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Cos






Mathematica Notation

Traditional Notation









Elementary Functions > Cos[z] > Integration > Indefinite integration > Involving one direct function and elementary functions > Involving trigonometric and exponential functions > Involving rational functions of sin and exp > Involving ep zcos(c z)/a+b sin2(d z)





http://functions.wolfram.com/01.07.21.0964.01









  


  










Input Form





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










Standard Form





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MathML Form







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</mo> <mi> d </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> </msup> </mrow> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> a </mi> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msqrt> <mrow> <mi> a </mi> <mo> + </mo> <mi> b </mi> </mrow> </msqrt> <mo> &#8290; </mo> <msqrt> <mi> a </mi> </msqrt> </mrow> <mo> + </mo> <mi> b </mi> </mrow> </mfrac> </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[RowBox[List[&quot;1&quot;, &quot;-&quot;, FractionBox[RowBox[List[&quot;c&quot;, &quot;-&quot;, RowBox[List[&quot;\[ImaginaryI]&quot;, &quot; &quot;, &quot;p&quot;]]]], RowBox[List[&quot;2&quot;, &quot; &quot;, &quot;d&quot;]]]]], 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&quot;, SqrtBox[&quot;a&quot;]]], &quot;+&quot;, &quot;b&quot;]]], Hypergeometric2F1]]], &quot;)&quot;]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]]], Hypergeometric2F1] </annotation> </semantics> </mrow> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> a </mi> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msqrt> <mrow> <mi> a </mi> <mo> + </mo> <mi> b </mi> </mrow> </msqrt> <mo> &#8290; </mo> <msqrt> <mi> a </mi> </msqrt> </mrow> <mo> + </mo> <mi> b </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <semantics> <mrow> <mrow> <msub> <mo> &#8202; </mo> <mn> 2 </mn> </msub> <msub> <mi> F </mi> <mn> 1 </mn> </msub> </mrow> <mo> &#8289; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mn> 1 </mn> <mo> - </mo> <mfrac> <mrow> <mi> c </mi> <mo> - </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> p </mi> </mrow> </mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> d </mi> </mrow> </mfrac> </mrow> 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</apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <ci> b </ci> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> -2 </cn> <imaginaryi /> <ci> d </ci> <ci> z </ci> </apply> </apply> <apply> <power /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> a </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <apply> <plus /> <ci> a </ci> <ci> b </ci> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <ci> a </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <ci> b </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </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