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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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