If \( I=\int \frac{e^{x}}{e^{4 x}+e^{2 x}+1} d x \) \( \mathrm{P}^{...

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If \( I=\int \frac{e^{x}}{e^{4 x}+e^{2 x}+1} d x \)
\( \mathrm{P}^{12 i} \)
W
\( f=\int \frac{e^{-x}}{e^{-4 x}+e^{-2 x}+1} d x \). Then, for an arbitrary
constant c. the valu of \( f-I \) equals
(1) \( \frac{1}{2} \log \left|\frac{e^{4 x}-e^{2 x}+1}{e^{4 x}+e^{2 x}+1}\right|+C \)
(2) \( \frac{1}{2} \log \left|\frac{e^{2 x}+e^{x}+1}{e^{2 x}-e^{x}+1}\right|+C \)
(3) \( \frac{1}{2} \log \left|\frac{e^{2 x}-e^{x}+1}{e^{2 x}+e^{x}+1}\right|+C \)
(4) \( \frac{1}{2} \log \left|\frac{e^{4 x}+e^{2 x}+1}{e^{4 x}-e^{2 x}+1}\right|+C \)
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