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Exp




Mathematica Notation

Traditional Notation









Elementary Functions > Exp[z] > Integration > Indefinite integration > Involving functions of the direct function > Involving products of the direct function > Involving products of two direct functions > Involving ab zr+ehc zr+g





http://functions.wolfram.com/01.03.21.0281.01









  


  








Input Form





Integrate[a^(b z^2 + e) h^(c z^2 + g), z] == (a^e h^g Sqrt[Pi] Erfi[z Sqrt[b Log[a] + c Log[h]]])/ (2 Sqrt[b Log[a] + c Log[h]])








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["\[Integral]", RowBox[List[SuperscriptBox["a", RowBox[List[RowBox[List["b", " ", SuperscriptBox["z", "2"]]], "+", "e"]]], SuperscriptBox["h", RowBox[List[RowBox[List["c", " ", SuperscriptBox["z", "2"]]], "+", "g"]]], " ", RowBox[List["\[DifferentialD]", "z"]]]]]], "\[Equal]", FractionBox[RowBox[List[SuperscriptBox["a", "e"], " ", SuperscriptBox["h", "g"], " ", SqrtBox["\[Pi]"], " ", RowBox[List["Erfi", "[", RowBox[List["z", " ", SqrtBox[RowBox[List[RowBox[List["b", " ", RowBox[List["Log", "[", "a", "]"]]]], "+", RowBox[List["c", " ", RowBox[List["Log", "[", "h", "]"]]]]]]]]], "]"]]]], RowBox[List["2", " ", SqrtBox[RowBox[List[RowBox[List["b", " ", RowBox[List["Log", "[", "a", "]"]]]], "+", RowBox[List["c", " ", RowBox[List["Log", "[", "h", "]"]]]]]]]]]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mo> &#8747; </mo> <mrow> <mrow> <msup> <mi> a </mi> <mrow> <mrow> <mi> b </mi> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mi> e </mi> </mrow> </msup> <mo> &#8290; </mo> <msup> <mi> h </mi> <mrow> <mrow> <mi> c </mi> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mi> g </mi> </mrow> </msup> </mrow> <mo> &#8290; </mo> <mrow> <mo> &#8518; </mo> <mi> z </mi> </mrow> </mrow> </mrow> <mo> &#10869; </mo> <mfrac> <mrow> <msup> <mi> a </mi> <mi> e </mi> </msup> <mo> &#8290; </mo> <msup> <mi> h </mi> <mi> g </mi> </msup> <mo> &#8290; </mo> <msqrt> <mi> &#960; </mi> </msqrt> <mo> &#8290; </mo> <mrow> <mi> erfi </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> z </mi> <mo> &#8290; </mo> <msqrt> <mrow> <mrow> <mi> b </mi> <mo> &#8290; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> a </mi> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mi> c </mi> <mo> &#8290; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> h </mi> <mo> ) </mo> </mrow> </mrow> </mrow> </msqrt> </mrow> <mo> ) </mo> </mrow> </mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msqrt> <mrow> <mrow> <mi> b </mi> <mo> &#8290; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> a </mi> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mi> c </mi> <mo> &#8290; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> h </mi> <mo> ) </mo> </mrow> </mrow> </mrow> </msqrt> </mrow> </mfrac> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <int /> <bvar> <ci> z </ci> </bvar> <apply> <times /> <apply> <power /> <ci> a </ci> <apply> <plus /> <apply> <times /> <ci> b </ci> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <ci> e </ci> </apply> </apply> <apply> <power /> <ci> h </ci> <apply> <plus /> <apply> <times /> <ci> c </ci> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <ci> g </ci> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <power /> <ci> a </ci> <ci> e </ci> </apply> <apply> <power /> <ci> h </ci> <ci> g </ci> </apply> <apply> <power /> <pi /> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <ci> Erfi </ci> <apply> <times /> <ci> z </ci> <apply> <power /> <apply> <plus /> <apply> <times /> <ci> b </ci> <apply> <ln /> <ci> a </ci> </apply> </apply> <apply> <times /> <ci> c </ci> <apply> <ln /> <ci> h </ci> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <apply> <plus /> <apply> <times /> <ci> b </ci> <apply> <ln /> <ci> a </ci> </apply> </apply> <apply> <times /> <ci> c </ci> <apply> <ln /> <ci> h </ci> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["\[Integral]", RowBox[List[RowBox[List[SuperscriptBox["a_", RowBox[List[RowBox[List["b_", " ", SuperscriptBox["z_", "2"]]], "+", "e_"]]], " ", SuperscriptBox["h_", RowBox[List[RowBox[List["c_", " ", SuperscriptBox["z_", "2"]]], "+", "g_"]]]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[SuperscriptBox["a", "e"], " ", SuperscriptBox["h", "g"], " ", SqrtBox["\[Pi]"], " ", RowBox[List["Erfi", "[", RowBox[List["z", " ", SqrtBox[RowBox[List[RowBox[List["b", " ", RowBox[List["Log", "[", "a", "]"]]]], "+", RowBox[List["c", " ", RowBox[List["Log", "[", "h", "]"]]]]]]]]], "]"]]]], RowBox[List["2", " ", SqrtBox[RowBox[List[RowBox[List["b", " ", RowBox[List["Log", "[", "a", "]"]]]], "+", RowBox[List["c", " ", RowBox[List["Log", "[", "h", "]"]]]]]]]]]]]]]]


Date Added to functions.wolfram.com (modification date)





2002-12-18