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ArcCsch






Mathematica Notation

Traditional Notation









Elementary Functions > ArcCsch[z] > Integration > Indefinite integration > Involving one direct function and elementary functions > Arguments involving trigonometric functions > Involving sec





http://functions.wolfram.com/01.29.21.0020.01









  


  










Input Form





Integrate[ArcCsch[Sec[z]], z] == (1/4) (4 z ArcCsch[Sec[z]] - 2 Pi ArcTanh[(Sqrt[2] Cos[z])/Sqrt[3 + Cos[2 z]]] + (1/2) (Pi - 2 z) (-Log[(1/2) (1 + E^(2 I z) - 2 E^(I z) Sqrt[1 + Cos[z]^2])] + Log[(1/2) (1 + E^(2 I z) + 2 E^(I z) Sqrt[1 + Cos[z]^2])] - Log[(E^(I z) - Sqrt[1 + Cos[z]^2] - I Sin[z])/E^(I z)] + Log[(E^(I z) + Sqrt[1 + Cos[z]^2] - I Sin[z])/E^(I z)]) - ArcTan[Sin[z]/Sqrt[1 + Cos[z]^2]] (Log[(1/2) (1 + E^(2 I z) - 2 E^(I z) Sqrt[1 + Cos[z]^2])] + Log[(1/2) (1 + E^(2 I z) + 2 E^(I z) Sqrt[1 + Cos[z]^2])] + Log[(E^(I z) - Sqrt[1 + Cos[z]^2] - I Sin[z])/E^(I z)] + Log[(E^(I z) + Sqrt[1 + Cos[z]^2] - I Sin[z])/E^(I z)]) + I (-PolyLog[2, (-E^((-I) z)) (Sqrt[1 + Cos[z]^2] - I Sin[z])] - PolyLog[2, E^(I z) (Sqrt[1 + Cos[z]^2] - I Sin[z])] + PolyLog[2, (Sqrt[1 + Cos[z]^2] + I Sin[z])/E^(I z)] + PolyLog[2, (-E^(I z)) (Sqrt[1 + Cos[z]^2] + I Sin[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