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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 functions > Involving cos > Involving cos(b zr+d z+e) sinh(c zr+f z)





http://functions.wolfram.com/01.19.21.0754.01









  


  








Input Form





Integrate[Cos[b Sqrt[z] + d z + e] Sinh[c Sqrt[z] + f z], z] == (1/4) I ((1/(-d + I f)^(3/2)) (2 Sqrt[-d + I f] Cos[e - (-b + I c) Sqrt[z] - (-d + I f) z] + (-b + I c) Sqrt[2 Pi] Cos[e + (-b + I c)^2/(4 (-d + I f))] FresnelS[(-b + I c + 2 (-d + I f) Sqrt[z])/(Sqrt[-d + I f] Sqrt[2 Pi])] + (b - I c) Sqrt[2 Pi] FresnelC[(-b + I c + 2 (-d + I f) Sqrt[z])/(Sqrt[-d + I f] Sqrt[2 Pi])] Sin[e + (-b + I c)^2/(4 (-d + I f))]) + (1/(-d - I f)^(3/2)) (-2 Sqrt[-d - I f] Cos[e - (-b - I c) Sqrt[z] - (-d - I f) z] - (-b - I c) Sqrt[2 Pi] Cos[e + (-b - I c)^2/(4 (-d - I f))] FresnelS[(-b - I c + 2 (-d - I f) Sqrt[z])/(Sqrt[-d - I f] Sqrt[2 Pi])] - (b + I c) Sqrt[2 Pi] FresnelC[(-b - I c + 2 (-d - I f) Sqrt[z])/(Sqrt[-d - I f] Sqrt[2 Pi])] Sin[e + (-b - I c)^2/(4 (-d - I f))]))








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