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 Cosh

 http://functions.wolfram.com/01.20.21.0711.01

 Input Form

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

 Standard Form

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 MathML Form

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

 Rule Form

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

 2002-12-18