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Cosh




Mathematica Notation

Traditional Notation









Elementary Functions > Cosh[z] > Integration > Indefinite integration > Involving functions of the direct function and hyperbolic functions > Involving powers of the direct function and hyperbolic functions > Involving rational functions of sinh > Involving 1/a+b sinh(c z)





http://functions.wolfram.com/01.20.21.4240.01









  


  








Input Form





Integrate[1/(Sqrt[Cosh[2 c z]] (a + b Sinh[c z])), z] == (1/(b c)) ((-(1/(Sqrt[1 + a^2/b^2] Sqrt[1 + (2 a^2)/b^2]))) ArcTanh[(Sqrt[1 + (2 a^2)/b^2] Cosh[c z])/(Sqrt[1 + a^2/b^2] Sqrt[Cosh[2 c z]])] - (I b EllipticPi[-(b^2/a^2), I c z, 2])/a)








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