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int(ln((x-1)/(x+1)))/(x^2-1)dxi se q u a...

`int(ln((x-1)/(x+1)))/(x^2-1)dxi se q u a lto` `1/2(ln((x-1)/(x+1)))^2+C` `1/2(ln((x+1)/(x-1)))^2+C` `1/4(ln((x-1)/(x+1)))^2+C` `1/4(ln((x+1)/(x-1)))^2+C`

A

`(1)/(2)("In"((x-1)/(x+1)))^(2)+C`

B

`(1)/(2)("In"((x+1)/(x-1)))^(2)+C`

C

`(1)/(4)("In"((x-1)/(x+1)))^(2)+C`

D

`(1)/(4)("In"((x+1)/(x-1)))`

Text Solution

Verified by Experts

The correct Answer is:
C
`I=int("In"((x-1)/(x+1)))/(x^(2)-1)dx`
Let `t="In"((x-1)/(x+1))`
or `(dt)/(dx)=(x+1)/(x-1){(x+1-(x-1))/((x+1)^(2))}=(2)/((x^(2)-1))`
or `(dx)/(x^(2)-1)=(dt)/(2)`
` :. I=(1)/(2)int t dt=(1)/(4)t^(2)+C=(1)/(4)("In"((x-1)/(x+1)))^(2)+C`
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