Let
$$I = \int\frac{e^x}{e^{4x}+e^{2x}+1}dx, J = \int\frac{e^{-x}}{e^{-4x}+e^{-2x}+1}dx$$.
Then, for an arbitrary constant C, the value of J - I equals

A

$$\frac{1}{2}\log\left(\frac{e^{4x} - e^{2x} + 1}{e^{4x} + e^{2x} + 1}\right)+C$$

B

$$\frac{1}{2}\log\left(\frac{e^{2x} + e^{x} + 1}{e^{2x} - e^{x} + 1}\right)+C$$

C

$$\frac{1}{2}\log\left(\frac{e^{2x} - e^{x} + 1}{e^{2x} + e^{x} + 1}\right)+C$$

D

$$\frac{1}{2}\log\left(\frac{e^{4x} + e^{2x} + 1}{e^{4x} - e^{2x} + 1}\right)+C$$