## 101Ryan101 Group Title what is the anit-derivative of tanx 3 years ago 3 years ago

1. roshan2004

ln sec x

2. abstracted

$-\ln (\left| cosx \right|)+C$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.

3. abstracted

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$