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Cosh






Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/01.20.21.4647.01









  


  










Input Form





Integrate[E^(p z) Sinh[d + c z]^m Cosh[b + a z]^\[Nu], z] == (I/2)^m Cosh[b + a z]^\[Nu] (-((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 (b + a z))] (-1 + Mod[m, 2]))/(1 + E^(2 (b + a z)))^\[Nu])) + Sum[(-1)^k E^(d (-2 k + m)) Binomial[m, k] ((E^(4 d k - 2 d m + I m Pi + 2 c k z - c m z + p z) Hypergeometric2F1[-((2 c k - c m + p + a \[Nu])/(2 a)), -\[Nu], -((2 c k - c m + p + a (-2 + \[Nu]))/(2 a)), -E^(-2 (b + a z))])/ (2 c k - c m + p + a \[Nu]) + (E^((c (-2 k + m) + p) z) Hypergeometric2F1[-((c (-2 k + m) + p + a \[Nu])/(2 a)), -\[Nu], -((-2 c k + c m + p + a (-2 + \[Nu]))/(2 a)), -E^(-2 (b + a z))])/ (c (-2 k + m) + p + a \[Nu])), {k, 0, Floor[(1/2) (-1 + m)]}]/ (I^m (1 + E^(-2 (b + 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