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   http://functions.wolfram.com/01.20.21.0299.01
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    Integrate[(E^(b z) Cosh[c z])/z^4, z] == 
 (1/(12 z^3)) ((-E^((b - c) z)) (2 - c z + b^2 z^2 + c^2 z^2 + 
     b (z - 2 c z^2) + E^(2 c z) (2 + c z + b^2 z^2 + c^2 z^2 + 
       b z (1 + 2 c z))) + (b - c)^3 z^3 ExpIntegralEi[(b - c) z] + 
   (b + c)^3 z^3 ExpIntegralEi[(b + 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>  <msup>  <mi> ⅇ </mi>  <mrow>  <mi> b </mi>  <mo> ⁢ </mo>  <mi> z </mi>  </mrow>  </msup>  <mo> ⁢ </mo>  <mrow>  <mi> cosh </mi>  <mo> ⁡ </mo>  <mo> ( </mo>  <mrow>  <mi> c </mi>  <mo> ⁢ </mo>  <mi> z </mi>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  <msup>  <mi> z </mi>  <mn> 4 </mn>  </msup>  </mfrac>  <mo> ⁢ </mo>  <mrow>  <mo> ⅆ </mo>  <mi> z </mi>  </mrow>  </mrow>  </mrow>  <mo> ⩵ </mo>  <mrow>  <mfrac>  <mn> 1 </mn>  <mrow>  <mn> 12 </mn>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 3 </mn>  </msup>  </mrow>  </mfrac>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mrow>  <msup>  <mrow>  <mo> ( </mo>  <mrow>  <mi> b </mi>  <mo> - </mo>  <mi> c </mi>  </mrow>  <mo> ) </mo>  </mrow>  <mn> 3 </mn>  </msup>  <mo> ⁢ </mo>  <mrow>  <mi> Ei </mi>  <mo> ⁡ </mo>  <mo> ( </mo>  <mrow>  <mrow>  <mo> ( </mo>  <mrow>  <mi> b </mi>  <mo> - </mo>  <mi> c </mi>  </mrow>  <mo> ) </mo>  </mrow>  <mo> ⁢ </mo>  <mi> z </mi>  </mrow>  <mo> ) </mo>  </mrow>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 3 </mn>  </msup>  </mrow>  <mo> + </mo>  <mrow>  <msup>  <mrow>  <mo> ( </mo>  <mrow>  <mi> b </mi>  <mo> + </mo>  <mi> c </mi>  </mrow>  <mo> ) </mo>  </mrow>  <mn> 3 </mn>  </msup>  <mo> ⁢ </mo>  <mrow>  <mi> Ei </mi>  <mo> ⁡ </mo>  <mo> ( </mo>  <mrow>  <mrow>  <mo> ( </mo>  <mrow>  <mi> b </mi>  <mo> + </mo>  <mi> c </mi>  </mrow>  <mo> ) </mo>  </mrow>  <mo> ⁢ </mo>  <mi> z </mi>  </mrow>  <mo> ) </mo>  </mrow>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 3 </mn>  </msup>  </mrow>  <mo> - </mo>  <mrow>  <msup>  <mi> ⅇ </mi>  <mrow>  <mrow>  <mo> ( </mo>  <mrow>  <mi> b </mi>  <mo> - </mo>  <mi> c </mi>  </mrow>  <mo> ) </mo>  </mrow>  <mo> ⁢ </mo>  <mi> z </mi>  </mrow>  </msup>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mrow>  <msup>  <mi> b </mi>  <mn> 2 </mn>  </msup>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 2 </mn>  </msup>  </mrow>  <mo> + </mo>  <mrow>  <msup>  <mi> c </mi>  <mn> 2 </mn>  </msup>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 2 </mn>  </msup>  </mrow>  <mo> - </mo>  <mrow>  <mi> c </mi>  <mo> ⁢ </mo>  <mi> z </mi>  </mrow>  <mo> + </mo>  <mrow>  <mi> b </mi>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mi> z </mi>  <mo> - </mo>  <mrow>  <mn> 2 </mn>  <mo> ⁢ </mo>  <mi> c </mi>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 2 </mn>  </msup>  </mrow>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  <mo> + </mo>  <mrow>  <msup>  <mi> ⅇ </mi>  <mrow>  <mn> 2 </mn>  <mo> ⁢ </mo>  <mi> c </mi>  <mo> ⁢ </mo>  <mi> z </mi>  </mrow>  </msup>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mrow>  <msup>  <mi> b </mi>  <mn> 2 </mn>  </msup>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 2 </mn>  </msup>  </mrow>  <mo> + </mo>  <mrow>  <msup>  <mi> c </mi>  <mn> 2 </mn>  </msup>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 2 </mn>  </msup>  </mrow>  <mo> + </mo>  <mrow>  <mi> c </mi>  <mo> ⁢ </mo>  <mi> z </mi>  </mrow>  <mo> + </mo>  <mrow>  <mi> b </mi>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mrow>  <mn> 2 </mn>  <mo> ⁢ </mo>  <mi> c </mi>  <mo> ⁢ </mo>  <mi> z </mi>  </mrow>  <mo> + </mo>  <mn> 1 </mn>  </mrow>  <mo> ) </mo>  </mrow>  <mo> ⁢ </mo>  <mi> z </mi>  </mrow>  <mo> + </mo>  <mn> 2 </mn>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  <mo> + </mo>  <mn> 2 </mn>  </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 />  <apply>  <power />  <exponentiale />  <apply>  <times />  <ci> b </ci>  <ci> z </ci>  </apply>  </apply>  <apply>  <cosh />  <apply>  <times />  <ci> c </ci>  <ci> z </ci>  </apply>  </apply>  <apply>  <power />  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 4 </cn>  </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'> 12 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 3 </cn>  </apply>  </apply>  <cn type='integer'> -1 </cn>  </apply>  </apply>  <apply>  <plus />  <apply>  <times />  <apply>  <power />  <apply>  <plus />  <ci> b </ci>  <apply>  <times />  <cn type='integer'> -1 </cn>  <ci> c </ci>  </apply>  </apply>  <cn type='integer'> 3 </cn>  </apply>  <apply>  <ci> ExpIntegralEi </ci>  <apply>  <times />  <apply>  <plus />  <ci> b </ci>  <apply>  <times />  <cn type='integer'> -1 </cn>  <ci> c </ci>  </apply>  </apply>  <ci> z </ci>  </apply>  </apply>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 3 </cn>  </apply>  </apply>  <apply>  <times />  <apply>  <power />  <apply>  <plus />  <ci> b </ci>  <ci> c </ci>  </apply>  <cn type='integer'> 3 </cn>  </apply>  <apply>  <ci> ExpIntegralEi </ci>  <apply>  <times />  <apply>  <plus />  <ci> b </ci>  <ci> c </ci>  </apply>  <ci> z </ci>  </apply>  </apply>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 3 </cn>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> -1 </cn>  <apply>  <times />  <apply>  <power />  <exponentiale />  <apply>  <times />  <apply>  <plus />  <ci> b </ci>  <apply>  <times />  <cn type='integer'> -1 </cn>  <ci> c </ci>  </apply>  </apply>  <ci> z </ci>  </apply>  </apply>  <apply>  <plus />  <apply>  <times />  <apply>  <power />  <ci> b </ci>  <cn type='integer'> 2 </cn>  </apply>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 2 </cn>  </apply>  </apply>  <apply>  <times />  <apply>  <power />  <ci> c </ci>  <cn type='integer'> 2 </cn>  </apply>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 2 </cn>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> -1 </cn>  <apply>  <times />  <ci> c </ci>  <ci> z </ci>  </apply>  </apply>  <apply>  <times />  <ci> b </ci>  <apply>  <plus />  <ci> z </ci>  <apply>  <times />  <cn type='integer'> -1 </cn>  <apply>  <times />  <cn type='integer'> 2 </cn>  <ci> c </ci>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 2 </cn>  </apply>  </apply>  </apply>  </apply>  </apply>  <apply>  <times />  <apply>  <power />  <exponentiale />  <apply>  <times />  <cn type='integer'> 2 </cn>  <ci> c </ci>  <ci> z </ci>  </apply>  </apply>  <apply>  <plus />  <apply>  <times />  <apply>  <power />  <ci> b </ci>  <cn type='integer'> 2 </cn>  </apply>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 2 </cn>  </apply>  </apply>  <apply>  <times />  <apply>  <power />  <ci> c </ci>  <cn type='integer'> 2 </cn>  </apply>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 2 </cn>  </apply>  </apply>  <apply>  <times />  <ci> c </ci>  <ci> z </ci>  </apply>  <apply>  <times />  <ci> b </ci>  <apply>  <plus />  <apply>  <times />  <cn type='integer'> 2 </cn>  <ci> c </ci>  <ci> z </ci>  </apply>  <cn type='integer'> 1 </cn>  </apply>  <ci> z </ci>  </apply>  <cn type='integer'> 2 </cn>  </apply>  </apply>  <cn type='integer'> 2 </cn>  </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[SuperscriptBox["\[ExponentialE]", RowBox[List["b_", " ", "z_"]]], " ", RowBox[List["Cosh", "[", RowBox[List["c_", " ", "z_"]], "]"]]]], SuperscriptBox["z_", "4"]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List[RowBox[List["-", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["(", RowBox[List["b", "-", "c"]], ")"]], " ", "z"]]]]], " ", RowBox[List["(", RowBox[List["2", "-", RowBox[List["c", " ", "z"]], "+", RowBox[List[SuperscriptBox["b", "2"], " ", SuperscriptBox["z", "2"]]], "+", RowBox[List[SuperscriptBox["c", "2"], " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["b", " ", RowBox[List["(", RowBox[List["z", "-", RowBox[List["2", " ", "c", " ", SuperscriptBox["z", "2"]]]]], ")"]]]], "+", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["2", " ", "c", " ", "z"]]], " ", RowBox[List["(", RowBox[List["2", "+", RowBox[List["c", " ", "z"]], "+", RowBox[List[SuperscriptBox["b", "2"], " ", SuperscriptBox["z", "2"]]], "+", RowBox[List[SuperscriptBox["c", "2"], " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["b", " ", "z", " ", RowBox[List["(", RowBox[List["1", "+", RowBox[List["2", " ", "c", " ", "z"]]]], ")"]]]]]], ")"]]]]]], ")"]]]], "+", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["b", "-", "c"]], ")"]], "3"], " ", SuperscriptBox["z", "3"], " ", RowBox[List["ExpIntegralEi", "[", RowBox[List[RowBox[List["(", RowBox[List["b", "-", "c"]], ")"]], " ", "z"]], "]"]]]], "+", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["b", "+", "c"]], ")"]], "3"], " ", SuperscriptBox["z", "3"], " ", RowBox[List["ExpIntegralEi", "[", RowBox[List[RowBox[List["(", RowBox[List["b", "+", "c"]], ")"]], " ", "z"]], "]"]]]]]], RowBox[List["12", " ", SuperscriptBox["z", "3"]]]]]]]]  |  
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   Date Added to functions.wolfram.com (modification date)
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