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ArcSech






Mathematica Notation

Traditional Notation









Elementary Functions > ArcSech[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/01.30.21.0028.01









  


  










Input Form





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










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





© 1998-2014 Wolfram Research, Inc.