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Cosh






Mathematica Notation

Traditional Notation









Elementary Functions > Cosh[z] > Integration > Indefinite integration > Involving functions of the direct function, trigonometric and exponential functions > Involving powers of the direct function, trigonometric and exponential functions > Involving powers of sin and exp > Involving ep zsinmu(c z+d) coshnu(a z)





http://functions.wolfram.com/01.20.21.3762.01









  


  










Input Form





Integrate[E^(p z) Sin[d + c z]^m Cosh[a z]^\[Nu], z] == (1/(p - a \[Nu])) ((E^(p z) Binomial[m, m/2] Hypergeometric2F1[ (p - a \[Nu])/(2 a), -\[Nu], (1/2) (2 + p/a - \[Nu]), -E^(2 a z)] (1 - Mod[m, 2]) Cosh[a z]^\[Nu])/(2^m (1 + E^(2 a z))^\[Nu])) + (Cosh[a z]^\[Nu] Sum[(-1)^k E^(I d (-2 k + m)) Binomial[m, k] ((E^(-2 I d (-2 k + m) + I m Pi + ((-I) c (-2 k + m) + p) z) Hypergeometric2F1[((-I) c (-2 k + m) + p - a \[Nu])/(2 a), -\[Nu], (1/2) (2 + ((-I) c (-2 k + m) + p)/a - \[Nu]), -E^(2 a z)])/ ((-I) c (-2 k + m) + p - a \[Nu]) + (E^((I c (-2 k + m) + p) z) Hypergeometric2F1[(I c (-2 k + m) + p - a \[Nu])/(2 a), -\[Nu], (1/2) (2 + (I c (-2 k + m) + p)/a - \[Nu]), -E^(2 a z)])/ (I c (-2 k + m) + p - a \[Nu])), {k, 0, Floor[(1/2) (-1 + m)]}])/ (2^m I^m (1 + E^(2 a z))^\[Nu]) /; 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