrt(t^(2)+(sqrt(5))^(2))+5log|t+sqrt(t^(2)+(sqrt(5))^(2))|}+C`
`:.l=(1)/(2){(x+1)sqrt(x^(2)+2x+6+5log|(x+1)+sqrt(x^(2)+2x+6)|}+C`