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int (dx)/(e^x + e^-x)...

`int (dx)/(e^x + e^-x)`

A

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

B

`tan^(-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)+(1)/(e^(x))))=int(e^(x))/((1+e^(2x)))dx`.
`=int(1)/((1+t^(2)))dt," where "e^(x)=t ande^(x)dx=dt`.
`=tan^(-1)(t)+C=tan^(-1)(e^(x))+C`.
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