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 Cosh

 http://functions.wolfram.com/01.20.21.0575.01

 Input Form

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

 Standard Form

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 MathML Form

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

 Rule Form

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

 2002-12-18