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int(dx)/(sqrt(2x+3)+sqrt(2x-3))...

`int(dx)/(sqrt(2x+3)+sqrt(2x-3))`

A

`(1)/(18)(2x+3)^((3)/(2))+(1)/(18)(2x-3)^((3)/(2))+C`

B

`(1)/(18)(2x+3)^((3)/(2))-(1)/(18)(2x-3)^((3)/(2))+C`

C

`(1)/(12)(2x+3)^((3)/(2))-(1)/(12)(2x-3)^((3)/(2))+C`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
`I=int(1)/({sqrt(2x+3)+sqrt(2x-3)})xx({sqrt(2x+3)-sqrt(2x-3)})/({(2x+3)-sqrt(2x-3)})dx`.
`=int({sqrt(2x+3)-sqrt(2x-3)})/({(2x+3)-(2x-3)})dx=(1)/(6)int{sqrt(2x+3)-sqrt(2x-3)}dx`
`=(1)/(18)(2x+3)^((3)/(2))-(1)/(18)(2x+3)^((3)/(2))+C`.
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