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intsqrt((x-1)/(x+1))dx is equal to...

`intsqrt((x-1)/(x+1))dx` is equal to

A

`2sqrt(x^(2)+1)+sin^(-1)x+C`

B

`sqrt(x^(2)-1)-sin^(-1)x+C`

C

`sqrt(x^(2)-1)+sin^(-1)x+C`

D

`(sqrt(x^(2)-1))/(2)+sin^(-1)x+C`

Text Solution

Verified by Experts

The correct Answer is:
B
Let `l=intsqrt((x-1)/(x+1))dx`
`rArr" "l=int(x-1)/(sqrt(x^(2)-1))dx=int(x)/(sqrt(x^(2)-1))dx-int(1)/(sqrt(x^(2)-1))dx`
`=sqrt(x^(2)-1)-sin^(-1)x+C`
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