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 Cosh

 http://functions.wolfram.com/01.20.21.3900.01

 Input Form

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

 Standard Form

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RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "a"]], "+", SqrtBox[RowBox[List[RowBox[List["4", " ", SuperscriptBox["a", "2"]]], "-", RowBox[List["4", " ", SuperscriptBox["b", "2"]]]]]]]]]]], ")"]], RowBox[List["-", "\[Beta]"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", FractionBox[RowBox[List["2", " ", "b", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["c", " ", "z"]]]]], RowBox[List[RowBox[List["2", " ", "a"]], "+", SqrtBox[RowBox[List[RowBox[List["4", " ", SuperscriptBox["a", "2"]]], "-", RowBox[List["4", " ", SuperscriptBox["b", "2"]]]]]]]]]]], ")"]], RowBox[List["-", "\[Beta]"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["a", "+", RowBox[List[FractionBox["1", "2"], " ", "b", " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", "c"]], " ", "z"]]], " ", RowBox[List["(", RowBox[List["1", "+", SuperscriptBox["\[ExponentialE]", RowBox[List["2", " ", "c", " ", "z"]]]]], ")"]]]]]], ")"]], "\[Beta]"], " ", RowBox[List["AppellF1", "[", 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SuperscriptBox["\[ExponentialE]", RowBox[List["c", " ", "z"]]]]], RowBox[List[RowBox[List["2", " ", "a"]], "+", SqrtBox[RowBox[List[RowBox[List["4", " ", SuperscriptBox["a", "2"]]], "-", RowBox[List["4", " ", SuperscriptBox["b", "2"]]]]]]]]]]], ",", FractionBox[RowBox[List["2", " ", "b", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["c", " ", "z"]]]]], RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "a"]], "+", SqrtBox[RowBox[List[RowBox[List["4", " ", SuperscriptBox["a", "2"]]], "-", RowBox[List["4", " ", SuperscriptBox["b", "2"]]]]]]]]]]], "]"]]]], ")"]]]]]], ")"]]]]]]]]

 MathML Form

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

 Rule Form

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

 2002-12-18