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 Cosh

 http://functions.wolfram.com/01.20.21.0545.01

 Input Form

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

 Standard Form

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 MathML Form

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

 Rule Form

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

 2002-12-18