what is the anit-derivative of tanx

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what is the anit-derivative of tanx

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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ln sec x
\[-\ln (\left| cosx \right|)+C\]or\[\ln (\left| secx \right|)+C\]You just have to memorize trig integrals like this, or you may also be able to find it by using integration by parts.
Actually I just realized with this one you do this:\[\int\limits_{}^{}(tanx) dx\]\[\int\limits_{}^{}(sinx/cosx)dx\]\[-\int\limits_{}^{}(-sinx/cosx)dx\]Now use substitution where u=cosx and du=-sinx \[-\int\limits_{}^{}(1/u)du\]\[-\ln \left| u \right|+C\]\[-\ln \left| cosx \right|+C\]

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