I'm looking for an example of a function $f$ (apart from inverse trigonometric and linear functions) such that $\int\tan(f(x))dx$ is known. Special functions included in the typical CAS are acceptable for both $f$ and the antiderivative.
2026-04-02 14:13:55.1775139235
Are there examples of nontrivial $f$ for which the antiderivative of $\tan\circ f$ is known?
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$\int \tan(\ln x)\; dx = -ix+x{\it LerchPhi} \left( -{x}^{2\,i},1,-i/2 \right)$