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ArcCsch






Mathematica Notation

Traditional Notation









Elementary Functions > ArcCsch[z] > Integration > Indefinite integration > Involving one direct function and elementary functions > Involving logarithm and a power function > Involving log and power





http://functions.wolfram.com/01.29.21.0027.01









  


  










Input Form





Integrate[z^(\[Alpha] - 1) Log[b z] ArcCsch[a z], z] == (1/\[Alpha]^3) (z^\[Alpha] (\[Alpha] ArcCsch[a z] (-1 + \[Alpha] Log[b z]) - (1/(a Sqrt[1 + 1/(a^2 z^2)] z)) (Sqrt[1 + a^2 z^2] (HypergeometricPFQ[{1/2, \[Alpha]/2, \[Alpha]/2}, {1 + \[Alpha]/2, 1 + \[Alpha]/2}, (-a^2) z^2] - \[Alpha] Hypergeometric2F1[1/2, \[Alpha]/2, 1 + \[Alpha]/2, (-a^2) z^2] Log[z] + Hypergeometric2F1[\[Alpha]/2, 1/2, 1 + \[Alpha]/2, (-a^2) z^2] (1 + \[Alpha] Log[z] - \[Alpha] Log[b 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





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