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 Tanh

 http://functions.wolfram.com/01.21.21.0189.01

 Input Form

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

 Standard Form

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"z"]]]]]]], "]"]]]], ")"]]]]]], ")"]]]]]]]]

 MathML Form

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

 Rule Form

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

 2002-12-18