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int e^(-x)Tan^(-1)(e^(x))dx=f (x)-(1)/(2...

`int e^(-x)Tan^(-1)(e^(x))dx=f (x)-(1)/(2)log (1+e^(2x))+c rArr f(x)=`

A

`e^(x)-e^(-x)Tan^(-1)(e^(x))`

B

`e^(x)+e^(-x)Tan^(-1)(e^(x))`

C

`-e^(-x)Tan^(-1)(e^(x))`

D

`x-e^(x)Tan^(-1)(e^(x))`

Text Solution

Verified by Experts

The correct Answer is:
D
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