Find: ∫ (e^4 x-1)/(e^4 x+1) d x

Dividing numerator and denominator by \(\displaystyle e^{2x}\): \[\begin{aligned} \int \frac{e^{4x}-1}{e^{4x}+1}\,dx &= \int \frac{e^{2x}-e^{-2x}}{e^{2x}+e^{-2x}}\,dx \\ &= \frac{1}{2}\int \frac{2\left(e^{2x}-e^{-2x}\right)}{e^{2x}+e^{-2x}}\,dx \\ &= \frac{1}{2}\log\left|e^{2x}+e^{-2x}\right| + C \end{aligned} \]