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 Cosh

 http://functions.wolfram.com/01.20.21.0589.01

 Input Form

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

 Standard Form

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 MathML Form

 sin ( e + d z ) cosh ( z c + g + f z ) z - 1 4 ( 1 ( - d - f ) 3 / 2 ( - 2 - d - f cos ( e + g + ( d + f ) z + c z ) - c 2 π ( cos ( c 2 4 ( d + f ) + e + g ) 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 ) + e + g ) ) ) + 1 ( f - d ) 3 / 2 ( - 2 f - d cos ( e - g - ( f - d ) z - c z ) - c 2 π ( cos ( - c 2 4 ( f - d ) + e - g ) 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 ) + e - g ) ) ) ) z e d z z 1 2 c g f z -1 1 4 1 -1 d -1 f 3 2 -1 -2 -1 d -1 f 1 2 e g d f z c z 1 2 -1 c 2 1 2 c 2 4 d f -1 e g 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 e g 1 f -1 d 3 2 -1 -2 f -1 d 1 2 e -1 g -1 f -1 d z -1 c z 1 2 -1 c 2 1 2 -1 c 2 4 f -1 d -1 e -1 g FresnelS 2 z 1 2 f -1 d c f -1 d 1 2 2 1 2 -1 -1 FresnelC 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 g [/itex]

 Rule Form

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

 2002-12-18