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int(dx)/(e^(x)+e^(-x)+2) is equal to...

`int(dx)/(e^(x)+e^(-x)+2)` is equal to

A

`(1)/(e^(x)+1)+C`

B

`(1)/(e^(x)+1)+C`

C

`(1)/(1+e^(-x))+C`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
D
`l=int(dx)/(e^(x)+e^(-x)+2)=int(e^(x)dx)/(e^(2x)+2e^(x)+1)=int(e^(x))/((e^(x)+1)^(2))dx`
Put, `e^(x)+1=t`
`therefore" "e^(x)dx=dt`
`therefore" "l=int(dt)/(t^(2))=-(1)/(t)+C=(-1)/(e^(x)+1)+C`
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