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If I=int(e^x)/(e^(4x)+e^(2x)+1) dx. J=in...

If `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-I` equal to

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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