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   http://functions.wolfram.com/01.20.21.0151.01
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    Integrate[(z Cosh[c z])/(a z^2 + b), z] == 
 (1/(2 a)) (Cos[(Sqrt[b] c)/Sqrt[a]] CosIntegral[-((Sqrt[b] c)/Sqrt[a]) + 
      I c z] + Cos[(Sqrt[b] c)/Sqrt[a]] CosIntegral[
     (Sqrt[b] c)/Sqrt[a] + I c z] + Sin[(Sqrt[b] c)/Sqrt[a]] 
    (SinIntegral[(Sqrt[b] c)/Sqrt[a] - I c z] + 
     SinIntegral[(Sqrt[b] c)/Sqrt[a] + I c z])) 
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   Cell[BoxData[RowBox[List[RowBox[List["\[Integral]", RowBox[List[FractionBox[RowBox[List["z", " ", RowBox[List["Cosh", "[", RowBox[List["c", " ", "z"]], "]"]]]], RowBox[List[RowBox[List["a", " ", SuperscriptBox["z", "2"]]], "+", "b"]]], RowBox[List["\[DifferentialD]", "z"]]]]]], "\[Equal]", RowBox[List[FractionBox["1", RowBox[List["2", " ", "a"]]], RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["Cos", "[", FractionBox[RowBox[List[SqrtBox["b"], " ", "c"]], SqrtBox["a"]], "]"]], " ", RowBox[List["CosIntegral", "[", RowBox[List[RowBox[List["-", FractionBox[RowBox[List[SqrtBox["b"], " ", "c"]], SqrtBox["a"]]]], "+", RowBox[List["\[ImaginaryI]", " ", "c", " ", "z"]]]], "]"]]]], "+", RowBox[List[RowBox[List["Cos", "[", FractionBox[RowBox[List[SqrtBox["b"], " ", "c"]], SqrtBox["a"]], "]"]], " ", RowBox[List["CosIntegral", "[", RowBox[List[FractionBox[RowBox[List[SqrtBox["b"], " ", "c"]], SqrtBox["a"]], "+", RowBox[List["\[ImaginaryI]", " ", "c", " ", "z"]]]], "]"]]]], "+", RowBox[List[RowBox[List["Sin", "[", FractionBox[RowBox[List[SqrtBox["b"], " ", "c"]], SqrtBox["a"]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List["SinIntegral", "[", RowBox[List[FractionBox[RowBox[List[SqrtBox["b"], " ", "c"]], SqrtBox["a"]], "-", RowBox[List["\[ImaginaryI]", " ", "c", " ", "z"]]]], "]"]], "+", RowBox[List["SinIntegral", "[", RowBox[List[FractionBox[RowBox[List[SqrtBox["b"], " ", "c"]], SqrtBox["a"]], "+", RowBox[List["\[ImaginaryI]", " ", "c", " ", "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>  <mfrac>  <mrow>  <mi> z </mi>  <mo> ⁢ </mo>  <mrow>  <mi> cosh </mi>  <mo> ⁡ </mo>  <mo> ( </mo>  <mrow>  <mi> c </mi>  <mo> ⁢ </mo>  <mi> z </mi>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  <mrow>  <mrow>  <mi> a </mi>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 2 </mn>  </msup>  </mrow>  <mo> + </mo>  <mi> b </mi>  </mrow>  </mfrac>  <mo> ⁢ </mo>  <mrow>  <mo> ⅆ </mo>  <mi> z </mi>  </mrow>  </mrow>  </mrow>  <mo> ⩵ </mo>  <mrow>  <mfrac>  <mn> 1 </mn>  <mrow>  <mn> 2 </mn>  <mo> ⁢ </mo>  <mi> a </mi>  </mrow>  </mfrac>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mrow>  <mrow>  <mi> cos </mi>  <mo> ⁡ </mo>  <mo> ( </mo>  <mfrac>  <mrow>  <msqrt>  <mi> b </mi>  </msqrt>  <mo> ⁢ </mo>  <mi> c </mi>  </mrow>  <msqrt>  <mi> a </mi>  </msqrt>  </mfrac>  <mo> ) </mo>  </mrow>  <mo> ⁢ </mo>  <mrow>  <mi> Ci </mi>  <mo> ⁡ </mo>  <mo> ( </mo>  <mrow>  <mrow>  <mi> ⅈ </mi>  <mo> ⁢ </mo>  <mi> z </mi>  <mo> ⁢ </mo>  <mi> c </mi>  </mrow>  <mo> + </mo>  <mfrac>  <mrow>  <msqrt>  <mi> b </mi>  </msqrt>  <mo> ⁢ </mo>  <mi> c </mi>  </mrow>  <msqrt>  <mi> a </mi>  </msqrt>  </mfrac>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  <mo> + </mo>  <mrow>  <mrow>  <mi> cos </mi>  <mo> ⁡ </mo>  <mo> ( </mo>  <mfrac>  <mrow>  <msqrt>  <mi> b </mi>  </msqrt>  <mo> ⁢ </mo>  <mi> c </mi>  </mrow>  <msqrt>  <mi> a </mi>  </msqrt>  </mfrac>  <mo> ) </mo>  </mrow>  <mo> ⁢ </mo>  <mrow>  <mi> Ci </mi>  <mo> ⁡ </mo>  <mo> ( </mo>  <mrow>  <mrow>  <mi> ⅈ </mi>  <mo> ⁢ </mo>  <mi> c </mi>  <mo> ⁢ </mo>  <mi> z </mi>  </mrow>  <mo> - </mo>  <mfrac>  <mrow>  <msqrt>  <mi> b </mi>  </msqrt>  <mo> ⁢ </mo>  <mi> c </mi>  </mrow>  <msqrt>  <mi> a </mi>  </msqrt>  </mfrac>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  <mo> + </mo>  <mrow>  <mrow>  <mi> sin </mi>  <mo> ⁡ </mo>  <mo> ( </mo>  <mfrac>  <mrow>  <msqrt>  <mi> b </mi>  </msqrt>  <mo> ⁢ </mo>  <mi> c </mi>  </mrow>  <msqrt>  <mi> a </mi>  </msqrt>  </mfrac>  <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> z </mi>  <mo> ⁢ </mo>  <mi> c </mi>  </mrow>  <mo> + </mo>  <mfrac>  <mrow>  <msqrt>  <mi> b </mi>  </msqrt>  <mo> ⁢ </mo>  <mi> c </mi>  </mrow>  <msqrt>  <mi> a </mi>  </msqrt>  </mfrac>  </mrow>  <mo> ) </mo>  </mrow>  <mo> + </mo>  <mrow>  <mi> Si </mi>  <mo> ⁡ </mo>  <mo> ( </mo>  <mrow>  <mfrac>  <mrow>  <msqrt>  <mi> b </mi>  </msqrt>  <mo> ⁢ </mo>  <mi> c </mi>  </mrow>  <msqrt>  <mi> a </mi>  </msqrt>  </mfrac>  <mo> - </mo>  <mrow>  <mi> ⅈ </mi>  <mo> ⁢ </mo>  <mi> c </mi>  <mo> ⁢ </mo>  <mi> z </mi>  </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>  <times />  <ci> z </ci>  <apply>  <cosh />  <apply>  <times />  <ci> c </ci>  <ci> z </ci>  </apply>  </apply>  <apply>  <power />  <apply>  <plus />  <apply>  <times />  <ci> a </ci>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 2 </cn>  </apply>  </apply>  <ci> b </ci>  </apply>  <cn type='integer'> -1 </cn>  </apply>  </apply>  </apply>  <apply>  <times />  <apply>  <times />  <cn type='integer'> 1 </cn>  <apply>  <power />  <apply>  <times />  <cn type='integer'> 2 </cn>  <ci> a </ci>  </apply>  <cn type='integer'> -1 </cn>  </apply>  </apply>  <apply>  <plus />  <apply>  <times />  <apply>  <cos />  <apply>  <times />  <apply>  <power />  <ci> b </ci>  <cn type='rational'> 1 <sep /> 2 </cn>  </apply>  <ci> c </ci>  <apply>  <power />  <apply>  <power />  <ci> a </ci>  <cn type='rational'> 1 <sep /> 2 </cn>  </apply>  <cn type='integer'> -1 </cn>  </apply>  </apply>  </apply>  <apply>  <ci> CosIntegral </ci>  <apply>  <plus />  <apply>  <times />  <imaginaryi />  <ci> z </ci>  <ci> c </ci>  </apply>  <apply>  <times />  <apply>  <power />  <ci> b </ci>  <cn type='rational'> 1 <sep /> 2 </cn>  </apply>  <ci> c </ci>  <apply>  <power />  <apply>  <power />  <ci> a </ci>  <cn type='rational'> 1 <sep /> 2 </cn>  </apply>  <cn type='integer'> -1 </cn>  </apply>  </apply>  </apply>  </apply>  </apply>  <apply>  <times />  <apply>  <cos />  <apply>  <times />  <apply>  <power />  <ci> b </ci>  <cn type='rational'> 1 <sep /> 2 </cn>  </apply>  <ci> c </ci>  <apply>  <power />  <apply>  <power />  <ci> a </ci>  <cn type='rational'> 1 <sep /> 2 </cn>  </apply>  <cn type='integer'> -1 </cn>  </apply>  </apply>  </apply>  <apply>  <ci> CosIntegral </ci>  <apply>  <plus />  <apply>  <times />  <imaginaryi />  <ci> c </ci>  <ci> z </ci>  </apply>  <apply>  <times />  <cn type='integer'> -1 </cn>  <apply>  <times />  <apply>  <power />  <ci> b </ci>  <cn type='rational'> 1 <sep /> 2 </cn>  </apply>  <ci> c </ci>  <apply>  <power />  <apply>  <power />  <ci> a </ci>  <cn type='rational'> 1 <sep /> 2 </cn>  </apply>  <cn type='integer'> -1 </cn>  </apply>  </apply>  </apply>  </apply>  </apply>  </apply>  <apply>  <times />  <apply>  <sin />  <apply>  <times />  <apply>  <power />  <ci> b </ci>  <cn type='rational'> 1 <sep /> 2 </cn>  </apply>  <ci> c </ci>  <apply>  <power />  <apply>  <power />  <ci> a </ci>  <cn type='rational'> 1 <sep /> 2 </cn>  </apply>  <cn type='integer'> -1 </cn>  </apply>  </apply>  </apply>  <apply>  <plus />  <apply>  <ci> SinIntegral </ci>  <apply>  <plus />  <apply>  <times />  <imaginaryi />  <ci> z </ci>  <ci> c </ci>  </apply>  <apply>  <times />  <apply>  <power />  <ci> b </ci>  <cn type='rational'> 1 <sep /> 2 </cn>  </apply>  <ci> c </ci>  <apply>  <power />  <apply>  <power />  <ci> a </ci>  <cn type='rational'> 1 <sep /> 2 </cn>  </apply>  <cn type='integer'> -1 </cn>  </apply>  </apply>  </apply>  </apply>  <apply>  <ci> SinIntegral </ci>  <apply>  <plus />  <apply>  <times />  <apply>  <power />  <ci> b </ci>  <cn type='rational'> 1 <sep /> 2 </cn>  </apply>  <ci> c </ci>  <apply>  <power />  <apply>  <power />  <ci> a </ci>  <cn type='rational'> 1 <sep /> 2 </cn>  </apply>  <cn type='integer'> -1 </cn>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> -1 </cn>  <apply>  <times />  <imaginaryi />  <ci> c </ci>  <ci> z </ci>  </apply>  </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[RowBox[List["z_", " ", RowBox[List["Cosh", "[", RowBox[List["c_", " ", "z_"]], "]"]]]], RowBox[List[RowBox[List["a_", " ", SuperscriptBox["z_", "2"]]], "+", "b_"]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List[RowBox[List["Cos", "[", FractionBox[RowBox[List[SqrtBox["b"], " ", "c"]], SqrtBox["a"]], "]"]], " ", RowBox[List["CosIntegral", "[", RowBox[List[RowBox[List["-", FractionBox[RowBox[List[SqrtBox["b"], " ", "c"]], SqrtBox["a"]]]], "+", RowBox[List["\[ImaginaryI]", " ", "c", " ", "z"]]]], "]"]]]], "+", RowBox[List[RowBox[List["Cos", "[", FractionBox[RowBox[List[SqrtBox["b"], " ", "c"]], SqrtBox["a"]], "]"]], " ", RowBox[List["CosIntegral", "[", RowBox[List[FractionBox[RowBox[List[SqrtBox["b"], " ", "c"]], SqrtBox["a"]], "+", RowBox[List["\[ImaginaryI]", " ", "c", " ", "z"]]]], "]"]]]], "+", RowBox[List[RowBox[List["Sin", "[", FractionBox[RowBox[List[SqrtBox["b"], " ", "c"]], SqrtBox["a"]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List["SinIntegral", "[", RowBox[List[FractionBox[RowBox[List[SqrtBox["b"], " ", "c"]], SqrtBox["a"]], "-", RowBox[List["\[ImaginaryI]", " ", "c", " ", "z"]]]], "]"]], "+", RowBox[List["SinIntegral", "[", RowBox[List[FractionBox[RowBox[List[SqrtBox["b"], " ", "c"]], SqrtBox["a"]], "+", RowBox[List["\[ImaginaryI]", " ", "c", " ", "z"]]]], "]"]]]], ")"]]]]]], RowBox[List["2", " ", "a"]]]]]]]  |  
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   Date Added to functions.wolfram.com (modification date)
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