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 Cosh

 http://functions.wolfram.com/01.20.21.0876.01

 Input Form

 Integrate[Tan[b z] Cosh[c z], z] == (1/(2 (c^3 + 4 c b^2))) ((I ((-c) (c - 2 I b) E^(2 (c + I b) z) Hypergeometric2F1[1 - (I c)/(2 b), 1, 2 - (I c)/(2 b), -E^(2 I b z)] + (c + 2 I b) (c E^(2 I b z) Hypergeometric2F1[1 + (I c)/(2 b), 1, 2 + (I c)/(2 b), -E^(2 I b z)] + (c - 2 I b) (E^(2 c z) Hypergeometric2F1[ -((I c)/(2 b)), 1, 1 - (I c)/(2 b), -E^(2 I b z)] - Hypergeometric2F1[(I c)/(2 b), 1, 1 + (I c)/(2 b), -E^(2 I b z)]))))/ E^(c z))

 Standard Form

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 MathML Form

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

 Rule Form

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

 2002-12-18