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Cos




Mathematica Notation

Traditional Notation









Elementary Functions > Cos[z] > Integration > Indefinite integration > Involving functions of the direct function and trigonometric functions > Involving algebraic functions of the direct function and trigonometric functions > Involving sin > Involving sin(d z)(a+b cos2(c z))beta





http://functions.wolfram.com/01.07.21.2360.01









  


  








Input Form





Integrate[Sin[c z]/Sqrt[a + b Cos[c z]^2], z] == -(Log[2 (Sqrt[b] Cos[c z] + Sqrt[a + b Cos[c z]^2])]/(Sqrt[b] c))








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["\[Integral]", RowBox[List[FractionBox[RowBox[List["Sin", "[", RowBox[List["c", " ", "z"]], "]"]], SqrtBox[RowBox[List["a", "+", RowBox[List["b", " ", SuperscriptBox[RowBox[List["Cos", "[", RowBox[List["c", " ", "z"]], "]"]], "2"]]]]]]], RowBox[List["\[DifferentialD]", "z"]]]]]], "\[Equal]", RowBox[List["-", FractionBox[RowBox[List["Log", "[", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List[SqrtBox["b"], " ", RowBox[List["Cos", "[", RowBox[List["c", " ", "z"]], "]"]]]], "+", SqrtBox[RowBox[List["a", "+", RowBox[List["b", " ", SuperscriptBox[RowBox[List["Cos", "[", RowBox[List["c", " ", "z"]], "]"]], "2"]]]]]]]], ")"]]]], "]"]], RowBox[List[SqrtBox["b"], " ", "c"]]]]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mo> &#8747; </mo> <mrow> <mfrac> <mrow> <mi> sin </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> c </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <msqrt> <mrow> <mi> a </mi> <mo> + </mo> <mrow> <mi> b </mi> <mo> &#8290; </mo> <mrow> <msup> <mi> cos </mi> <mn> 2 </mn> </msup> <mo> ( </mo> <mrow> <mi> c </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </msqrt> </mfrac> <mo> &#8290; </mo> <mrow> <mo> &#8518; </mo> <mi> z </mi> </mrow> </mrow> </mrow> <mo> &#10869; </mo> <mrow> <mo> - </mo> <mfrac> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <msqrt> <mi> b </mi> </msqrt> <mo> &#8290; </mo> <mrow> <mi> cos </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> c </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <msqrt> <mrow> <mrow> <mi> b </mi> <mo> &#8290; </mo> <mrow> <msup> <mi> cos </mi> <mn> 2 </mn> </msup> <mo> ( </mo> <mrow> <mi> c </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mi> a </mi> </mrow> </msqrt> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mrow> <msqrt> <mi> b </mi> </msqrt> <mo> &#8290; </mo> <mi> c </mi> </mrow> </mfrac> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <int /> <bvar> <ci> z </ci> </bvar> <apply> <times /> <apply> <sin /> <apply> <times /> <ci> c </ci> <ci> z </ci> </apply> </apply> <apply> <power /> <apply> <power /> <apply> <plus /> <ci> a </ci> <apply> <times /> <ci> b </ci> <apply> <power /> <apply> <cos /> <apply> <times /> <ci> c </ci> <ci> z </ci> </apply> </apply> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <ln /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <plus /> <apply> <times /> <apply> <power /> <ci> b </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <cos /> <apply> <times /> <ci> c </ci> <ci> z </ci> </apply> </apply> </apply> <apply> <power /> <apply> <plus /> <apply> <times /> <ci> b </ci> <apply> <power /> <apply> <cos /> <apply> <times /> <ci> c </ci> <ci> z </ci> </apply> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <ci> a </ci> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <apply> <power /> <ci> b </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <ci> c </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["\[Integral]", RowBox[List[FractionBox[RowBox[List["Sin", "[", RowBox[List["c_", " ", "z_"]], "]"]], SqrtBox[RowBox[List["a_", "+", RowBox[List["b_", " ", SuperscriptBox[RowBox[List["Cos", "[", RowBox[List["c_", " ", "z_"]], "]"]], "2"]]]]]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List["-", FractionBox[RowBox[List["Log", "[", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List[SqrtBox["b"], " ", RowBox[List["Cos", "[", RowBox[List["c", " ", "z"]], "]"]]]], "+", SqrtBox[RowBox[List["a", "+", RowBox[List["b", " ", SuperscriptBox[RowBox[List["Cos", "[", RowBox[List["c", " ", "z"]], "]"]], "2"]]]]]]]], ")"]]]], "]"]], RowBox[List[SqrtBox["b"], " ", "c"]]]]]]]]]


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





2002-12-18