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Tanh






Mathematica Notation

Traditional Notation









Elementary Functions > Tanh[z] > Integration > Indefinite integration > Involving one direct function and elementary functions > Involving hyperbolic and trigonometric functions > Involving powers of sin and powers of cosh > Involving sinm(a z) coshu(b z) tanh(c z)





http://functions.wolfram.com/01.21.21.0167.01









  


  










Input Form





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










Standard Form





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MathML Form







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Date Added to functions.wolfram.com (modification date)





2002-12-18