html, body, form { margin: 0; padding: 0; width: 100%; } #calculate { position: relative; width: 177px; height: 110px; background: transparent url(/images/alphabox/embed_functions_inside.gif) no-repeat scroll 0 0; } #i { position: relative; left: 18px; top: 44px; width: 133px; border: 0 none; outline: 0; font-size: 11px; } #eq { width: 9px; height: 10px; background: transparent; position: absolute; top: 47px; right: 18px; cursor: pointer; }

 Cos

 http://functions.wolfram.com/01.07.21.2653.01

 Input Form

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

 Standard Form

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 MathML Form

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

 Rule Form

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

 2002-12-18