JEE Math Practice Question

$$\text { The integral } \int \frac{\left(x^8-x^2\right) \mathrm{d} x}{\left(x^{12}+3 x^6+1\right) \tan ^{-1}\left(x^3+\frac{1}{x^3}\right)} \text { is equal to : }$$

1. A.$$\log _{\mathrm{e}}\left(\left|\tan ^{-1}\left(x^3+\frac{1}{x^3}\right)\right|\right)^{1 / 3}+\mathrm{C}$$
2. B.$$\log _{\mathrm{e}}\left(\left|\tan ^{-1}\left(x^3+\frac{1}{x^3}\right)\right|\right)+\mathrm{C}$$
3. C.$$\log _{\mathrm{e}}\left(\left|\tan ^{-1}\left(x^3+\frac{1}{x^3}\right)\right|\right)^{1 / 2}+\mathrm{C}$$
4. D.$$\log _{\mathrm{e}}\left(\left|\tan ^{-1}\left(x^3+\frac{1}{x^3}\right)\right|\right)^3+\mathrm{C}$$