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ArcSech




Mathematica Notation

Traditional Notation









Elementary Functions > ArcSech[z] > Integration > Indefinite integration > Involving one direct function and elementary functions > Arguments involving hyperbolic functions > Involving tanh





http://functions.wolfram.com/01.30.21.0024.01









  


  








Input Form





Integrate[ArcSech[Tanh[z]], z] == Cosh[z] Sinh[z] (ArcSech[Tanh[z]] Sech[z] (Cosh[(1/2) ArcSech[Tanh[z]]]^2 (Log[1 + E^(-2 ArcSech[Tanh[z]])] - 2 Log[1 + E^(-ArcSech[Tanh[z]])]) (-Cosh[z] + Sinh[z]) + (Log[1 + E^(-2 ArcSech[Tanh[z]])] - 2 Log[1 - E^(-ArcSech[Tanh[z]])]) (Cosh[z] + Sinh[z]) Sinh[(1/2) ArcSech[Tanh[z]]]^2) + 2 Cosh[(1/2) ArcSech[Tanh[z]]]^2 PolyLog[2, -E^(-ArcSech[Tanh[z]])] (-1 + Tanh[z]) + 2 PolyLog[2, E^(-ArcSech[Tanh[z]])] Sinh[(1/2) ArcSech[Tanh[z]]]^2 (1 + Tanh[z]))








Standard Form





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MathML Form







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Rule Form





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Date Added to functions.wolfram.com (modification date)





2001-10-29