DLMF:4.26.E5 (Q1821)

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DLMF:4.26.E5
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    sec x d x = gd - 1 ( x ) , 𝑥 𝑥 inverse-Gudermannian 𝑥 {\displaystyle{\displaystyle\int\sec x\mathrm{d}x={\operatorname{gd}^{-1}}% \left(x\right),}}
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    - 1 2 π < x < 1 2 π 1 2 𝜋 𝑥 1 2 𝜋 {\displaystyle{\displaystyle-\frac{1}{2}\pi<x<\frac{1}{2}\pi}}
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