In calculus, the integral of the secant function can be evaluated using a variety of methods and there are multiple ways of expressing the antiderivative, all of which can be shown to be equivalent via trigonometric identities, ∫ sec ⁡ θ d θ = { 1 2 ln ⁡ 1 + sin ⁡ θ 1 − sin ⁡ θ + C ln ⁡ | sec ⁡ θ + tan ⁡ θ | + C ln ⁡ | tan | + C {\displaystyle \int \sec \theta \,d\theta ={\begin{cases}{\dfrac {1}{2}}\ln {\dfrac {1+\sin \theta }{1-\sin \theta }}+C\\[15mu]\ln {{\bigl |}\sec \theta +\tan \theta \,{\bigr |}}+C\\[15mu]\ln {\left|\,{\tan }{\biggl }\right|}+C\end{cases}}} This formula is useful for evaluating various trigonometric integrals. Wikipedia