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 | | http://functions.wolfram.com/01.07.21.1260.01 | 
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 | | Integrate[(A + B Cos[c z])/(1 + Cos[c z])^2, z] == 
 ((2 A + B + (A + 2 B) Cos[c z]) Sin[c z])/(3 c (1 + Cos[c z])^2) | 
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 | | Cell[BoxData[RowBox[List[RowBox[List["\[Integral]", RowBox[List[FractionBox[RowBox[List["A", "+", RowBox[List["B", " ", RowBox[List["Cos", "[", RowBox[List["c", " ", "z"]], "]"]]]]]], SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", RowBox[List["Cos", "[", RowBox[List["c", " ", "z"]], "]"]]]], ")"]], "2"]], RowBox[List["\[DifferentialD]", "z"]]]]]], "\[Equal]", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["2", " ", "A"]], "+", "B", "+", RowBox[List[RowBox[List["(", RowBox[List["A", "+", RowBox[List["2", " ", "B"]]]], ")"]], " ", RowBox[List["Cos", "[", RowBox[List["c", " ", "z"]], "]"]]]]]], ")"]], " ", RowBox[List["Sin", "[", RowBox[List["c", " ", "z"]], "]"]]]], RowBox[List["3", " ", "c", " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", RowBox[List["Cos", "[", RowBox[List["c", " ", "z"]], "]"]]]], ")"]], "2"]]]]]]]] | 
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   <math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'>  <semantics>  <mrow>  <mrow>  <mo> ∫ </mo>  <mrow>  <mfrac>  <mrow>  <mi> A </mi>  <mo> + </mo>  <mrow>  <mi> B </mi>  <mo> ⁢ </mo>  <mrow>  <mi> cos </mi>  <mo> ⁡ </mo>  <mo> ( </mo>  <mrow>  <mi> c </mi>  <mo> ⁢ </mo>  <mi> z </mi>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  </mrow>  <msup>  <mrow>  <mo> ( </mo>  <mrow>  <mrow>  <mi> cos </mi>  <mo> ⁡ </mo>  <mo> ( </mo>  <mrow>  <mi> c </mi>  <mo> ⁢ </mo>  <mi> z </mi>  </mrow>  <mo> ) </mo>  </mrow>  <mo> + </mo>  <mn> 1 </mn>  </mrow>  <mo> ) </mo>  </mrow>  <mn> 2 </mn>  </msup>  </mfrac>  <mo> ⁢ </mo>  <mrow>  <mo> ⅆ </mo>  <mi> z </mi>  </mrow>  </mrow>  </mrow>  <mo> ⩵ </mo>  <mfrac>  <mrow>  <mrow>  <mo> ( </mo>  <mrow>  <mrow>  <mn> 2 </mn>  <mo> ⁢ </mo>  <mi> A </mi>  </mrow>  <mo> + </mo>  <mi> B </mi>  <mo> + </mo>  <mrow>  <mrow>  <mo> ( </mo>  <mrow>  <mi> A </mi>  <mo> + </mo>  <mrow>  <mn> 2 </mn>  <mo> ⁢ </mo>  <mi> B </mi>  </mrow>  </mrow>  <mo> ) </mo>  </mrow>  <mo> ⁢ </mo>  <mrow>  <mi> cos </mi>  <mo> ⁡ </mo>  <mo> ( </mo>  <mrow>  <mi> c </mi>  <mo> ⁢ </mo>  <mi> z </mi>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  </mrow>  <mo> ) </mo>  </mrow>  <mo> ⁢ </mo>  <mrow>  <mi> sin </mi>  <mo> ⁡ </mo>  <mo> ( </mo>  <mrow>  <mi> c </mi>  <mo> ⁢ </mo>  <mi> z </mi>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  <mrow>  <mn> 3 </mn>  <mo> ⁢ </mo>  <mi> c </mi>  <mo> ⁢ </mo>  <msup>  <mrow>  <mo> ( </mo>  <mrow>  <mrow>  <mi> cos </mi>  <mo> ⁡ </mo>  <mo> ( </mo>  <mrow>  <mi> c </mi>  <mo> ⁢ </mo>  <mi> z </mi>  </mrow>  <mo> ) </mo>  </mrow>  <mo> + </mo>  <mn> 1 </mn>  </mrow>  <mo> ) </mo>  </mrow>  <mn> 2 </mn>  </msup>  </mrow>  </mfrac>  </mrow>  <annotation-xml encoding='MathML-Content'>  <apply>  <eq />  <apply>  <int />  <bvar>  <ci> z </ci>  </bvar>  <apply>  <times />  <apply>  <plus />  <ci> A </ci>  <apply>  <times />  <ci> B </ci>  <apply>  <cos />  <apply>  <times />  <ci> c </ci>  <ci> z </ci>  </apply>  </apply>  </apply>  </apply>  <apply>  <power />  <apply>  <power />  <apply>  <plus />  <apply>  <cos />  <apply>  <times />  <ci> c </ci>  <ci> z </ci>  </apply>  </apply>  <cn type='integer'> 1 </cn>  </apply>  <cn type='integer'> 2 </cn>  </apply>  <cn type='integer'> -1 </cn>  </apply>  </apply>  </apply>  <apply>  <times />  <apply>  <plus />  <apply>  <times />  <cn type='integer'> 2 </cn>  <ci> A </ci>  </apply>  <ci> B </ci>  <apply>  <times />  <apply>  <plus />  <ci> A </ci>  <apply>  <times />  <cn type='integer'> 2 </cn>  <ci> B </ci>  </apply>  </apply>  <apply>  <cos />  <apply>  <times />  <ci> c </ci>  <ci> z </ci>  </apply>  </apply>  </apply>  </apply>  <apply>  <sin />  <apply>  <times />  <ci> c </ci>  <ci> z </ci>  </apply>  </apply>  <apply>  <power />  <apply>  <times />  <cn type='integer'> 3 </cn>  <ci> c </ci>  <apply>  <power />  <apply>  <plus />  <apply>  <cos />  <apply>  <times />  <ci> c </ci>  <ci> z </ci>  </apply>  </apply>  <cn type='integer'> 1 </cn>  </apply>  <cn type='integer'> 2 </cn>  </apply>  </apply>  <cn type='integer'> -1 </cn>  </apply>  </apply>  </apply>  </annotation-xml>  </semantics>  </math> 
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 | | Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["\[Integral]", RowBox[List[FractionBox[RowBox[List["A_", "+", RowBox[List["B_", " ", RowBox[List["Cos", "[", RowBox[List["c_", " ", "z_"]], "]"]]]]]], SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", RowBox[List["Cos", "[", RowBox[List["c_", " ", "z_"]], "]"]]]], ")"]], "2"]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["2", " ", "A"]], "+", "B", "+", RowBox[List[RowBox[List["(", RowBox[List["A", "+", RowBox[List["2", " ", "B"]]]], ")"]], " ", RowBox[List["Cos", "[", RowBox[List["c", " ", "z"]], "]"]]]]]], ")"]], " ", RowBox[List["Sin", "[", RowBox[List["c", " ", "z"]], "]"]]]], RowBox[List["3", " ", "c", " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", RowBox[List["Cos", "[", RowBox[List["c", " ", "z"]], "]"]]]], ")"]], "2"]]]]]]]] | 
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 | | Date Added to functions.wolfram.com (modification date) | 
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