The integral \( \int \frac{\left(x^8-x^2\right) d x}{\left(x^{12}+3 x^6+1\right) \tan ^{-1}\left(x^3+\frac{1}{x^3}\right)}\) is equal to:
1
\( \log _e\left(\left\lvert\, \tan ^{-1}\left(x^3+\frac{1}{x^3}\right)\right|\right)^{1 / 3}+C\)
2
\( \log _e\left(\left\lvert\, \tan ^{-1}\left(x^3+\frac{1}{x^3}\right)\right|\right)^{1 / 2}+C\)
3
\( \log _e\left(\left|\tan ^{-1}\left(x^3+\frac{1}{x^3}\right)\right|\right)+C\)
4
\( \log _e\left(\left\lvert\, \tan ^{-1}\left(x^3+\frac{1}{x^3}\right)\right|\right)^3+C \)