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Let I = int (e^x)/(e^(4x)+e^(2x)+1)dx, ...

Let ` I = int (e^x)/(e^(4x)+e^(2x)+1)dx, J=int (e^(-x))/(e^(-4x)+e^(-2x)+1)dx`. Then , for an arbitrary constant c, the value of J-1 euqals :

A

`1/2 log |(e^(4x)-e^(2x)+1)/(e^(4x)+e^(2x)+1)|+C`

B

`1/2 log |(e^(2x)+e^(x)+1)/(e^(2x)-e^(x)+1)|+C`

C

`1/2 log |(e^(2x)-e^(x)+1)/(e^(2x)+e^(x)+1)|+C`

D

`1/2 log |(e^(4x)+e^(2x)+1)/(e^(4x)-e^(2x)+1)|+C`

Text Solution

Verified by Experts

The correct Answer is:
C
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