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http://functions.wolfram.com/01.08.21.0091.01
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Integrate[Tan[a z + b] Tan[a z], z] ==
((-a) z + Cot[b] (Log[Cos[a z]] - Log[Cos[b + a z]]))/a
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Cell[BoxData[RowBox[List[RowBox[List["\[Integral]", RowBox[List[RowBox[List["Tan", "[", RowBox[List[RowBox[List["a", " ", "z"]], "+", "b"]], "]"]], " ", RowBox[List["Tan", "[", RowBox[List["a", " ", "z"]], "]"]], RowBox[List["\[DifferentialD]", "z"]]]]]], "\[Equal]", FractionBox[RowBox[List[RowBox[List[RowBox[List["-", "a"]], " ", "z"]], "+", RowBox[List[RowBox[List["Cot", "[", "b", "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List["Log", "[", RowBox[List["Cos", "[", RowBox[List["a", " ", "z"]], "]"]], "]"]], "-", RowBox[List["Log", "[", RowBox[List["Cos", "[", RowBox[List["b", "+", RowBox[List["a", " ", "z"]]]], "]"]], "]"]]]], ")"]]]]]], "a"]]]]]
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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> <mrow> <mi> tan </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> b </mi> <mo> + </mo> <mrow> <mi> a </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> tan </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> a </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ⁢ </mo> <mrow> <mo> ⅆ </mo> <mi> z </mi> </mrow> </mrow> </mrow> <mo> ⩵ </mo> <mfrac> <mrow> <mrow> <mrow> <mi> cot </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> b </mi> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> a </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo> ) </mo> </mrow> <mo> - </mo> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> b </mi> <mo> + </mo> <mrow> <mi> a </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mi> a </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> </mrow> <mi> a </mi> </mfrac> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <int /> <bvar> <ci> z </ci> </bvar> <apply> <times /> <apply> <tan /> <apply> <plus /> <ci> b </ci> <apply> <times /> <ci> a </ci> <ci> z </ci> </apply> </apply> </apply> <apply> <tan /> <apply> <times /> <ci> a </ci> <ci> z </ci> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <plus /> <apply> <times /> <apply> <cot /> <ci> b </ci> </apply> <apply> <plus /> <apply> <ln /> <apply> <cos /> <apply> <times /> <ci> a </ci> <ci> z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ln /> <apply> <cos /> <apply> <plus /> <ci> b </ci> <apply> <times /> <ci> a </ci> <ci> z </ci> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> a </ci> <ci> z </ci> </apply> </apply> </apply> <apply> <power /> <ci> a </ci> <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[RowBox[List[RowBox[List["Tan", "[", RowBox[List[RowBox[List["a_", " ", "z_"]], "+", "b_"]], "]"]], " ", RowBox[List["Tan", "[", RowBox[List["a_", " ", "z_"]], "]"]]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List[RowBox[List["-", "a"]], " ", "z"]], "+", RowBox[List[RowBox[List["Cot", "[", "b", "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List["Log", "[", RowBox[List["Cos", "[", RowBox[List["a", " ", "z"]], "]"]], "]"]], "-", RowBox[List["Log", "[", RowBox[List["Cos", "[", RowBox[List["b", "+", RowBox[List["a", " ", "z"]]]], "]"]], "]"]]]], ")"]]]]]], "a"]]]]] |
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Date Added to functions.wolfram.com (modification date)
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