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Evaluate int(dx)/(sqrt(3x^(2)+6x+12))dx...

Evaluate `int(dx)/(sqrt(3x^(2)+6x+12))dx`.

A

`log |(x+1)+sqrt(x^(2)+2x+4)|+C`

B

`(1)/(3)log |(x+1)+sqrt(x^(2)+2x+4)|+C`

C

`(1)/(sqrt(3))log |(x+1)+sqrt(x^(2)+2x+4)|+C`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
C
`I=int (dx)/(sqrt(3(x^(2)+2x+4)))=(1)/(sqrt(3))int (dx)/(sqrt(x^(2)+2x+4))=(1)/(sqrt(3))int(dx)/(sqrt((x+1)^(2)+(sqrt(3))^(2)))`
`=(1)/(sqrt(3))int(dt)/(sqrt(t^(2)+(sqrt(3))^(2)))=(1)/(sqrt(3))log |t+sqrt(t^(2)+3)|+C`
`=(1)/(sqrt(3)).log |(x+1)+sqrt(x^(2)+2x+4)|+C.`
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