$If\int \frac{x^4+1}{x^6+1}dx={\tan }^{-1}f\left(x\right)-\frac{2}{3}{\tan }^{-1}g\left(x\right)+C,then$ both $f\left(x\right)andg\left(x\right)$ are odd functions $f\left(x\right)$ is monotonic function $f\left(x\right)=g\left(x\right)$ has no real roots $\int \frac{f\left(x\right)}{g\left(x\right)}dx=-\frac{1}{x}+\frac{3}{x^3}+c$

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