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 Cosh

 http://functions.wolfram.com/01.20.21.0745.01

 Input Form

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

 Standard Form

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 MathML Form

 cos ( e + d z ) cosh ( z c + f z ) z 1 4 ( 1 ( f - d ) 3 / 2 ( - c 2 π cos ( - c 2 4 ( f - d ) + e ) C TagBox["C", FresnelC] ( 2 z ( f - d ) + c f - d 2 π ) - c 2 π S TagBox["S", FresnelS] ( 2 z ( f - d ) + c f - d 2 π ) sin ( - c 2 4 ( f - d ) + e ) - 2 f - d sin ( e - ( f - d ) z - c z ) ) - 1 ( - d - f ) 3 / 2 ( c 2 π cos ( c 2 4 ( d + f ) + e ) C TagBox["C", FresnelC] ( 2 z ( d + f ) + c - d - f 2 π ) + c 2 π S TagBox["S", FresnelS] ( 2 z ( d + f ) + c - d - f 2 π ) sin ( c 2 4 ( d + f ) + e ) + 2 - d - f sin ( e + ( d + f ) z + c z ) ) ) z e d z z 1 2 c f z 1 4 1 f -1 d 3 2 -1 -1 c 2 1 2 -1 c 2 4 f -1 d -1 e FresnelC 2 z 1 2 f -1 d c f -1 d 1 2 2 1 2 -1 -1 c 2 1 2 FresnelS 2 z 1 2 f -1 d c f -1 d 1 2 2 1 2 -1 -1 c 2 4 f -1 d -1 e -1 2 f -1 d 1 2 e -1 f -1 d z -1 c z 1 2 -1 1 -1 d -1 f 3 2 -1 c 2 1 2 c 2 4 d f -1 e FresnelC 2 z 1 2 d f c -1 d -1 f 1 2 2 1 2 -1 c 2 1 2 FresnelS 2 z 1 2 d f c -1 d -1 f 1 2 2 1 2 -1 c 2 4 d f -1 e 2 -1 d -1 f 1 2 e d f z c z 1 2 [/itex]

 Rule Form

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

 2002-12-18