Let's do some calculus! (6)

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

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 .
• $x \in \mathbb{R}^{+}$

For more problems on calculus, click here .