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Evaluate int(dx)/((e^(x)-1))....

Evaluate `int(dx)/((e^(x)-1)).`

A

`log|e^(x)-1|+C`

B

`log|1-e^(-x)|+C`

C

`log|e^(x)-1|+C`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
`I=int(dx)/(e^(x)(e^(x)(1-e^(-x))))=int(e^(-x))/((1-e^(-x)))dx`.
Put `(1-e^(-x))=t ande^(-x)dx=dt`
`:." "I=int(1)/(t)dt=log|t|+C+log|1-e^(-x)|+C`.
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