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http://functions.wolfram.com/01.07.21.0480.01
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Integrate[Cos[a Tan[z]], z] ==
(1/2) ((-I) Cosh[a] CosIntegral[(-a) (-I + Tan[z])] +
I Cosh[a] CosIntegral[a (I + Tan[z])] +
Sinh[a] (-SinIntegral[a (I + Tan[z])] + SinIntegral[I a - a Tan[z]]))
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Cell[BoxData[RowBox[List[RowBox[List["\[Integral]", RowBox[List[RowBox[List["Cos", "[", RowBox[List["a", " ", RowBox[List["Tan", "[", "z", "]"]]]], "]"]], RowBox[List["\[DifferentialD]", "z"]]]]]], "\[Equal]", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", RowBox[List["Cosh", "[", "a", "]"]], " ", RowBox[List["CosIntegral", "[", RowBox[List[RowBox[List["-", "a"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], "+", RowBox[List["Tan", "[", "z", "]"]]]], ")"]]]], "]"]]]], "+", RowBox[List["\[ImaginaryI]", " ", RowBox[List["Cosh", "[", "a", "]"]], " ", RowBox[List["CosIntegral", "[", RowBox[List["a", " ", RowBox[List["(", RowBox[List["\[ImaginaryI]", "+", RowBox[List["Tan", "[", "z", "]"]]]], ")"]]]], "]"]]]], "+", RowBox[List[RowBox[List["Sinh", "[", "a", "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", RowBox[List["SinIntegral", "[", RowBox[List["a", " ", RowBox[List["(", RowBox[List["\[ImaginaryI]", "+", RowBox[List["Tan", "[", "z", "]"]]]], ")"]]]], "]"]]]], "+", RowBox[List["SinIntegral", "[", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "-", RowBox[List["a", " ", RowBox[List["Tan", "[", "z", "]"]]]]]], "]"]]]], ")"]]]]]], ")"]]]]]]]]
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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> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> a </mi> <mo> ⁢ </mo> <mrow> <mi> tan </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ⅆ </mo> <mi> z </mi> </mrow> </mrow> </mrow> <mo> ⩵ </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> - </mo> <mi> ⅈ </mi> </mrow> <mo> ⁢ </mo> <mrow> <mi> cosh </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> a </mi> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> Ci </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> a </mi> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> ⅈ </mi> </mrow> <mo> + </mo> <mrow> <mi> tan </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mrow> <mi> cosh </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> a </mi> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> Ci </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> a </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> ⅈ </mi> <mo> + </mo> <mrow> <mi> tan </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mrow> <mi> sinh </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> a </mi> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> Si </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> a </mi> </mrow> <mo> - </mo> <mrow> <mi> a </mi> <mo> ⁢ </mo> <mrow> <mi> tan </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> - </mo> <mrow> <mi> Si </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> a </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> ⅈ </mi> <mo> + </mo> <mrow> <mi> tan </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </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> <cos /> <apply> <times /> <ci> a </ci> <apply> <tan /> <ci> z </ci> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <plus /> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <imaginaryi /> </apply> <apply> <cosh /> <ci> a </ci> </apply> <apply> <ci> CosIntegral </ci> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> a </ci> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <imaginaryi /> </apply> <apply> <tan /> <ci> z </ci> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <imaginaryi /> <apply> <cosh /> <ci> a </ci> </apply> <apply> <ci> CosIntegral </ci> <apply> <times /> <ci> a </ci> <apply> <plus /> <imaginaryi /> <apply> <tan /> <ci> z </ci> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <sinh /> <ci> a </ci> </apply> <apply> <plus /> <apply> <ci> SinIntegral </ci> <apply> <plus /> <apply> <times /> <imaginaryi /> <ci> a </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> a </ci> <apply> <tan /> <ci> z </ci> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> SinIntegral </ci> <apply> <times /> <ci> a </ci> <apply> <plus /> <imaginaryi /> <apply> <tan /> <ci> z </ci> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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Date Added to functions.wolfram.com (modification date)
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