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 Cosh

 http://functions.wolfram.com/01.20.21.1250.01

 Input Form

 Integrate[E^(p z) Sin[e z] Cosh[c z] (a + b Sin[d z])^\[Beta], z] == ((-(1/4)) I (-((E^((c - I e + p) z) AppellF1[(I (c - I e + p))/d - \[Beta], -\[Beta], -\[Beta], 1 + (I (c - I e + p))/d - \[Beta], -((I b)/(E^(I d z) (a + Sqrt[a^2 - b^2]))), -((I b)/(E^(I d z) (a - Sqrt[a^2 - b^2])))])/ (c - I e + p + I d \[Beta])) + (E^((-c + I e + p) z) AppellF1[(I (-c + I e + p))/d - \[Beta], -\[Beta], -\[Beta], 1 + (I (-c + I e + p))/d - \[Beta], -((I b)/(E^(I d z) (a + Sqrt[a^2 - b^2]))), -((I b)/(E^(I d z) (a - Sqrt[a^2 - b^2])))])/ (-c + I e + p + I d \[Beta]) + (E^((c + I e + p) z) AppellF1[(I (c + I e + p))/d - \[Beta], -\[Beta], -\[Beta], 1 + (I (c + I e + p))/d - \[Beta], -((I b)/(E^(I d z) (a + Sqrt[a^2 - b^2]))), -((I b)/(E^(I d z) (a - Sqrt[a^2 - b^2])))])/ (c + I e + p + I d \[Beta]) + (E^((-c - I e + p) z) AppellF1[-((I (c + I e - p - I d \[Beta]))/d), -\[Beta], -\[Beta], -((-d + I (c + I e - p) + d \[Beta])/d), -((I b)/(E^(I d z) (a + Sqrt[a^2 - b^2]))), -((I b)/(E^(I d z) (a - Sqrt[a^2 - b^2])))])/ (c + I e - p - I d \[Beta])) (a + b Sin[d z])^\[Beta])/ ((1 - (I b)/(E^(I d z) (-a + Sqrt[a^2 - b^2])))^\[Beta] (1 + (I b)/(E^(I d z) (a + Sqrt[a^2 - b^2])))^\[Beta])

 Standard Form

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"2"], "-", SuperscriptBox["b", "2"]]]]]]]]], ",", RowBox[List["-", FractionBox[RowBox[List["\[ImaginaryI]", " ", "b", " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "d", " ", "z"]]]]], RowBox[List["a", "-", SqrtBox[RowBox[List[SuperscriptBox["a", "2"], "-", SuperscriptBox["b", "2"]]]]]]]]]]], "]"]]]], ")"]], "/", RowBox[List["(", RowBox[List["c", "+", RowBox[List["\[ImaginaryI]", " ", "e"]], "-", "p", "-", RowBox[List["\[ImaginaryI]", " ", "d", " ", "\[Beta]"]]]], ")"]]]]]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["a", "+", RowBox[List["b", " ", RowBox[List["Sin", "[", RowBox[List["d", " ", "z"]], "]"]]]]]], ")"]], "\[Beta]"]]]]]]]

 MathML Form

 p z sin ( e z ) cosh ( c z ) ( a + b sin ( d z ) ) β z - 1 4 ( 1 - b - d z a 2 - b 2 - a ) - β ( 1 + b - d z a + a 2 - b 2 ) - β ( 1 c + e - p - d β ( ( - c - e + p ) z F 1 AppellF1 ( - ( c + e - p - d β ) d ; - β , - β ; - β d - d + ( c + e - p ) d ; - b - d z a + a 2 - b 2 , - b - d z a - a 2 - b 2 ) ) + 1 - c + e + p + d β ( ( - c + e + p ) z F 1 AppellF1 ( ( - c + e + p ) d - β ; - β , - β ; ( - c + e + p ) d - β + 1 ; - b - d z a + a 2 - b 2 , - b - d z a - a 2 - b 2 ) ) + 1 c + e + p + d β ( ( c + e + p ) z F 1 AppellF1 ( ( c + e + p ) d - β ; - β , - β ; ( c + e + p ) d - β + 1 ; - b - d z a + a 2 - b 2 , - b - d z a - a 2 - b 2 ) ) - 1 c - e + p + d β ( ( c - e + p ) z F 1 AppellF1 ( ( c - e + p ) d - β ; - β , - β ; ( c - e + p ) d - β + 1 ; - b - d z a + a 2 - b 2 , - b - d z a - a 2 - b 2 ) ) ) ( a + b sin ( d z ) ) β z p z e z c z a b d z β -1 1 4 1 -1 b -1 d z a 2 -1 b 2 1 2 -1 a -1 -1 β 1 b -1 d z a a 2 -1 b 2 1 2 -1 -1 β 1 c e -1 p -1 d β -1 -1 c -1 e p z AppellF1 -1 c e -1 p -1 d β d -1 -1 β -1 β -1 β d -1 d c e -1 p d -1 -1 b -1 d z a a 2 -1 b 2 1 2 -1 -1 b -1 d z a -1 a 2 -1 b 2 1 2 -1 1 -1 c e p d β -1 -1 c e p z AppellF1 -1 c e p d -1 -1 β -1 β -1 β -1 c e p d -1 -1 β 1 -1 b -1 d z a a 2 -1 b 2 1 2 -1 -1 b -1 d z a -1 a 2 -1 b 2 1 2 -1 1 c e p d β -1 c e p z AppellF1 c e p d -1 -1 β -1 β -1 β c e p d -1 -1 β 1 -1 b -1 d z a a 2 -1 b 2 1 2 -1 -1 b -1 d z a -1 a 2 -1 b 2 1 2 -1 -1 1 c -1 e p d β -1 c -1 e p z AppellF1 c -1 e p d -1 -1 β -1 β -1 β c -1 e p d -1 -1 β 1 -1 b -1 d z a a 2 -1 b 2 1 2 -1 -1 b -1 d z a -1 a 2 -1 b 2 1 2 -1 a b d z β [/itex]

 Rule Form

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

 2002-12-18