Answer
$$ \displaystyle\int \mathrm{arcsec}\left(3x\right)\, \mathrm d x = -{{\ln \left({{3\,\left| x\right| +\sqrt{9\,x^2-1}}\over{3\, \left| x\right| }}\right)-\ln \left(-{{\sqrt{9\,x^2-1}-3\,\left| x \right| }\over{3\,\left| x\right| }}\right)-6\,x\,{\rm arcsec}\; \left(3\,x\right)}\over{6}} $$
Explanation
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