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Cos






Mathematica Notation

Traditional Notation









Elementary Functions > Cos[z] > Integration > Indefinite integration > Involving functions of the direct function, trigonometric and exponential functions > Involving powers of the direct function, trigonometric and exponential functions > Involving powers of sin and exp > Involving ep zsinmu(c z+d)cosnu(a z)





http://functions.wolfram.com/01.07.21.2614.01









  


  










Input Form





Integrate[E^(p z) Sin[d + c z]^\[Mu] Cos[a z]^v, z] == (-((1/(p - I c \[Mu])) ((E^(p z) Binomial[v, v/2] Hypergeometric2F1[ -((I p + c \[Mu])/(2 c)), -\[Mu], (1/2) (2 - (I p)/c - \[Mu]), E^(2 I (d + c z))] (-1 + Mod[v, 2]) Sin[d + c z]^\[Mu])/ (1 - E^(2 (I d + I c z)))^\[Mu])) + (Sin[d + c z]^\[Mu] Sum[Binomial[v, s] ((E^((p + 2 I a s - I a v) z) Hypergeometric2F1[ -((I (p + 2 I a s - I a v - I c \[Mu]))/(2 c)), -\[Mu], -((I (p + 2 I a s - I a v - I c (-2 + \[Mu])))/(2 c)), E^(2 I (d + c z))])/(p + 2 I a s - I a v - I c \[Mu]) + (E^((p + I a (-2 s + v)) z) Hypergeometric2F1[ -((I (p - 2 I a s + I a v - I c \[Mu]))/(2 c)), -\[Mu], (1/2) (2 - (I (p - 2 I a s + I a v))/c - \[Mu]), E^(2 I (d + c z))])/(p - 2 I a s + I a v - I c \[Mu])), {s, 0, Floor[(1/2) (-1 + v)]}])/(1 - E^(2 (I d + I c z)))^\[Mu])/ 2^v /; Element[v, Integers] && v > 0










Standard Form





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MathML Form







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</mo> <mi> z </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </msup> </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;-&quot;, FractionBox[RowBox[List[&quot;\[ImaginaryI]&quot;, &quot; &quot;, RowBox[List[&quot;(&quot;, RowBox[List[&quot;p&quot;, &quot;+&quot;, RowBox[List[&quot;2&quot;, &quot; &quot;, &quot;\[ImaginaryI]&quot;, &quot; &quot;, &quot;a&quot;, &quot; &quot;, &quot;s&quot;]], &quot;-&quot;, RowBox[List[&quot;\[ImaginaryI]&quot;, &quot; &quot;, &quot;a&quot;, &quot; &quot;, &quot;v&quot;]], &quot;-&quot;, RowBox[List[&quot;\[ImaginaryI]&quot;, &quot; &quot;, &quot;c&quot;, &quot; &quot;, &quot;\[Mu]&quot;]]]], &quot;)&quot;]]]], RowBox[List[&quot;2&quot;, &quot; 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</ci> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <plus /> <ci> p </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> c </ci> <ci> &#956; </ci> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <apply> <power /> <exponentiale /> <apply> <times /> <ci> p </ci> <ci> z </ci> </apply> </apply> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <plus /> <apply> <times /> <imaginaryi /> <ci> d </ci> </apply> <apply> <times /> <imaginaryi /> <ci> c </ci> <ci> z </ci> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> &#956; 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</ci> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <in /> <ci> v </ci> <apply> <ci> SuperPlus </ci> <ci> &#8469; </ci> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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





2002-12-18