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Cosh






Mathematica Notation

Traditional Notation









Elementary Functions > Cosh[z] > Integration > Indefinite integration > Involving functions of the direct function and hyperbolic functions > Involving powers of the direct function and hyperbolic functions > Involving sinh > Involving sinh(b zr+d z) coshv(f z+g)





http://functions.wolfram.com/01.20.21.4057.01









  


  










Input Form





Integrate[Sinh[b z^2 + d z] Cosh[f z + g]^v, z] == (1/b) ((2^(-2 - v) Sqrt[Pi] Binomial[v, v/2] (Sqrt[-b] E^(d^2/(2 b)) Erfi[(Sqrt[-b] (d + 2 b z))/(2 b)] + Sqrt[b] Erfi[(d + 2 b z)/(2 Sqrt[b])]) (1 - Mod[v, 2]))/ E^(d^2/(4 b))) + 2^(-2 - v) Sqrt[Pi] Sum[Binomial[v, s] ((Sqrt[-b] E^(g (2 s - v) + (d - 2 f s + f v)^2/(4 b)) Erfi[(-d + f (2 s - v) - 2 b z)/(2 Sqrt[-b])])/b + (E^(g (-2 s + v) - (d - 2 f s + f v)^2/(4 b)) Erfi[(d - f (2 s - v) + 2 b z)/(2 Sqrt[b])])/Sqrt[b] + (1/b) (E^(g (-2 s + v) + (-d + f (-2 s + v))^2/(4 b)) (Sqrt[-b] Erfi[(-d - f (2 s - v) - 2 b z)/(2 Sqrt[-b])] + Sqrt[b] E^(2 (g (2 s - v) - (-d - 2 f s + f v)^2/(4 b))) Erfi[(d + f (2 s - v) + 2 b z)/(2 Sqrt[b])]))), {s, 0, Floor[(1/2) (-1 + v)]}] /; Element[v, Integers] && v > 0










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