`(4x+2)sqrt(x^(2)+x+1)`

Explanation

`int(4x+2)sqrt(x^(2)+x+1)dx" माना "x^(2)+x+1=t`
`=2int(2x+1)sqrt(x^(2)+x+1)dx" "rArr (2x+1)dx=dt`
`=2int(2x+1)sqrt(x^(2)+x+1)dx`
`=2intsqrttdt=2.(t^(3//2))/(3//2)+c`
`=(4)/(3)(x^(2)+x+1)^(3//2)+c`