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   http://functions.wolfram.com/01.20.21.1259.01
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    Integrate[E^(p z^2) Cos[b z] Cosh[c z], z] == 
 (1/(8 Sqrt[p])) (Sqrt[Pi] (Erfi[((-I) b - c + 2 p z)/(2 Sqrt[p])]/
     E^(((-I) b - c)^2/(4 p)) + Erfi[(I b - c + 2 p z)/(2 Sqrt[p])]/
     E^((I b - c)^2/(4 p)) + Erfi[((-I) b + c + 2 p z)/(2 Sqrt[p])]/
     E^(((-I) b + c)^2/(4 p)) + Erfi[(I b + c + 2 p z)/(2 Sqrt[p])]/
     E^((I b + c)^2/(4 p)))) 
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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>  <msup>  <mi> ⅇ </mi>  <mrow>  <mi> p </mi>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 2 </mn>  </msup>  </mrow>  </msup>  <mo> ⁢ </mo>  <mrow>  <mi> cos </mi>  <mo> ⁡ </mo>  <mo> ( </mo>  <mrow>  <mi> b </mi>  <mo> ⁢ </mo>  <mi> z </mi>  </mrow>  <mo> ) </mo>  </mrow>  <mo> ⁢ </mo>  <mrow>  <mi> cosh </mi>  <mo> ⁡ </mo>  <mo> ( </mo>  <mrow>  <mi> c </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>  <mrow>  <mfrac>  <mn> 1 </mn>  <mrow>  <mn> 8 </mn>  <mo> ⁢ </mo>  <msqrt>  <mi> p </mi>  </msqrt>  </mrow>  </mfrac>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <msqrt>  <mi> π </mi>  </msqrt>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mrow>  <msup>  <mi> ⅇ </mi>  <mrow>  <mo> - </mo>  <mfrac>  <msup>  <mrow>  <mo> ( </mo>  <mrow>  <mrow>  <mo> - </mo>  <mi> c </mi>  </mrow>  <mo> - </mo>  <mrow>  <mi> ⅈ </mi>  <mo> ⁢ </mo>  <mi> b </mi>  </mrow>  </mrow>  <mtext>   </mtext>  <mo> ) </mo>  </mrow>  <mn> 2 </mn>  </msup>  <mrow>  <mn> 4 </mn>  <mo> ⁢ </mo>  <mi> p </mi>  </mrow>  </mfrac>  </mrow>  </msup>  <mo> ⁢ </mo>  <mrow>  <mi> erfi </mi>  <mo> ⁡ </mo>  <mo> ( </mo>  <mfrac>  <mrow>  <mrow>  <mo> - </mo>  <mi> c </mi>  </mrow>  <mo> - </mo>  <mrow>  <mi> ⅈ </mi>  <mo> ⁢ </mo>  <mi> b </mi>  </mrow>  <mtext>   </mtext>  <mo> + </mo>  <mrow>  <mn> 2 </mn>  <mo> ⁢ </mo>  <mi> p </mi>  <mo> ⁢ </mo>  <mi> z </mi>  </mrow>  </mrow>  <mrow>  <mn> 2 </mn>  <mo> ⁢ </mo>  <msqrt>  <mi> p </mi>  </msqrt>  </mrow>  </mfrac>  <mo> ) </mo>  </mrow>  </mrow>  <mo> + </mo>  <mrow>  <msup>  <mi> ⅇ </mi>  <mrow>  <mo> - </mo>  <mfrac>  <msup>  <mrow>  <mo> ( </mo>  <mrow>  <mrow>  <mi> ⅈ </mi>  <mo> ⁢ </mo>  <mi> b </mi>  </mrow>  <mo> - </mo>  <mi> c </mi>  </mrow>  <mo> ) </mo>  </mrow>  <mn> 2 </mn>  </msup>  <mrow>  <mn> 4 </mn>  <mo> ⁢ </mo>  <mi> p </mi>  </mrow>  </mfrac>  </mrow>  </msup>  <mo> ⁢ </mo>  <mrow>  <mi> erfi </mi>  <mo> ⁡ </mo>  <mo> ( </mo>  <mfrac>  <mrow>  <mrow>  <mo> - </mo>  <mi> c </mi>  </mrow>  <mo> + </mo>  <mrow>  <mi> ⅈ </mi>  <mo> ⁢ </mo>  <mi> b </mi>  </mrow>  <mtext>   </mtext>  <mo> + </mo>  <mrow>  <mn> 2 </mn>  <mo> ⁢ </mo>  <mi> p </mi>  <mo> ⁢ </mo>  <mi> z </mi>  </mrow>  </mrow>  <mrow>  <mn> 2 </mn>  <mo> ⁢ </mo>  <msqrt>  <mi> p </mi>  </msqrt>  </mrow>  </mfrac>  <mo> ) </mo>  </mrow>  </mrow>  <mo> + </mo>  <mrow>  <msup>  <mi> ⅇ </mi>  <mrow>  <mo> - </mo>  <mfrac>  <msup>  <mrow>  <mo> ( </mo>  <mrow>  <mi> c </mi>  <mo> - </mo>  <mrow>  <mi> ⅈ </mi>  <mo> ⁢ </mo>  <mi> b </mi>  </mrow>  </mrow>  <mo> ) </mo>  </mrow>  <mn> 2 </mn>  </msup>  <mrow>  <mn> 4 </mn>  <mo> ⁢ </mo>  <mi> p </mi>  </mrow>  </mfrac>  </mrow>  </msup>  <mo> ⁢ </mo>  <mrow>  <mi> erfi </mi>  <mo> ⁡ </mo>  <mo> ( </mo>  <mfrac>  <mrow>  <mi> c </mi>  <mo> - </mo>  <mrow>  <mi> ⅈ </mi>  <mo> ⁢ </mo>  <mi> b </mi>  </mrow>  <mtext>   </mtext>  <mo> + </mo>  <mrow>  <mn> 2 </mn>  <mo> ⁢ </mo>  <mi> p </mi>  <mo> ⁢ </mo>  <mi> z </mi>  </mrow>  </mrow>  <mrow>  <mn> 2 </mn>  <mo> ⁢ </mo>  <msqrt>  <mi> p </mi>  </msqrt>  </mrow>  </mfrac>  <mo> ) </mo>  </mrow>  </mrow>  <mo> + </mo>  <mrow>  <msup>  <mi> ⅇ </mi>  <mrow>  <mo> - </mo>  <mfrac>  <msup>  <mrow>  <mo> ( </mo>  <mrow>  <mi> c </mi>  <mo> + </mo>  <mrow>  <mi> ⅈ </mi>  <mo> ⁢ </mo>  <mi> b </mi>  </mrow>  </mrow>  <mtext>   </mtext>  <mo> ) </mo>  </mrow>  <mn> 2 </mn>  </msup>  <mrow>  <mn> 4 </mn>  <mo> ⁢ </mo>  <mi> p </mi>  </mrow>  </mfrac>  </mrow>  </msup>  <mo> ⁢ </mo>  <mrow>  <mi> erfi </mi>  <mo> ⁡ </mo>  <mo> ( </mo>  <mfrac>  <mrow>  <mi> c </mi>  <mo> + </mo>  <mrow>  <mi> ⅈ </mi>  <mo> ⁢ </mo>  <mi> b </mi>  </mrow>  <mtext>   </mtext>  <mo> + </mo>  <mrow>  <mn> 2 </mn>  <mo> ⁢ </mo>  <mi> p </mi>  <mo> ⁢ </mo>  <mi> z </mi>  </mrow>  </mrow>  <mrow>  <mn> 2 </mn>  <mo> ⁢ </mo>  <msqrt>  <mi> p </mi>  </msqrt>  </mrow>  </mfrac>  <mo> ) </mo>  </mrow>  </mrow>  </mrow>  <mo> ) </mo>  </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> p </ci>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 2 </cn>  </apply>  </apply>  </apply>  <apply>  <cos />  <apply>  <times />  <ci> b </ci>  <ci> z </ci>  </apply>  </apply>  <apply>  <cosh />  <apply>  <times />  <ci> c </ci>  <ci> z </ci>  </apply>  </apply>  </apply>  </apply>  <apply>  <times />  <apply>  <times />  <cn type='integer'> 1 </cn>  <apply>  <power />  <apply>  <times />  <cn type='integer'> 8 </cn>  <apply>  <power />  <ci> p </ci>  <cn type='rational'> 1 <sep /> 2 </cn>  </apply>  </apply>  <cn type='integer'> -1 </cn>  </apply>  </apply>  <apply>  <times />  <apply>  <power />  <pi />  <cn type='rational'> 1 <sep /> 2 </cn>  </apply>  <apply>  <plus />  <apply>  <times />  <apply>  <power />  <exponentiale />  <apply>  <times />  <cn type='integer'> -1 </cn>  <apply>  <times />  <apply>  <power />  <apply>  <plus />  <apply>  <times />  <cn type='integer'> -1 </cn>  <ci> c </ci>  </apply>  <apply>  <times />  <cn type='integer'> -1 </cn>  <apply>  <times />  <imaginaryi />  <ci> b </ci>  </apply>  </apply>  </apply>  <cn type='integer'> 2 </cn>  </apply>  <apply>  <power />  <apply>  <times />  <cn type='integer'> 4 </cn>  <ci> p </ci>  </apply>  <cn type='integer'> -1 </cn>  </apply>  </apply>  </apply>  </apply>  <apply>  <ci> Erfi </ci>  <apply>  <times />  <apply>  <plus />  <apply>  <times />  <cn type='integer'> -1 </cn>  <ci> c </ci>  </apply>  <apply>  <times />  <cn type='integer'> -1 </cn>  <apply>  <times />  <imaginaryi />  <ci> b </ci>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> 2 </cn>  <ci> p </ci>  <ci> z </ci>  </apply>  </apply>  <apply>  <power />  <apply>  <times />  <cn type='integer'> 2 </cn>  <apply>  <power />  <ci> p </ci>  <cn type='rational'> 1 <sep /> 2 </cn>  </apply>  </apply>  <cn type='integer'> -1 </cn>  </apply>  </apply>  </apply>  </apply>  <apply>  <times />  <apply>  <power />  <exponentiale />  <apply>  <times />  <cn type='integer'> -1 </cn>  <apply>  <times />  <apply>  <power />  <apply>  <plus />  <apply>  <times />  <imaginaryi />  <ci> b </ci>  </apply>  <apply>  <times />  <cn type='integer'> -1 </cn>  <ci> c </ci>  </apply>  </apply>  <cn type='integer'> 2 </cn>  </apply>  <apply>  <power />  <apply>  <times />  <cn type='integer'> 4 </cn>  <ci> p </ci>  </apply>  <cn type='integer'> -1 </cn>  </apply>  </apply>  </apply>  </apply>  <apply>  <ci> Erfi </ci>  <apply>  <times />  <apply>  <plus />  <apply>  <times />  <cn type='integer'> -1 </cn>  <ci> c </ci>  </apply>  <apply>  <times />  <imaginaryi />  <ci> b </ci>  </apply>  <apply>  <times />  <cn type='integer'> 2 </cn>  <ci> p </ci>  <ci> z </ci>  </apply>  </apply>  <apply>  <power />  <apply>  <times />  <cn type='integer'> 2 </cn>  <apply>  <power />  <ci> p </ci>  <cn type='rational'> 1 <sep /> 2 </cn>  </apply>  </apply>  <cn type='integer'> -1 </cn>  </apply>  </apply>  </apply>  </apply>  <apply>  <times />  <apply>  <power />  <exponentiale />  <apply>  <times />  <cn type='integer'> -1 </cn>  <apply>  <times />  <apply>  <power />  <apply>  <plus />  <ci> c </ci>  <apply>  <times />  <cn type='integer'> -1 </cn>  <apply>  <times />  <imaginaryi />  <ci> b </ci>  </apply>  </apply>  </apply>  <cn type='integer'> 2 </cn>  </apply>  <apply>  <power />  <apply>  <times />  <cn type='integer'> 4 </cn>  <ci> p </ci>  </apply>  <cn type='integer'> -1 </cn>  </apply>  </apply>  </apply>  </apply>  <apply>  <ci> Erfi </ci>  <apply>  <times />  <apply>  <plus />  <ci> c </ci>  <apply>  <times />  <cn type='integer'> -1 </cn>  <apply>  <times />  <imaginaryi />  <ci> b </ci>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> 2 </cn>  <ci> p </ci>  <ci> z </ci>  </apply>  </apply>  <apply>  <power />  <apply>  <times />  <cn type='integer'> 2 </cn>  <apply>  <power />  <ci> p </ci>  <cn type='rational'> 1 <sep /> 2 </cn>  </apply>  </apply>  <cn type='integer'> -1 </cn>  </apply>  </apply>  </apply>  </apply>  <apply>  <times />  <apply>  <power />  <exponentiale />  <apply>  <times />  <cn type='integer'> -1 </cn>  <apply>  <times />  <apply>  <power />  <apply>  <plus />  <ci> c </ci>  <apply>  <times />  <imaginaryi />  <ci> b </ci>  </apply>  </apply>  <cn type='integer'> 2 </cn>  </apply>  <apply>  <power />  <apply>  <times />  <cn type='integer'> 4 </cn>  <ci> p </ci>  </apply>  <cn type='integer'> -1 </cn>  </apply>  </apply>  </apply>  </apply>  <apply>  <ci> Erfi </ci>  <apply>  <times />  <apply>  <plus />  <ci> c </ci>  <apply>  <times />  <imaginaryi />  <ci> b </ci>  </apply>  <apply>  <times />  <cn type='integer'> 2 </cn>  <ci> p </ci>  <ci> z </ci>  </apply>  </apply>  <apply>  <power />  <apply>  <times />  <cn type='integer'> 2 </cn>  <apply>  <power />  <ci> p </ci>  <cn type='rational'> 1 <sep /> 2 </cn>  </apply>  </apply>  <cn type='integer'> -1 </cn>  </apply>  </apply>  </apply>  </apply>  </apply>  </apply>  </apply>  </apply>  </annotation-xml>  </semantics>  </math> 
   
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