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 Cosh

 http://functions.wolfram.com/01.20.21.1244.01

 Input Form

 Integrate[(E^(p z) Sin[e z] Cosh[c z])/(a + b Sin[d z]), z] == (-(1/4)) I ((I E^((-c + I d - I e + p) z) ((a + Sqrt[a^2 - b^2]) Hypergeometric2F1[-((I (-c + I d - I e + p))/d), 1, 2 - (I (-c - I e + p))/d, -((I b E^(I d z))/ (-a + Sqrt[a^2 - b^2]))] + (-a + Sqrt[a^2 - b^2]) Hypergeometric2F1[-((I (-c + I d - I e + p))/d), 1, 2 - (I (-c - I e + p))/d, (I b E^(I d z))/(a + Sqrt[a^2 - b^2])]))/ (b Sqrt[a^2 - b^2] (-c + I d - I e + p)) + (I E^((c + I d - I e + p) z) ((a + Sqrt[a^2 - b^2]) Hypergeometric2F1[-((I (c + I d - I e + p))/d), 1, 2 - (I (c - I e + p))/d, -((I b E^(I d z))/(-a + Sqrt[a^2 - b^2]))] + (-a + Sqrt[a^2 - b^2]) Hypergeometric2F1[-((I (c + I d - I e + p))/d), 1, 2 - (I (c - I e + p))/d, (I b E^(I d z))/(a + Sqrt[a^2 - b^2])]))/ (b Sqrt[a^2 - b^2] (c + I d - I e + p)) - (I E^((-c + I d + I e + p) z) ((a + Sqrt[a^2 - b^2]) Hypergeometric2F1[-((I (-c + I d + I e + p))/d), 1, 2 - (I (-c + I e + p))/d, -((I b E^(I d z))/ (-a + Sqrt[a^2 - b^2]))] + (-a + Sqrt[a^2 - b^2]) Hypergeometric2F1[-((I (-c + I d + I e + p))/d), 1, 2 - (I (-c + I e + p))/d, (I b E^(I d z))/(a + Sqrt[a^2 - b^2])]))/ (b Sqrt[a^2 - b^2] (-c + I d + I e + p)) - (I E^((c + I d + I e + p) z) ((a + Sqrt[a^2 - b^2]) Hypergeometric2F1[-((I (c + I d + I e + p))/d), 1, 2 - (I (c + I e + p))/d, -((I b E^(I d z))/(-a + Sqrt[a^2 - b^2]))] + (-a + Sqrt[a^2 - b^2]) Hypergeometric2F1[-((I (c + I d + I e + p))/d), 1, 2 - (I (c + I e + p))/d, (I b E^(I d z))/(a + Sqrt[a^2 - b^2])]))/ (b Sqrt[a^2 - b^2] (c + I d + I e + p)))

 Standard Form

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 MathML Form

 p z sin ( e z ) cosh ( c z ) a + b sin ( d z ) z - 1 4 ( ( ( - c - e + d + p ) z ( ( a + a 2 - b 2 ) 2 F 1 ( - ( - c - e + d + p ) d , 1 ; 2 - ( - c - e + p ) d ; - b d z a 2 - b 2 - a ) 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]", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "c"]], "-", RowBox[List["\[ImaginaryI]", " ", "e"]], "+", RowBox[List["\[ImaginaryI]", " ", "d"]], " ", "+", "p"]], ")"]]]], "d"]]], Hypergeometric2F1], ",", TagBox["1", Hypergeometric2F1]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1], ";", TagBox[TagBox[TagBox[RowBox[List["2", "-", FractionBox[RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "c"]], "-", RowBox[List["\[ImaginaryI]", " ", "e"]], "+", "p"]], ")"]]]], "d"]]], Hypergeometric2F1], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1], ";", TagBox[RowBox[List["-", FractionBox[RowBox[List["\[ImaginaryI]", " ", "b", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["\[ImaginaryI]", " ", "d", " ", "z"]]]]], RowBox[List[SqrtBox[RowBox[List[SuperscriptBox["a", "2"], "-", SuperscriptBox["b", "2"]]]], "-", "a"]]]]], Hypergeometric2F1]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]]], Hypergeometric2F1] + ( a 2 - b 2 - a ) 2 F 1 ( - ( - c - e + d + p ) d , 1 ; 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 Rule Form

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

 2002-12-18