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Tanh






Mathematica Notation

Traditional Notation









Elementary Functions > Tanh[z] > Integration > Indefinite integration > Involving one direct function and elementary functions > Involving trigonometric functions > Involving power of cos > Involving cosm(b z)





http://functions.wolfram.com/01.21.21.0043.01









  


  










Input Form





Integrate[Cos[b z]^m Tanh[c z], z] == (Binomial[m, m/2] Log[Cosh[c z]] (1 - Mod[m, 2]))/(2^m c) + Sum[Binomial[m, k] ((-(1/(b (-2 k + m)))) ((I Hypergeometric2F1[-((I b (-2 k + m))/(2 c)), 1, (2 c - I b (-2 k + m))/(2 c), -E^(2 c z)])/E^(I b (-2 k + m) z)) + (1/(b (-2 k + m))) (I E^(I b (-2 k + m) z) Hypergeometric2F1[ (I b (-2 k + m))/(2 c), 1, (2 c + I b (-2 k + m))/(2 c), -E^(2 c z)]) + (E^((2 c - I b (-2 k + m)) z) Hypergeometric2F1[ (2 c - I b (-2 k + m))/(2 c), 1, (4 c - I b (-2 k + m))/(2 c), -E^(2 c z)])/(2 c - I b (-2 k + m)) + (E^((2 c + I b (-2 k + m)) z) Hypergeometric2F1[(2 c + I b (-2 k + m))/ (2 c), 1, (4 c + I b (-2 k + m))/(2 c), -E^(2 c z)])/ (2 c + I b (-2 k + m))), {k, 0, Floor[(1/2) (-1 + m)]}]/2^m /; Element[m, Integers] && m > 0










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