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ArcSech






Mathematica Notation

Traditional Notation









Elementary Functions > ArcSech[z] > Integration > Indefinite integration > Involving functions of the direct function and elementary functions > Involving elementary functions of the direct function and elementary functions > Involving powers of the direct function and a power function





http://functions.wolfram.com/01.30.21.0036.01









  


  










Input Form





Integrate[z^3 ArcSech[a z]^3, z] == (1/4) (z^4 ArcSech[a z]^3 + (1/a^4) (Sqrt[(1 - a z)/(1 + a z)] (1 + a z) - (-2 + 2 Sqrt[(1 - a z)/(1 + a z)] + 2 a z Sqrt[(1 - a z)/(1 + a z)] + a^2 z^2 Sqrt[(1 - a z)/(1 + a z)] + a^3 z^3 Sqrt[(1 - a z)/(1 + a z)]) ArcSech[a z]^2 + ArcSech[a z] ((-a^2) z^2 + 4 Log[1 + E^(-2 ArcSech[a z])]) - 2 PolyLog[2, -E^(-2 ArcSech[a z])]))










Standard Form





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MathML Form







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Rule Form





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2001-10-29





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