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 | | http://functions.wolfram.com/01.10.21.0090.01 | 
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 | | Integrate[1/(a + b Csc[z]^2), z] == 
 (1/a) (z - (Sqrt[b]/Sqrt[a + b]) ArcTan[(Sqrt[a + b] Tan[z])/Sqrt[b]]) | 
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 | | Cell[BoxData[RowBox[List[RowBox[List["\[Integral]", RowBox[List[FractionBox["1", RowBox[List["a", "+", RowBox[List["b", " ", SuperscriptBox[RowBox[List["Csc", "[", "z", "]"]], "2"]]]]]], RowBox[List["\[DifferentialD]", "z"]]]]]], "\[Equal]", RowBox[List[FractionBox["1", "a"], RowBox[List["(", RowBox[List["z", "-", RowBox[List[FractionBox[RowBox[List[SqrtBox["b"], " "]], SqrtBox[RowBox[List["a", "+", "b"]]]], RowBox[List["ArcTan", "[", FractionBox[RowBox[List[SqrtBox[RowBox[List["a", "+", "b"]]], " ", RowBox[List["Tan", "[", "z", "]"]]]], SqrtBox["b"]], "]"]]]]]], ")"]]]]]]]] | 
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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>  <mn> 1 </mn>  <mrow>  <mi> a </mi>  <mo> + </mo>  <mrow>  <mi> b </mi>  <mo> ⁢ </mo>  <mrow>  <msup>  <mi> csc </mi>  <mn> 2 </mn>  </msup>  <mo> ( </mo>  <mi> z </mi>  <mo> ) </mo>  </mrow>  </mrow>  </mrow>  </mfrac>  <mo> ⁢ </mo>  <mrow>  <mo> ⅆ </mo>  <mi> z </mi>  </mrow>  </mrow>  </mrow>  <mo> ⩵ </mo>  <mrow>  <mfrac>  <mn> 1 </mn>  <mi> a </mi>  </mfrac>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mi> z </mi>  <mo> - </mo>  <mrow>  <mfrac>  <mrow>  <msqrt>  <mi> b </mi>  </msqrt>  <mtext>   </mtext>  </mrow>  <msqrt>  <mrow>  <mi> a </mi>  <mo> + </mo>  <mi> b </mi>  </mrow>  </msqrt>  </mfrac>  <mo> ⁢ </mo>  <mrow>  <msup>  <mi> tan </mi>  <mrow>  <mo> - </mo>  <mn> 1 </mn>  </mrow>  </msup>  <mo> ( </mo>  <mfrac>  <mrow>  <msqrt>  <mrow>  <mi> a </mi>  <mo> + </mo>  <mi> b </mi>  </mrow>  </msqrt>  <mo> ⁢ </mo>  <mrow>  <mi> tan </mi>  <mo> ⁡ </mo>  <mo> ( </mo>  <mi> z </mi>  <mo> ) </mo>  </mrow>  </mrow>  <msqrt>  <mi> b </mi>  </msqrt>  </mfrac>  <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>  <times />  <cn type='integer'> 1 </cn>  <apply>  <power />  <apply>  <plus />  <ci> a </ci>  <apply>  <times />  <ci> b </ci>  <apply>  <power />  <apply>  <csc />  <ci> z </ci>  </apply>  <cn type='integer'> 2 </cn>  </apply>  </apply>  </apply>  <cn type='integer'> -1 </cn>  </apply>  </apply>  </apply>  <apply>  <times />  <apply>  <times />  <cn type='integer'> 1 </cn>  <apply>  <power />  <ci> a </ci>  <cn type='integer'> -1 </cn>  </apply>  </apply>  <apply>  <plus />  <ci> z </ci>  <apply>  <times />  <cn type='integer'> -1 </cn>  <apply>  <times />  <apply>  <times />  <apply>  <power />  <ci> b </ci>  <cn type='rational'> 1 <sep /> 2 </cn>  </apply>  <apply>  <power />  <apply>  <power />  <apply>  <plus />  <ci> a </ci>  <ci> b </ci>  </apply>  <cn type='rational'> 1 <sep /> 2 </cn>  </apply>  <cn type='integer'> -1 </cn>  </apply>  </apply>  <apply>  <arctan />  <apply>  <times />  <apply>  <power />  <apply>  <plus />  <ci> a </ci>  <ci> b </ci>  </apply>  <cn type='rational'> 1 <sep /> 2 </cn>  </apply>  <apply>  <tan />  <ci> z </ci>  </apply>  <apply>  <power />  <apply>  <power />  <ci> b </ci>  <cn type='rational'> 1 <sep /> 2 </cn>  </apply>  <cn type='integer'> -1 </cn>  </apply>  </apply>  </apply>  </apply>  </apply>  </apply>  </apply>  </apply>  </annotation-xml>  </semantics>  </math> 
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 | | Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["\[Integral]", RowBox[List[FractionBox["1", RowBox[List["a_", "+", RowBox[List["b_", " ", SuperscriptBox[RowBox[List["Csc", "[", "z_", "]"]], "2"]]]]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List["z", "-", FractionBox[RowBox[List[SqrtBox["b"], " ", RowBox[List["ArcTan", "[", FractionBox[RowBox[List[SqrtBox[RowBox[List["a", "+", "b"]]], " ", RowBox[List["Tan", "[", "z", "]"]]]], SqrtBox["b"]], "]"]]]], SqrtBox[RowBox[List["a", "+", "b"]]]]]], "a"]]]]] | 
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 | | Date Added to functions.wolfram.com (modification date) | 
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