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Sinh






Mathematica Notation

Traditional Notation









Elementary Functions > Sinh[z] > Integration > Indefinite integration > Involving functions of the direct function > Involving algebraic functions of the direct function > Involving ((a+b sinh2(c z))nu)betasinh(d z)





http://functions.wolfram.com/01.19.21.1786.01









  


  










Input Form





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










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