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 Cosh

 http://functions.wolfram.com/01.20.21.0859.01

 Input Form

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

 Standard Form

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

 MathML Form

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

 Rule Form

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

 2002-12-18