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Evaluate: int(x+1)\ sqrt(x^2-x+1)\ dx...

Evaluate: `int(x+1)\ sqrt(x^2-x+1)\ dx`

A

`(1)/(3)sqrt((x^2+x+1)^3)-(1)/(8)(2x+1)sqrt(x^2+x+1)+(3)/(16)log|(2x+1)/(2)+sqrt(x^2+x+1)|c`

B

`(1)/(3)sqrt((x^2+x+1)^3)+(1)/(8)(2x+1)sqrt(x^2+x+1)-(3)/(16)log|(2x+1)/(2)+sqrt(x^2+x+1)|c`

C

`(1)/(3)sqrt((x^2+x+1)^3)-(1)/(8)(2x+1)sqrt(x^2+x+1)-(3)/(16)log|(2x+1)/(2)+sqrt(x^2+x+1)|c`

D

`(1)/(3)sqrt((x^2+x+1)^3)+(1)/(8)(2x+1)sqrt(x^2+x+1)+(3)/(16)log|(2x+1)/(2)+sqrt(x^2+x+1)|c`

Text Solution

Verified by Experts

The correct Answer is:
D
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