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Let f ((x + 1 ) /( x - 1 )) = 2x + 1...

Let ` f ((x + 1 ) /( x - 1 )) = 2x + 1 `, then integral ` int f (x ) dx ` is ` (x ne 1 )`.

A

`x^(2)+x+c`

B

`2x+In|x+1|+c`

C

`3x+4In|x-1|+c`

D

`2x+3(n|x+1|+c`

Text Solution

Verified by Experts

The correct Answer is:
C
`f((x+1)/(x-1))=2x+1`
Put `(x+1)/(x-1)=t`
`rArr x=(t+1)/(t-1) rArr f(x)=2((t+1)/(t-1))+1`
`rArr f(x)=(3x+1)/(x-1) int(3x+1)/(x-1) dx = int(3+4/(x-1))dx`
`=x+4ln |x-1|+c`
`int f(x) dx =3x + 4 ln |x-1|+c`
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