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

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

A

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

B

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

C

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

D

`tan^(-1) (e^(2x)) +C`

Text Solution

Verified by Experts

The correct Answer is:
A
`I= int(1)/(e^(x)+e^(-x))dx= int(1)/(e^(x)+(1)/(e^(x)))dx`
`=(e^(x))/((e^(x))^(2)+1)dx" " underset(rArr e^(x) dx=dt)(" Let " e^(x)=t)`
`:. I= int(1dt)/(t^(2)+1)=tan^(-1) (t)+C =tan^(-1)e^(x)+C`
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