$\begin{aligned} I &= \int{\dfrac{e^{x}}{e^{4x}+e^{2x}+1}}\,dx \\ J & = \int{\dfrac{e^{-x}}{e^{-4x}+e^{-2x}+1}}\,dx \end{aligned}$

For $I$ and $J$ as defined above, find $J-I$.

**Notations:**

- $e \approx 2.718$ is the Euler's number.
- $\log (\cdot)$ denotes the natural logarithm function, that is $\log_{e}{(\cdot)}$ or $\ln(\cdot)$.
- $C$ denotes the constant of integration.
- $x \in \mathbb{R}^{+}$