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Cosh






Mathematica Notation

Traditional Notation









Elementary Functions > Cosh[z] > Integration > Indefinite integration > Involving functions of the direct function, hyperbolic, exponential and trigonometric functions > Involving rational functions of the direct function, hyperbolic, exponential and trigonometric functions > Involving cos, rational functions of sinh and exp > Involving ep zcos(d z)(a+b sinh(e z)+c cosh(e z))-n





http://functions.wolfram.com/01.20.21.4892.01









  


  










Input Form





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










Standard Form





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MathML Form







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TagBox[TagBox[TagBox[RowBox[List[FractionBox[RowBox[List[RowBox[List[&quot;\[ImaginaryI]&quot;, &quot; &quot;, &quot;d&quot;]], &quot;+&quot;, &quot;p&quot;]], &quot;e&quot;], &quot;+&quot;, &quot;2&quot;]], Hypergeometric2F1], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1], &quot;;&quot;, TagBox[FractionBox[RowBox[List[RowBox[List[&quot;(&quot;, RowBox[List[&quot;b&quot;, &quot;+&quot;, &quot;c&quot;]], &quot;)&quot;]], &quot; &quot;, SuperscriptBox[&quot;\[ExponentialE]&quot;, RowBox[List[&quot;e&quot;, &quot; &quot;, &quot;z&quot;]]]]], RowBox[List[SqrtBox[RowBox[List[SuperscriptBox[&quot;a&quot;, &quot;2&quot;], &quot;+&quot;, SuperscriptBox[&quot;b&quot;, &quot;2&quot;], &quot;-&quot;, SuperscriptBox[&quot;c&quot;, &quot;2&quot;]]]], &quot;-&quot;, &quot;a&quot;]]], Hypergeometric2F1]]], &quot;)&quot;]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]]], Hypergeometric2F1] </annotation> </semantics> </mrow> <mo> + </mo> <mrow> 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</mrow> <mo> &#8290; </mo> <msup> <mi> &#8519; </mi> <mrow> <mi> e </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> </msup> </mrow> <mrow> <mi> a </mi> <mo> + </mo> <msqrt> <mrow> <msup> <mi> a </mi> <mn> 2 </mn> </msup> <mo> + </mo> <msup> <mi> b </mi> <mn> 2 </mn> </msup> <mo> - </mo> <msup> <mi> c </mi> <mn> 2 </mn> </msup> </mrow> </msqrt> </mrow> </mfrac> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation encoding='Mathematica'> TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox[&quot;\[InvisiblePrefixScriptBase]&quot;, FormBox[&quot;2&quot;, TraditionalForm]], SubscriptBox[&quot;F&quot;, FormBox[&quot;1&quot;, TraditionalForm]]]], &quot;\[InvisibleApplication]&quot;, RowBox[List[&quot;(&quot;, RowBox[List[TagBox[TagBox[RowBox[List[TagBox[FractionBox[RowBox[List[&quot;e&quot;, &quot;+&quot;, RowBox[List[&quot;\[ImaginaryI]&quot;, &quot; &quot;, &quot;d&quot;]], &quot; &quot;, &quot;+&quot;, &quot;p&quot;]], &quot;e&quot;], Hypergeometric2F1], &quot;,&quot;, 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&quot;)&quot;]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]]], Hypergeometric2F1] </annotation> </semantics> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> / </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> b </mi> <mo> - </mo> <mi> c </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msqrt> <mrow> <msup> <mi> a </mi> <mn> 2 </mn> </msup> <mo> + </mo> <msup> <mi> b </mi> <mn> 2 </mn> </msup> <mo> - </mo> <msup> <mi> c </mi> <mn> 2 </mn> </msup> </mrow> </msqrt> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> e </mi> <mo> + </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> d </mi> </mrow> <mtext> </mtext> <mo> + </mo> <mi> p </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <int /> <bvar> <ci> z </ci> </bvar> <apply> <times /> <apply> <power /> <exponentiale /> <apply> 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a </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> c </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <plus /> <ci> e </ci> <apply> <times /> <imaginaryi /> <ci> d </ci> </apply> <ci> p </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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





2002-12-18