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 Tanh

 http://functions.wolfram.com/01.21.21.0042.01

 Input Form

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

 Standard Form

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 MathML Form

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

 Rule Form

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

 2002-12-18