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

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

A

`((x^(2)+x+1)^(3//2))/(3)+(3(2x+1))/(8)sqrt(x^(2)+x+1)-(9)/(16)sqrt(x^(2)+x+1)+c`

B

`((x^(2)+x+1)^(3//2))/(3)+(3(2x+1))/(8)sqrt(x^(2)+x+1)+(9)/(16)log|(x+(1)/(2))|+c`

C

`((x^(2)+x+1)^(3//2))/(3)+(3(2x+1))/(8)sqrt(x^(2)+x+1)+(9)/(16)log|(x+(1)/(2))+sqrt(x^(2)+x+1)|+c`

D

`(3(2x+1))/(8)sqrt(x^(2)+x+1)+(9)/(16)log|(x+(1)/(2))+sqrt(x^(2)+x+1)|+c`

Text Solution

Verified by Experts

The correct Answer is:
C
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