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Cosh






Mathematica Notation

Traditional Notation









Elementary Functions > Cosh[z] > Integration > Indefinite integration > Involving one direct function and elementary functions > Involving hyperbolic and exponential functions > Involving sinh and exp > Involving eb zr+d z+e sinh(a zr+p z+q) cosh(c zr+f z+g)





http://functions.wolfram.com/01.20.21.1834.01









  


  










Input Form





Integrate[E^(b Sqrt[z] + d z + e) Sinh[a Sqrt[z] + p z + q] Cosh[c Sqrt[z] + f z + g], z] == (1/8) E^(e - g - q) (-((2 E^((-(a - b + c)) Sqrt[z] - (-d + f + p) z))/(d - f - p)) + (2 E^(2 g + 2 q + (a + b + c) Sqrt[z] + (d + f + p) z))/(d + f + p) - ((a - b + c) Sqrt[Pi] Erfi[(-a + b - c + 2 (d - f - p) Sqrt[z])/ (2 Sqrt[d - f - p])])/(E^((a - b + c)^2/(4 (d - f - p))) (d - f - p)^(3/2)) + E^(2 q) (-((2 E^(2 g - 2 q + (-a + b + c) Sqrt[z] + (d + f - p) z))/ (d + f - p)) + (2 E^((a + b - c) Sqrt[z] + (d - f + p) z))/ (d - f + p) + ((-a + b + c) E^(2 g - (-a + b + c)^2/(4 (d + f - p)) - 2 q) Sqrt[Pi] Erfi[(-a + b + c + 2 (d + f - p) Sqrt[z])/ (2 Sqrt[d + f - p])])/(d + f - p)^(3/2) - ((a + b - c) Sqrt[Pi] Erfi[(a + b - c + 2 (d - f + p) Sqrt[z])/ (2 Sqrt[d - f + p])])/(E^((a + b - c)^2/(4 (d - f + p))) (d - f + p)^(3/2))) - ((a + b + c) E^(2 g - (a + b + c)^2/(4 (d + f + p)) + 2 q) Sqrt[Pi] Erfi[(a + b + c + 2 (d + f + p) Sqrt[z])/(2 Sqrt[d + f + p])])/ (d + f + p)^(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