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 Tan

 http://functions.wolfram.com/01.08.21.0066.01

 Input Form

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

 Standard Form

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 MathML Form

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

 Rule Form

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

 2002-12-18