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If intsqrt(x+sqrt(x^(2)+2))dx=A{x+sqrt(x...

If `intsqrt(x+sqrt(x^(2)+2))dx=A{x+sqrt(x^(2)+2)}^(3//2)+(B)/(sqrt(x+sqrt(x^(2)+2)))+c.` then the value of 3AB is

A

`-1`

B

`-2`

C

1

D

2

Text Solution

Verified by Experts

The correct Answer is:
B
Put `x+sqrt(x^(2)+2)=t`
`rArr" "x^(2)+2=t^(2)+x^(2)-2tx`
`rArr" "x=(1)/(2)(t-(2)/(t))`
`"So "I=intsqrt(x+sqrt(x^(2)+2))dx`
`=(1)/(2)intt^(1//2)(1+(2)/(t^(2)))dt`
`=(1)/(2)intt^(1//2)dt+intt^(-3//2)dt=(1)/(3)t^(3//2)-(2)/(sqrtt)+c`
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CENGAGE PUBLICATION-INDEFINITE INTEGRATION-Single Correct Answer Type
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  12. If I=intx^(27)(6x^(2)+5x+4)(x^(2)+x+1)^(6)dx=f(x)+C, then f(x) is eq...

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