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int (2x+1)(sqrt(x^(2)+x+1))dx...

`int (2x+1)(sqrt(x^(2)+x+1))dx`

A

`(3)/(2)(x^(2)+x+1)^((3)/(2))+C`

B

`(2)/(3)(x^(2)+x+1)^((3)/(2))+C`

C

`(3)/(2)(2x+1)^(3//2)+C`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
Put `x^(2)+x+1=t and(2x+1)dx=dt`. ,
`I=intsqrt(t)dt=(t^((3)/(2)))/(((3)/(2)))+C=(2)/(3)(x^(2)+x+1)^((3)/(2))+C`.
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