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If int (e^x-1)/(e^x+1)dx=f(x)+C, then f(...

If `int (e^x-1)/(e^x+1)dx=f(x)+C,` then f(x) is equal to

A

`2log (e^(x)+1)`

B

`log(e^(2x)-1)`

C

`2log(e^(x)+1)-x`

D

`log(e^(2x)+1)`

Text Solution

Verified by Experts

The correct Answer is:
C
`int(e^(x)-1)/(e^(x)+1)dx=int((2e^(x))/(e^(x)+1)-1)dx`
`=2log(e^(x)+1)-x+C-=f(x)+C" [given]"`
`therefore" "f(x)=2log(e^(x)+1)-x`
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