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Cosh




Mathematica Notation

Traditional Notation









Elementary Functions > Cosh[z] > Integration > Indefinite integration > Involving one direct function and elementary functions > Involving trigonometric functions > Involving cos > Involving cos(b zr+d z) cosh(c zr+f z)





http://functions.wolfram.com/01.20.21.0751.01









  


  








Input Form





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








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