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 Tanh

 http://functions.wolfram.com/01.21.21.0050.01

 Input Form

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

 Standard Form

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 MathML Form

 p z sin ( b z ) tanh ( c z ) z 1 2 ( ( - b + p ) z 2 F 1 ( - b + p 2 c , 1 ; 2 c - b + p 2 c ; - 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[RowBox[List["-", "\[ImaginaryI]"]], " ", "b"]], "+", "p"]], RowBox[List["2", " ", "c"]]], Hypergeometric2F1], ",", TagBox["1", Hypergeometric2F1]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1], ";", TagBox[TagBox[TagBox[FractionBox[RowBox[List[RowBox[List["2", " ", "c"]], "-", RowBox[List["\[ImaginaryI]", " ", "b"]], " ", "+", "p"]], RowBox[List["2", " ", "c"]]], 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 + p + ( b + p ) z 2 F 1 ( b + p 2 c , 1 ; 2 c + b + p 2 c ; - 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["\[ImaginaryI]", " ", "b"]], "+", "p"]], RowBox[List["2", " ", "c"]]], Hypergeometric2F1], ",", TagBox["1", Hypergeometric2F1]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1], ";", TagBox[TagBox[TagBox[FractionBox[RowBox[List[RowBox[List["2", " ", "c"]], "+", RowBox[List["\[ImaginaryI]", " ", "b"]], " ", "+", "p"]], RowBox[List["2", " ", "c"]]], 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 - p - ( 2 c - b + p ) z 2 F 1 ( 2 c - b + p 2 c , 1 ; 4 c - b + p 2 c ; - 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["2", " ", "c"]], "-", RowBox[List["\[ImaginaryI]", " ", "b"]], " ", "+", "p"]], RowBox[List["2", " ", "c"]]], Hypergeometric2F1], ",", TagBox["1", Hypergeometric2F1]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1], ";", TagBox[TagBox[TagBox[FractionBox[RowBox[List[RowBox[List["4", " ", "c"]], "-", RowBox[List["\[ImaginaryI]", " ", "b"]], " ", "+", "p"]], RowBox[List["2", " ", "c"]]], 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 + p ) + ( 2 c + b + p ) z 2 F 1 ( 2 c + b + p 2 c , 1 ; 4 c + b + p 2 c ; - 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["2", " ", "c"]], "+", RowBox[List["\[ImaginaryI]", " ", "b"]], " ", "+", "p"]], RowBox[List["2", " ", "c"]]], Hypergeometric2F1], ",", TagBox["1", Hypergeometric2F1]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1], ";", TagBox[TagBox[TagBox[FractionBox[RowBox[List[RowBox[List["4", " ", "c"]], "+", RowBox[List["\[ImaginaryI]", " ", "b"]], " ", "+", "p"]], RowBox[List["2", " ", "c"]]], 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] ( 2 c + p ) - b ) z p z b z c z 1 2 -1 b p z Hypergeometric2F1 -1 b p 2 c -1 1 2 c -1 b p 2 c -1 -1 2 c z b p -1 b p z Hypergeometric2F1 b p 2 c -1 1 2 c b p 2 c -1 -1 2 c z b -1 p -1 -1 2 c -1 b p z Hypergeometric2F1 2 c -1 b p 2 c -1 1 4 c -1 b p 2 c -1 -1 2 c z b 2 c p -1 2 c b p z Hypergeometric2F1 2 c b p 2 c -1 1 4 c b p 2 c -1 -1 2 c z 2 c p -1 b -1 [/itex]

 Rule Form

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

 2002-12-18