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Tanh






Mathematica Notation

Traditional Notation









Elementary Functions > Tanh[z] > Integration > Indefinite integration > Involving functions of the direct function > Involving algebraic functions of the direct function > Involving (a+b tanh1/2(c z))beta





http://functions.wolfram.com/01.21.21.0261.01









  


  










Input Form





Integrate[Tanh[c z]/(a + b Sqrt[Tanh[c z]])^2, z] == (-(1/(4 c))) (-((2 I ArcTan[Sqrt[Tanh[c z]]])/(a - I b)^2) + (2 I ArcTan[Sqrt[Tanh[c z]]])/(a + I b)^2 + (2 Log[-1 + Sqrt[Tanh[c z]]])/ (a + b)^2 + (2 Log[1 + Sqrt[Tanh[c z]]])/(a - b)^2 - (8 (a^6 + 3 a^2 b^4) Log[a + b Sqrt[Tanh[c z]]])/(a^4 - b^4)^2 + Log[1 + Tanh[c z]]/(a - I b)^2 + Log[1 + Tanh[c z]]/(a + I b)^2 + (8 a^3)/((a^4 - b^4) (a + b Sqrt[Tanh[c 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)





2002-12-18