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Cosh






Mathematica Notation

Traditional Notation









Elementary Functions > Cosh[z] > Integration > Indefinite integration > Involving functions of the direct function > Involving algebraic functions of the direct function > Involving ((a+b cosh2(c z))nu)betacosh(d z)





http://functions.wolfram.com/01.20.21.2396.01









  


  










Input Form





Integrate[((a + b Cosh[c z]^2)^\[Nu])^\[Beta] Cosh[d z], z] == (2^(\[Beta] \[Nu]) (a + ((1/4) b (1 + E^(2 c z))^2)/E^(2 c z))^ (\[Beta] \[Nu]) (E^(2 d z) (d + 2 c \[Beta] \[Nu]) AppellF1[d/(2 c) - \[Beta] \[Nu], (-\[Beta]) \[Nu], (-\[Beta]) \[Nu], 1 + d/(2 c) - \[Beta] \[Nu], -((b E^(2 c z))/ (2 a + b + 2 Sqrt[a (a + b)])), -((b E^(2 c z))/(2 a + b - 2 Sqrt[a (a + b)]))] - (d - 2 c \[Beta] \[Nu]) AppellF1[-((d + 2 c \[Beta] \[Nu])/(2 c)), (-\[Beta]) \[Nu], (-\[Beta]) \[Nu], 1 - d/(2 c) - \[Beta] \[Nu], -((b E^(2 c z))/(2 a + b + 2 Sqrt[a (a + b)])), -((b E^(2 c z))/(2 a + b - 2 Sqrt[a (a + b)]))]) ((2 a + b + b Cosh[2 c z])^\[Nu]/2^\[Nu])^\[Beta] Cosh[d z])/ ((1 + (b E^(2 c z))/(2 a + b - 2 Sqrt[a (a + b)]))^(\[Beta] \[Nu]) (1 + (b E^(2 c z))/(2 a + b + 2 Sqrt[a (a + b)]))^(\[Beta] \[Nu]) (2 a + b + b Cosh[2 c z])^(\[Beta] \[Nu]))/ ((1 + E^(2 d z)) (d^2 - 4 c^2 \[Beta]^2 \[Nu]^2))










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