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int(dx)/(sqrt(2x^(2)+4x+6))...

`int(dx)/(sqrt(2x^(2)+4x+6))`

A

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

B

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

C

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

D

None of these

Text Solution

Verified by Experts

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