How do we evaluate $\int \sec x^4 dx$?

Question

Question

$$\int \sec \left(x^4\right) dx$$

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Seriously, how do we do this?

I know that there is no elementary function who's derivative is $\sec x^4$. But still how can we do this?

Or Perhaps even better:

$$\int \sec (x^n) dx$$

where $n>1$