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 Cosh

 http://functions.wolfram.com/01.20.21.1342.01

 Input Form

 Integrate[E^(b z) Tan[a z] Cosh[c z], z] == (1/2) ((I E^((b - c) z) Hypergeometric2F1[-((I (b - c))/(2 a)), 1, 1 - (I (b - c))/(2 a), -E^(2 I a z)])/(b - c) - (1/(2 a - I b + I c)) (E^((2 I a + b - c) z) Hypergeometric2F1[ (2 a - I b + I c)/(2 a), 1, (4 a - I b + I c)/(2 a), -E^(2 I a z)]) + (I E^((b + c) z) Hypergeometric2F1[-((I (b + c))/(2 a)), 1, 1 - (I (b + c))/(2 a), -E^(2 I a z)])/(b + c) - (1/(2 a - I (b + c))) (E^((2 I a + b + c) z) Hypergeometric2F1[ (2 a - I (b + c))/(2 a), 1, (4 a - I (b + c))/(2 a), -E^(2 I a z)]))

 Standard Form

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 MathML Form

 b z tan ( a z ) cosh ( c z ) z 1 2 ( - ( b - c + 2 a ) z 2 a - b + c 2 F 1 ( 2 a - b + c 2 a , 1 ; 4 a - b + c 2 a ; - 2 a z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["2", TraditionalForm]], SubscriptBox["F", FormBox["1", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[FractionBox[RowBox[List[RowBox[List["2", " ", "a"]], "-", RowBox[List["\[ImaginaryI]", " ", "b"]], "+", RowBox[List["\[ImaginaryI]", " ", "c", " "]]]], RowBox[List["2", " ", "a"]]], Hypergeometric2F1], ",", TagBox["1", Hypergeometric2F1]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1], ";", TagBox[TagBox[TagBox[FractionBox[RowBox[List[RowBox[List["4", " ", "a"]], "-", RowBox[List["\[ImaginaryI]", " ", "b"]], "+", RowBox[List["\[ImaginaryI]", " ", "c", " "]]]], RowBox[List["2", " ", "a"]]], Hypergeometric2F1], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1], ";", TagBox[RowBox[List["-", SuperscriptBox["\[ExponentialE]", RowBox[List["2", " ", "\[ImaginaryI]", " ", "a", " ", "z"]]]]], Hypergeometric2F1]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]]], Hypergeometric2F1] - ( b + c + 2 a ) z 2 a - ( b + c ) 2 F 1 ( 2 a - ( b + c ) 2 a , 1 ; 4 a - ( b + c ) 2 a ; - 2 a z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["2", TraditionalForm]], SubscriptBox["F", FormBox["1", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[FractionBox[RowBox[List[RowBox[List["2", " ", "a"]], "-", RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List["b", "+", "c"]], ")"]]]]]], RowBox[List["2", " ", "a"]]], Hypergeometric2F1], ",", TagBox["1", Hypergeometric2F1]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1], ";", TagBox[TagBox[TagBox[FractionBox[RowBox[List[RowBox[List["4", " ", "a"]], "-", RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List["b", "+", "c"]], ")"]]]]]], RowBox[List["2", " ", "a"]]], Hypergeometric2F1], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1], ";", TagBox[RowBox[List["-", SuperscriptBox["\[ExponentialE]", RowBox[List["2", " ", "\[ImaginaryI]", " ", "a", " ", "z"]]]]], Hypergeometric2F1]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]]], Hypergeometric2F1] + ( b - c ) z b - c 2 F 1 ( - ( b - c ) 2 a , 1 ; 1 - ( b - c ) 2 a ; - 2 a z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["2", TraditionalForm]], SubscriptBox["F", FormBox["1", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[RowBox[List["-", FractionBox[RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List["b", "-", "c"]], ")"]]]], RowBox[List["2", " ", "a"]]]]], Hypergeometric2F1], ",", TagBox["1", Hypergeometric2F1]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1], ";", TagBox[TagBox[TagBox[RowBox[List["1", "-", FractionBox[RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List["b", "-", "c"]], ")"]]]], RowBox[List["2", " ", "a"]]]]], Hypergeometric2F1], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1], ";", TagBox[RowBox[List["-", SuperscriptBox["\[ExponentialE]", RowBox[List["2", " ", "\[ImaginaryI]", " ", "a", " ", "z"]]]]], Hypergeometric2F1]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]]], Hypergeometric2F1] + ( b + c ) z b + c 2 F 1 ( - ( b + c ) 2 a , 1 ; 1 - ( b + c ) 2 a ; - 2 a z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["2", TraditionalForm]], SubscriptBox["F", FormBox["1", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[RowBox[List["-", FractionBox[RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List["b", "+", "c"]], ")"]]]], RowBox[List["2", " ", "a"]]]]], Hypergeometric2F1], ",", TagBox["1", Hypergeometric2F1]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1], ";", TagBox[TagBox[TagBox[RowBox[List["1", "-", FractionBox[RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List["b", "+", "c"]], ")"]]]], RowBox[List["2", " ", "a"]]]]], Hypergeometric2F1], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1], ";", TagBox[RowBox[List["-", SuperscriptBox["\[ExponentialE]", RowBox[List["2", " ", "\[ImaginaryI]", " ", "a", " ", "z"]]]]], Hypergeometric2F1]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]]], Hypergeometric2F1] ) z b z a z c z 1 2 -1 b -1 c 2 a z 2 a -1 b c -1 Hypergeometric2F1 2 a -1 b c 2 a -1 1 4 a -1 b c 2 a -1 -1 2 a z -1 b c 2 a z 2 a -1 b c -1 Hypergeometric2F1 2 a -1 b c 2 a -1 1 4 a -1 b c 2 a -1 -1 2 a z b -1 c z b -1 c -1 Hypergeometric2F1 -1 b -1 c 2 a -1 1 1 -1 b -1 c 2 a -1 -1 2 a z b c z b c -1 Hypergeometric2F1 -1 b c 2 a -1 1 1 -1 b c 2 a -1 -1 2 a z [/itex]

 Rule Form

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

 2002-12-18