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   http://functions.wolfram.com/01.20.21.1257.01
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    Integrate[E^(p z^2) Cos[b z^2] Cosh[c z], z] == 
 (1/8) Sqrt[Pi] ((Erfi[(-c + 2 ((-I) b + p) z)/(2 Sqrt[(-I) b + p])] + 
     Erfi[(c + 2 ((-I) b + p) z)/(2 Sqrt[(-I) b + p])])/
    (E^(c^2/(4 ((-I) b + p))) Sqrt[(-I) b + p]) + 
   (Erfi[(-c + 2 (I b + p) z)/(2 Sqrt[I b + p])] + 
     Erfi[(c + 2 (I b + p) z)/(2 Sqrt[I b + p])])/(E^(c^2/(4 (I b + p))) 
     Sqrt[I b + p])) 
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   Cell[BoxData[RowBox[List[RowBox[List["\[Integral]", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["p", " ", SuperscriptBox["z", "2"]]]], " ", RowBox[List["Cos", "[", RowBox[List["b", " ", SuperscriptBox["z", "2"]]], "]"]], " ", RowBox[List["Cosh", "[", RowBox[List["c", " ", "z"]], "]"]], RowBox[List["\[DifferentialD]", "z"]]]]]], "\[Equal]", RowBox[List[FractionBox["1", "8"], " ", SqrtBox["\[Pi]"], " ", RowBox[List["(", RowBox[List[FractionBox[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["-", FractionBox[SuperscriptBox["c", "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "b"]], "+", "p"]], ")"]]]]]]]], " ", RowBox[List["(", RowBox[List[RowBox[List["Erfi", "[", FractionBox[RowBox[List[RowBox[List["-", "c"]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "b"]], "+", "p"]], ")"]], " ", "z"]]]], RowBox[List["2", " ", SqrtBox[RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "b"]], "+", "p"]]]]]], "]"]], "+", RowBox[List["Erfi", "[", FractionBox[RowBox[List["c", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "b"]], "+", "p"]], ")"]], " ", "z"]]]], RowBox[List["2", " ", SqrtBox[RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "b"]], "+", "p"]]]]]], "]"]]]], ")"]]]], SqrtBox[RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "b"]], "+", "p"]]]], "+", FractionBox[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["-", FractionBox[SuperscriptBox["c", "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "b"]], "+", "p"]], ")"]]]]]]]], " ", RowBox[List["(", RowBox[List[RowBox[List["Erfi", "[", FractionBox[RowBox[List[RowBox[List["-", "c"]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "b"]], "+", "p"]], ")"]], " ", "z"]]]], RowBox[List["2", " ", SqrtBox[RowBox[List[RowBox[List["\[ImaginaryI]", " ", "b"]], "+", "p"]]]]]], "]"]], "+", RowBox[List["Erfi", "[", FractionBox[RowBox[List["c", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "b"]], "+", "p"]], ")"]], " ", "z"]]]], RowBox[List["2", " ", SqrtBox[RowBox[List[RowBox[List["\[ImaginaryI]", " ", "b"]], "+", "p"]]]]]], "]"]]]], ")"]]]], SqrtBox[RowBox[List[RowBox[List["\[ImaginaryI]", " ", "b"]], "+", "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>  <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>  <msup>  <mi> z </mi>  <mn> 2 </mn>  </msup>  </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>  <mo> ⁢ </mo>  <mrow>  <mo> ⅆ </mo>  <mi> z </mi>  </mrow>  </mrow>  </mrow>  <mo> ⩵ </mo>  <mrow>  <mfrac>  <mn> 1 </mn>  <mn> 8 </mn>  </mfrac>  <mo> ⁢ </mo>  <msqrt>  <mi> π </mi>  </msqrt>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mrow>  <mfrac>  <mn> 1 </mn>  <msqrt>  <mrow>  <mrow>  <mrow>  <mo> - </mo>  <mi> ⅈ </mi>  </mrow>  <mo> ⁢ </mo>  <mi> b 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<mi> p </mi>  </mrow>  </msqrt>  </mrow>  </mfrac>  <mo> ) </mo>  </mrow>  <mo> + </mo>  <mrow>  <mi> erfi </mi>  <mo> ⁡ </mo>  <mo> ( </mo>  <mfrac>  <mrow>  <mi> c </mi>  <mo> + </mo>  <mrow>  <mn> 2 </mn>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mrow>  <mrow>  <mo> - </mo>  <mi> ⅈ </mi>  </mrow>  <mo> ⁢ </mo>  <mi> b </mi>  </mrow>  <mo> + </mo>  <mi> p </mi>  </mrow>  <mo> ) </mo>  </mrow>  <mo> ⁢ </mo>  <mi> z </mi>  </mrow>  </mrow>  <mrow>  <mn> 2 </mn>  <mo> ⁢ </mo>  <msqrt>  <mrow>  <mrow>  <mrow>  <mo> - </mo>  <mi> ⅈ </mi>  </mrow>  <mo> ⁢ </mo>  <mi> b </mi>  </mrow>  <mo> + </mo>  <mi> p </mi>  </mrow>  </msqrt>  </mrow>  </mfrac>  <mo> ) </mo>  </mrow>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  <mo> + </mo>  <mrow>  <mfrac>  <mn> 1 </mn>  <msqrt>  <mrow>  <mrow>  <mi> ⅈ </mi>  <mo> ⁢ </mo>  <mi> b </mi>  </mrow>  <mo> + </mo>  <mi> p </mi>  </mrow>  </msqrt>  </mfrac>  <mo> ⁢ </mo>  <msup>  <mi> ⅇ </mi>  <mrow>  <mo> - </mo>  <mfrac>  <msup>  <mi> c </mi>  <mn> 2 </mn>  </msup>  <mrow>  <mn> 4 </mn>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mrow>  <mi> ⅈ </mi>  <mo> ⁢ </mo>  <mi> b </mi>  </mrow>  <mo> + </mo>  <mi> p </mi>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  </mfrac>  </mrow>  </msup>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mrow>  <mi> erfi </mi>  <mo> ⁡ </mo>  <mo> ( </mo>  <mfrac>  <mrow>  <mrow>  <mn> 2 </mn>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mrow>  <mi> ⅈ </mi>  <mo> ⁢ </mo>  <mi> b </mi>  </mrow>  <mo> + </mo>  <mi> p </mi>  </mrow>  <mo> ) </mo>  </mrow>  <mo> ⁢ </mo>  <mi> z </mi>  </mrow>  <mo> - </mo>  <mi> c </mi>  </mrow>  <mrow>  <mn> 2 </mn>  <mo> ⁢ </mo>  <msqrt>  <mrow>  <mrow>  <mi> ⅈ </mi>  <mo> ⁢ </mo>  <mi> b </mi>  </mrow>  <mo> + </mo>  <mi> p </mi>  </mrow>  </msqrt>  </mrow>  </mfrac>  <mo> ) </mo>  </mrow>  <mo> + </mo>  <mrow>  <mi> erfi </mi>  <mo> ⁡ </mo>  <mo> ( </mo>  <mfrac>  <mrow>  <mi> c </mi>  <mo> + </mo>  <mrow>  <mn> 2 </mn>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mrow>  <mi> ⅈ </mi>  <mo> ⁢ </mo>  <mi> b </mi>  </mrow>  <mo> + </mo>  <mi> p </mi>  </mrow>  <mo> ) </mo>  </mrow>  <mo> ⁢ </mo>  <mi> z </mi>  </mrow>  </mrow>  <mrow>  <mn> 2 </mn>  <mo> ⁢ </mo>  <msqrt>  <mrow>  <mrow>  <mi> ⅈ </mi>  <mo> ⁢ </mo>  <mi> b </mi>  </mrow>  <mo> + </mo>  <mi> p </mi>  </mrow>  </msqrt>  </mrow>  </mfrac>  <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 />  <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>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 2 </cn>  </apply>  </apply>  </apply>  <apply>  <cosh />  <apply>  <times />  <ci> c </ci>  <ci> z </ci>  </apply>  </apply>  </apply>  </apply>  <apply>  <times />  <cn type='rational'> 1 <sep /> 8 </cn>  <apply>  <power />  <pi />  <cn type='rational'> 1 <sep /> 2 </cn>  </apply>  <apply>  <plus />  <apply>  <times />  <apply>  <times />  <cn type='integer'> 1 </cn>  <apply>  <power />  <apply>  <power />  <apply>  <plus />  <apply>  <times />  <apply>  <times />  <cn type='integer'> -1 </cn>  <imaginaryi />  </apply>  <ci> b </ci>  </apply>  <ci> p </ci>  </apply>  <cn type='rational'> 1 <sep /> 2 </cn>  </apply>  <cn type='integer'> -1 </cn>  </apply>  </apply>  <apply>  <power />  <exponentiale />  <apply>  <times />  <cn type='integer'> -1 </cn>  <apply>  <times />  <apply>  <power />  <ci> c </ci>  <cn type='integer'> 2 </cn>  </apply>  <apply>  <power />  <apply>  <times />  <cn type='integer'> 4 </cn>  <apply>  <plus />  <apply>  <times />  <apply>  <times />  <cn type='integer'> -1 </cn>  <imaginaryi />  </apply>  <ci> b </ci>  </apply>  <ci> p </ci>  </apply>  </apply>  <cn type='integer'> -1 </cn>  </apply>  </apply>  </apply>  </apply>  <apply>  <plus />  <apply>  <ci> Erfi </ci>  <apply>  <times />  <apply>  <plus />  <apply>  <times />  <cn type='integer'> 2 </cn>  <apply>  <plus />  <apply>  <times />  <apply>  <times />  <cn type='integer'> -1 </cn>  <imaginaryi />  </apply>  <ci> b </ci>  </apply>  <ci> p </ci>  </apply>  <ci> z </ci>  </apply>  <apply>  <times />  <cn type='integer'> -1 </cn>  <ci> c </ci>  </apply>  </apply>  <apply>  <power />  <apply>  <times />  <cn type='integer'> 2 </cn>  <apply>  <power />  <apply>  <plus />  <apply>  <times />  <apply>  <times />  <cn type='integer'> -1 </cn>  <imaginaryi />  </apply>  <ci> b </ci>  </apply>  <ci> p </ci>  </apply>  <cn type='rational'> 1 <sep /> 2 </cn>  </apply>  </apply>  <cn type='integer'> -1 </cn>  </apply>  </apply>  </apply>  <apply>  <ci> Erfi </ci>  <apply>  <times />  <apply>  <plus />  <ci> c </ci>  <apply>  <times />  <cn type='integer'> 2 </cn>  <apply>  <plus />  <apply>  <times />  <apply>  <times />  <cn type='integer'> -1 </cn>  <imaginaryi />  </apply>  <ci> b </ci>  </apply>  <ci> p </ci>  </apply>  <ci> z </ci>  </apply>  </apply>  <apply>  <power />  <apply>  <times />  <cn type='integer'> 2 </cn>  <apply>  <power />  <apply>  <plus />  <apply>  <times />  <apply>  <times />  <cn type='integer'> -1 </cn>  <imaginaryi />  </apply>  <ci> b </ci>  </apply>  <ci> p </ci>  </apply>  <cn type='rational'> 1 <sep /> 2 </cn>  </apply>  </apply>  <cn type='integer'> -1 </cn>  </apply>  </apply>  </apply>  </apply>  </apply>  <apply>  <times />  <apply>  <times />  <cn type='integer'> 1 </cn>  <apply>  <power />  <apply>  <power />  <apply>  <plus />  <apply>  <times />  <imaginaryi />  <ci> b </ci>  </apply>  <ci> p </ci>  </apply>  <cn type='rational'> 1 <sep /> 2 </cn>  </apply>  <cn type='integer'> -1 </cn>  </apply>  </apply>  <apply>  <power />  <exponentiale />  <apply>  <times />  <cn type='integer'> -1 </cn>  <apply>  <times />  <apply>  <power />  <ci> c </ci>  <cn type='integer'> 2 </cn>  </apply>  <apply>  <power />  <apply>  <times />  <cn type='integer'> 4 </cn>  <apply>  <plus />  <apply>  <times />  <imaginaryi />  <ci> b </ci>  </apply>  <ci> p </ci>  </apply>  </apply>  <cn type='integer'> -1 </cn>  </apply>  </apply>  </apply>  </apply>  <apply>  <plus />  <apply>  <ci> Erfi </ci>  <apply>  <times />  <apply>  <plus />  <apply>  <times />  <cn type='integer'> 2 </cn>  <apply>  <plus />  <apply>  <times />  <imaginaryi />  <ci> b </ci>  </apply>  <ci> p </ci>  </apply>  <ci> z </ci>  </apply>  <apply>  <times />  <cn type='integer'> -1 </cn>  <ci> c </ci>  </apply>  </apply>  <apply>  <power />  <apply>  <times />  <cn type='integer'> 2 </cn>  <apply>  <power />  <apply>  <plus />  <apply>  <times />  <imaginaryi />  <ci> b </ci>  </apply>  <ci> p </ci>  </apply>  <cn type='rational'> 1 <sep /> 2 </cn>  </apply>  </apply>  <cn type='integer'> -1 </cn>  </apply>  </apply>  </apply>  <apply>  <ci> Erfi </ci>  <apply>  <times />  <apply>  <plus />  <ci> c </ci>  <apply>  <times />  <cn type='integer'> 2 </cn>  <apply>  <plus />  <apply>  <times />  <imaginaryi />  <ci> b </ci>  </apply>  <ci> p </ci>  </apply>  <ci> z </ci>  </apply>  </apply>  <apply>  <power />  <apply>  <times />  <cn type='integer'> 2 </cn>  <apply>  <power />  <apply>  <plus />  <apply>  <times />  <imaginaryi />  <ci> b </ci>  </apply>  <ci> p </ci>  </apply>  <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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