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http://functions.wolfram.com/01.06.21.1364.01
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Integrate[E^(b z^2 + d z + e) Sin[a z^2 + p z + q] Sin[c z^2 + f z + g],
z] == (-(1/8)) Sqrt[Pi]
(-((E^(e + I g - (-d^2 - 2 I d f + f^2 + 2 I d p - 2 f p + p^2)/
(4 (I a - b - I c)) - I q) Erf[(-d - I f + I p + 2 I a z - 2 b z -
2 I c z)/(2 Sqrt[I a - b - I c])])/Sqrt[I a - b - I c]) +
(E^(e - I g - (-d^2 + 2 I d f + f^2 + 2 I d p + 2 f p + p^2)/
(4 (I a - b + I c)) - I q)
Erf[(-d + I f + I p + 2 I a z - 2 b z + 2 I c z)/
(2 Sqrt[I a - b + I c])])/Sqrt[I a - b + I c] -
(E^(e - I g - (d^2 - 2 I d f - f^2 + 2 I d p + 2 f p - p^2)/
(4 (I a + b - I c)) + I q)
Erfi[(d - I f + I p + 2 I a z + 2 b z - 2 I c z)/
(2 Sqrt[I a + b - I c])])/Sqrt[I a + b - I c] +
(E^(e + I g - (d^2 + 2 I d f - f^2 + 2 I d p - 2 f p - p^2)/
(4 (I a + b + I c)) + I q)
Erfi[(d + I f + I p + 2 I a z + 2 b z + 2 I c z)/
(2 Sqrt[I a + b + I c])])/Sqrt[I a + b + I c])
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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> <mrow> <mi> b </mi> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mi> d </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> + </mo> <mi> e </mi> </mrow> </msup> <mo> ⁢ </mo> <mrow> <mi> sin </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mrow> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mi> p </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> + </mo> <mi> q </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> sin </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mrow> <mi> c </mi> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mi> f </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> + </mo> <mi> g </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ⁢ </mo> <mrow> <mo> ⅆ </mo> <mi> z 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<mo> ⁢ </mo> <mi> a </mi> </mrow> <mtext> </mtext> <mo> + </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> c </mi> <mtext> </mtext> </mrow> </mrow> </msqrt> </mrow> </mfrac> <mo> ) </mo> </mrow> </mrow> <msqrt> <mrow> <mrow> <mo> - </mo> <mi> b </mi> </mrow> <mo> + </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> a </mi> </mrow> <mtext> </mtext> <mo> + </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> c </mi> <mtext> </mtext> </mrow> </mrow> </msqrt> </mfrac> <mo> + </mo> <mfrac> <mrow> <msup> <mi> ⅇ </mi> <mrow> <mi> e </mi> <mo> + </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> g </mi> </mrow> <mtext> </mtext> <mo> + </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> q </mi> </mrow> <mo> - </mo> <mfrac> <mrow> <msup> <mi> d </mi> <mn> 2 </mn> </msup> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> f </mi> <mo> ⁢ </mo> <mi> d </mi> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> p </mi> <mo> ⁢ </mo> <mi> d </mi> </mrow> <mo> - </mo> <msup> <mi> f </mi> <mn> 2 </mn> </msup> <mo> - </mo> <msup> <mi> p </mi> <mn> 2 </mn> </msup> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> f </mi> <mo> ⁢ </mo> <mi> p </mi> </mrow> </mrow> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> b </mi> <mo> + </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> a </mi> </mrow> <mtext> </mtext> <mo> + </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> c </mi> </mrow> </mrow> <mtext> </mtext> <mo> ) </mo> </mrow> </mrow> </mfrac> </mrow> </msup> <mo> ⁢ </mo> <mrow> <mi> erfi </mi> <mo> ⁡ </mo> <mo> ( </mo> <mfrac> <mrow> <mi> d </mi> <mo> + </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> f </mi> </mrow> <mtext> </mtext> <mo> + </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> p </mi> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> a </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> ⅈ </mi> 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d </mi> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> p </mi> <mo> ⁢ </mo> <mi> d </mi> </mrow> <mo> + </mo> <msup> <mi> f </mi> <mn> 2 </mn> </msup> <mo> + </mo> <msup> <mi> p </mi> <mn> 2 </mn> </msup> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> f </mi> <mo> ⁢ </mo> <mi> p </mi> </mrow> </mrow> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> b </mi> </mrow> <mo> - </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> c </mi> </mrow> <mo> + </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> a </mi> </mrow> </mrow> <mtext> </mtext> <mo> ) </mo> </mrow> </mrow> </mfrac> </mrow> </msup> <mo> ⁢ </mo> <mrow> <mi> erf </mi> <mo> ⁡ </mo> <mo> ( </mo> <mfrac> <mrow> <mrow> <mo> - </mo> <mi> d </mi> </mrow> <mo> - </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> f </mi> </mrow> <mo> + </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> p </mi> </mrow> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <mi> z </mi> 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<apply> <times /> <imaginaryi /> <ci> c </ci> </apply> </apply> <apply> <times /> <imaginaryi /> <ci> a </ci> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <ci> Erfi </ci> <apply> <times /> <apply> <plus /> <ci> d </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> f </ci> </apply> </apply> <apply> <times /> <imaginaryi /> <ci> p </ci> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <ci> b </ci> <ci> z </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <ci> c </ci> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <ci> a </ci> <ci> z </ci> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <apply> <plus /> <ci> b </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> c </ci> </apply> </apply> <apply> <times /> <imaginaryi /> <ci> a </ci> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <power /> <apply> <plus /> <ci> b </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> c </ci> </apply> </apply> <apply> <times /> <imaginaryi /> <ci> a </ci> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", "b", "+", RowBox[List["\[ImaginaryI]", " ", "c"]]]], ")"]]]]], "+", RowBox[List["\[ImaginaryI]", " ", "q"]]]]], " ", RowBox[List["Erfi", "[", FractionBox[RowBox[List["d", "+", RowBox[List["\[ImaginaryI]", " ", "f"]], "+", RowBox[List["\[ImaginaryI]", " ", "p"]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "a", " ", "z"]], "+", RowBox[List["2", " ", "b", " ", "z"]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "c", " ", "z"]]]], RowBox[List["2", " ", SqrtBox[RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", "b", "+", RowBox[List["\[ImaginaryI]", " ", "c"]]]]]]]], "]"]]]], SqrtBox[RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", "b", "+", RowBox[List["\[ImaginaryI]", " ", "c"]]]]]]]], ")"]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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