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Sinh






Mathematica Notation

Traditional Notation









Elementary Functions > Sinh[z] > Integration > Indefinite integration > Involving one direct function and elementary functions > Involving trigonometric and exponential functions > Involving sin and exp > Involving ep zr sin(b z)sinh(c zr)





http://functions.wolfram.com/01.19.21.1193.01









  


  










Input Form





Integrate[E^(p Sqrt[z]) Sin[b z] Sinh[c Sqrt[z]], z] == (-(1/8)) I (-((8 I E^(p Sqrt[z]) Cos[b z] Sinh[c Sqrt[z]])/b) + (c E^((I (c + p)^2)/(4 b)) Sqrt[Pi] Erfi[(-c - p - 2 I b Sqrt[z])/ (2 Sqrt[I b])])/(I b)^(3/2) + (c Sqrt[Pi] Erfi[(-c + p - 2 I b Sqrt[z])/(2 Sqrt[(-I) b])])/ (E^((I (-c + p)^2)/(4 b)) ((-I) b)^(3/2)) - (p Sqrt[Pi] Erfi[(-c + p - 2 I b Sqrt[z])/(2 Sqrt[(-I) b])])/ (E^((I (-c + p)^2)/(4 b)) ((-I) b)^(3/2)) + (p Sqrt[Pi] Erfi[(c + p - 2 I b Sqrt[z])/(2 Sqrt[(-I) b])])/ (E^((I (c + p)^2)/(4 b)) ((-I) b)^(3/2)) - (c Sqrt[Pi] Erfi[(-c - p + 2 I b Sqrt[z])/(2 Sqrt[(-I) b])])/ (E^((I (c + p)^2)/(4 b)) ((-I) b)^(3/2)) - (c E^((I (-c + p)^2)/(4 b)) Sqrt[Pi] Erfi[(-c + p + 2 I b Sqrt[z])/ (2 Sqrt[I b])])/(I b)^(3/2) + (E^((I (-c + p)^2)/(4 b)) p Sqrt[Pi] Erfi[(-c + p + 2 I b Sqrt[z])/(2 Sqrt[I b])])/(I b)^(3/2) - (E^((I (c + p)^2)/(4 b)) p Sqrt[Pi] Erfi[(c + p + 2 I b Sqrt[z])/ (2 Sqrt[I b])])/(I b)^(3/2))










Standard Form





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MathML Form







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Date Added to functions.wolfram.com (modification date)





2002-12-18