Wolfram Researchfunctions.wolfram.comOther Wolfram Sites
Search Site
Function CategoriesGraphics GalleryNotationsGeneral IdentitiesAbout This Site ContributeEmail CommentsSign the Guestbook

View Related Information In
The Documentation Center
MathWorld

Download All Formulas For This Function
Mathematica Notebook
PDF File

 

Developed with Mathematica -- Download a Free Trial Version
 











Exp






Mathematica Notation

Traditional Notation









Elementary Functions > Exp[z] > Integration > Indefinite integration > Involving functions of the direct function and a power function > Involving rational functions of the direct function and a power function > Involving zn ec z/a+b ec z





http://functions.wolfram.com/01.03.21.0786.01









  


  










Input Form





Integrate[(z^3 e^(f z))/(a + b c^(d z)), z] == (e^(f z) (-6 f LerchPhi[-((b c^(d z))/a), 4, (f Log[e])/(d Log[c])] Log[e] + d z Log[c] (6 f LerchPhi[-((b c^(d z))/a), 3, (f Log[e])/(d Log[c])] Log[e] + d z Log[c] (d^2 z Hypergeometric2F1[1, (f Log[e])/(d Log[c]), 1 + (f Log[e])/(d Log[c]), -((b c^(d z))/a)] Log[c]^2 - 3 f LerchPhi[-((b c^(d z))/a), 2, (f Log[e])/(d Log[c])] Log[e]))))/ (a d^4 f Log[c]^4 Log[e])










Standard Form





Cell[BoxData[RowBox[List[RowBox[List["\[Integral]", RowBox[List[FractionBox[RowBox[List[SuperscriptBox["z", "3"], " ", SuperscriptBox["e", RowBox[List["f", " ", "z"]]]]], RowBox[List["a", "+", RowBox[List["b", " ", SuperscriptBox["c", RowBox[List["d", " ", "z"]]]]]]]], RowBox[List["\[DifferentialD]", "z"]]]]]], "\[Equal]", RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["e", RowBox[List["f", " ", "z"]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "6"]], " ", "f", " ", RowBox[List["LerchPhi", "[", RowBox[List[RowBox[List["-", FractionBox[RowBox[List["b", " ", SuperscriptBox["c", RowBox[List["d", " ", "z"]]]]], "a"]]], ",", "4", ",", FractionBox[RowBox[List["f", " ", RowBox[List["Log", "[", "e", "]"]]]], RowBox[List["d", " ", RowBox[List["Log", "[", "c", "]"]]]]]]], "]"]], " ", RowBox[List["Log", "[", "e", "]"]]]], "+", RowBox[List["d", " ", "z", " ", RowBox[List["Log", "[", "c", "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List["6", " ", "f", " ", RowBox[List["LerchPhi", "[", RowBox[List[RowBox[List["-", FractionBox[RowBox[List["b", " ", SuperscriptBox["c", RowBox[List["d", " ", "z"]]]]], "a"]]], ",", "3", ",", FractionBox[RowBox[List["f", " ", RowBox[List["Log", "[", "e", "]"]]]], RowBox[List["d", " ", RowBox[List["Log", "[", "c", "]"]]]]]]], "]"]], " ", RowBox[List["Log", "[", "e", "]"]]]], "+", RowBox[List["d", " ", "z", " ", RowBox[List["Log", "[", "c", "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List[SuperscriptBox["d", "2"], " ", "z", " ", RowBox[List["Hypergeometric2F1", "[", RowBox[List["1", ",", FractionBox[RowBox[List["f", " ", RowBox[List["Log", "[", "e", "]"]]]], RowBox[List["d", " ", RowBox[List["Log", "[", "c", "]"]]]]], ",", RowBox[List["1", "+", FractionBox[RowBox[List["f", " ", RowBox[List["Log", "[", "e", "]"]]]], RowBox[List["d", " ", RowBox[List["Log", "[", "c", "]"]]]]]]], ",", RowBox[List["-", FractionBox[RowBox[List["b", " ", SuperscriptBox["c", RowBox[List["d", " ", "z"]]]]], "a"]]]]], "]"]], " ", SuperscriptBox[RowBox[List["Log", "[", "c", "]"]], "2"]]], "-", RowBox[List["3", " ", "f", " ", RowBox[List["LerchPhi", "[", RowBox[List[RowBox[List["-", FractionBox[RowBox[List["b", " ", SuperscriptBox["c", RowBox[List["d", " ", "z"]]]]], "a"]]], ",", "2", ",", FractionBox[RowBox[List["f", " ", RowBox[List["Log", "[", "e", "]"]]]], RowBox[List["d", " ", RowBox[List["Log", "[", "c", "]"]]]]]]], "]"]], " ", RowBox[List["Log", "[", "e", "]"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]], ")"]], "/", RowBox[List["(", RowBox[List["a", " ", SuperscriptBox["d", "4"], " ", "f", " ", SuperscriptBox[RowBox[List["Log", "[", "c", "]"]], "4"], " ", RowBox[List["Log", "[", "e", "]"]]]], ")"]]]]]]]]










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> <mfrac> <mrow> <msup> <mi> z </mi> <mn> 3 </mn> </msup> <mo> &#8290; </mo> <msup> <mi> e </mi> <mrow> <mi> f </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> </msup> </mrow> <mrow> <mrow> <mi> b </mi> <mo> &#8290; </mo> <msup> <mi> c </mi> <mrow> <mi> d </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> </msup> </mrow> <mo> + </mo> <mi> a </mi> </mrow> </mfrac> <mo> &#8290; </mo> <mrow> <mo> &#8518; </mo> <mi> z </mi> </mrow> </mrow> </mrow> <mo> &#10869; </mo> <mrow> <mfrac> <mn> 1 </mn> <mrow> <mi> a </mi> <mo> &#8290; </mo> <msup> <mi> d </mi> <mn> 4 </mn> </msup> <mo> &#8290; </mo> <mi> f </mi> <mo> &#8290; </mo> <mrow> <msup> <mi> log </mi> <mn> 4 </mn> </msup> <mo> ( </mo> <mi> c </mi> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> e </mi> <mo> ) </mo> </mrow> </mrow> </mfrac> <mo> &#8290; </mo> <msup> <mi> e </mi> <mrow> <mi> f </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> </msup> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> d </mi> <mo> &#8290; </mo> <mi> z </mi> <mo> &#8290; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> c </mi> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 6 </mn> <mo> &#8290; </mo> <mi> f </mi> <mo> &#8290; </mo> <semantics> <mrow> <mi> &#934; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mfrac> <mrow> <mi> b </mi> <mo> &#8290; </mo> <msup> <mi> c </mi> <mrow> <mi> d </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> </msup> </mrow> <mi> a </mi> </mfrac> </mrow> <mo> , </mo> <mn> 3 </mn> <mo> , </mo> <mfrac> <mrow> <mi> f </mi> <mo> &#8290; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> e </mi> <mo> ) </mo> </mrow> </mrow> <mrow> <mi> d </mi> <mo> &#8290; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> c </mi> <mo> ) </mo> </mrow> </mrow> </mfrac> </mrow> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[&quot;\[CapitalPhi]&quot;, &quot;(&quot;, RowBox[List[TagBox[RowBox[List[&quot;-&quot;, FractionBox[RowBox[List[&quot;b&quot;, &quot; &quot;, SuperscriptBox[&quot;c&quot;, RowBox[List[&quot;d&quot;, &quot; &quot;, &quot;z&quot;]]]]], &quot;a&quot;]]], Rule[Editable, True]], &quot;,&quot;, TagBox[&quot;3&quot;, Rule[Editable, True]], &quot;,&quot;, TagBox[FractionBox[RowBox[List[&quot;f&quot;, &quot; &quot;, RowBox[List[&quot;log&quot;, &quot;(&quot;, &quot;e&quot;, &quot;)&quot;]]]], RowBox[List[&quot;d&quot;, &quot; &quot;, RowBox[List[&quot;log&quot;, &quot;(&quot;, &quot;c&quot;, &quot;)&quot;]]]]], Rule[Editable, True]]]], &quot;)&quot;]], InterpretTemplate[Function[List[$CellContext`e1, $CellContext`e2, $CellContext`e3], LerchPhi[$CellContext`e1, $CellContext`e2, $CellContext`e3]]]] </annotation> </semantics> <mo> &#8290; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> e </mi> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mi> d </mi> <mo> &#8290; </mo> <mi> z </mi> <mo> &#8290; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> c </mi> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <msup> <mi> d </mi> <mn> 2 </mn> </msup> <mo> &#8290; </mo> <mi> z </mi> <mo> &#8290; </mo> <semantics> <mrow> <mrow> <msub> <mo> &#8202; </mo> <mn> 2 </mn> </msub> <msub> <mi> F </mi> <mn> 1 </mn> </msub> </mrow> <mo> &#8289; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 1 </mn> <mo> , </mo> <mfrac> <mrow> <mi> f </mi> <mo> &#8290; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> e </mi> <mo> ) </mo> </mrow> </mrow> <mrow> <mi> d </mi> <mo> &#8290; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> c </mi> <mo> ) </mo> </mrow> </mrow> </mfrac> </mrow> <mo> ; </mo> <mrow> <mfrac> <mrow> <mi> f </mi> <mo> &#8290; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> e </mi> <mo> ) </mo> </mrow> </mrow> <mrow> <mi> d </mi> <mo> &#8290; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> c </mi> <mo> ) </mo> </mrow> </mrow> </mfrac> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ; </mo> <mrow> <mo> - </mo> <mfrac> <mrow> <mi> b </mi> <mo> &#8290; </mo> <msup> <mi> c </mi> <mrow> <mi> d </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> </msup> </mrow> <mi> a </mi> </mfrac> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation encoding='Mathematica'> TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox[&quot;\[InvisiblePrefixScriptBase]&quot;, FormBox[&quot;2&quot;, TraditionalForm]], SubscriptBox[&quot;F&quot;, FormBox[&quot;1&quot;, TraditionalForm]]]], &quot;\[InvisibleApplication]&quot;, RowBox[List[&quot;(&quot;, RowBox[List[TagBox[TagBox[RowBox[List[TagBox[&quot;1&quot;, Hypergeometric2F1, Rule[Editable, True]], &quot;,&quot;, TagBox[FractionBox[RowBox[List[&quot;f&quot;, &quot; &quot;, RowBox[List[&quot;log&quot;, &quot;(&quot;, &quot;e&quot;, &quot;)&quot;]]]], RowBox[List[&quot;d&quot;, &quot; &quot;, RowBox[List[&quot;log&quot;, &quot;(&quot;, &quot;c&quot;, &quot;)&quot;]]]]], Hypergeometric2F1, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1, Rule[Editable, False]], &quot;;&quot;, TagBox[TagBox[TagBox[RowBox[List[FractionBox[RowBox[List[&quot;f&quot;, &quot; &quot;, RowBox[List[&quot;log&quot;, &quot;(&quot;, &quot;e&quot;, &quot;)&quot;]]]], RowBox[List[&quot;d&quot;, &quot; &quot;, RowBox[List[&quot;log&quot;, &quot;(&quot;, &quot;c&quot;, &quot;)&quot;]]]]], &quot;+&quot;, &quot;1&quot;]], Hypergeometric2F1, Rule[Editable, True]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1, Rule[Editable, False]], &quot;;&quot;, TagBox[RowBox[List[&quot;-&quot;, FractionBox[RowBox[List[&quot;b&quot;, &quot; &quot;, SuperscriptBox[&quot;c&quot;, RowBox[List[&quot;d&quot;, &quot; &quot;, &quot;z&quot;]]]]], &quot;a&quot;]]], Hypergeometric2F1, Rule[Editable, True]]]], &quot;)&quot;]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False]], Hypergeometric2F1] </annotation> </semantics> <mo> &#8290; </mo> <mrow> <msup> <mi> log </mi> <mn> 2 </mn> </msup> <mo> ( </mo> <mi> c </mi> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mn> 3 </mn> <mo> &#8290; </mo> <mi> f </mi> <mo> &#8290; </mo> <semantics> <mrow> <mi> &#934; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mfrac> <mrow> <mi> b </mi> <mo> &#8290; </mo> <msup> <mi> c </mi> <mrow> <mi> d </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> </msup> </mrow> <mi> a </mi> </mfrac> </mrow> <mo> , </mo> <mn> 2 </mn> <mo> , </mo> <mfrac> <mrow> <mi> f </mi> <mo> &#8290; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> e </mi> <mo> ) </mo> </mrow> </mrow> <mrow> <mi> d </mi> <mo> &#8290; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> c </mi> <mo> ) </mo> </mrow> </mrow> </mfrac> </mrow> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[&quot;\[CapitalPhi]&quot;, &quot;(&quot;, RowBox[List[TagBox[RowBox[List[&quot;-&quot;, FractionBox[RowBox[List[&quot;b&quot;, &quot; &quot;, SuperscriptBox[&quot;c&quot;, RowBox[List[&quot;d&quot;, &quot; &quot;, &quot;z&quot;]]]]], &quot;a&quot;]]], Rule[Editable, True]], &quot;,&quot;, TagBox[&quot;2&quot;, Rule[Editable, True]], &quot;,&quot;, TagBox[FractionBox[RowBox[List[&quot;f&quot;, &quot; &quot;, RowBox[List[&quot;log&quot;, &quot;(&quot;, &quot;e&quot;, &quot;)&quot;]]]], RowBox[List[&quot;d&quot;, &quot; &quot;, RowBox[List[&quot;log&quot;, &quot;(&quot;, &quot;c&quot;, &quot;)&quot;]]]]], Rule[Editable, True]]]], &quot;)&quot;]], InterpretTemplate[Function[List[$CellContext`e1, $CellContext`e2, $CellContext`e3], LerchPhi[$CellContext`e1, $CellContext`e2, $CellContext`e3]]]] </annotation> </semantics> <mo> &#8290; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> e </mi> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mn> 6 </mn> <mo> &#8290; </mo> <mi> f </mi> <mo> &#8290; </mo> <semantics> <mrow> <mi> &#934; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mfrac> <mrow> <mi> b </mi> <mo> &#8290; </mo> <msup> <mi> c </mi> <mrow> <mi> d </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> </msup> </mrow> <mi> a </mi> </mfrac> </mrow> <mo> , </mo> <mn> 4 </mn> <mo> , </mo> <mfrac> <mrow> <mi> f </mi> <mo> &#8290; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> e </mi> <mo> ) </mo> </mrow> </mrow> <mrow> <mi> d </mi> <mo> &#8290; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> c </mi> <mo> ) </mo> </mrow> </mrow> </mfrac> </mrow> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[&quot;\[CapitalPhi]&quot;, &quot;(&quot;, RowBox[List[TagBox[RowBox[List[&quot;-&quot;, FractionBox[RowBox[List[&quot;b&quot;, &quot; &quot;, SuperscriptBox[&quot;c&quot;, RowBox[List[&quot;d&quot;, &quot; &quot;, &quot;z&quot;]]]]], &quot;a&quot;]]], Rule[Editable, True]], &quot;,&quot;, TagBox[&quot;4&quot;, Rule[Editable, True]], &quot;,&quot;, TagBox[FractionBox[RowBox[List[&quot;f&quot;, &quot; &quot;, RowBox[List[&quot;log&quot;, &quot;(&quot;, &quot;e&quot;, &quot;)&quot;]]]], RowBox[List[&quot;d&quot;, &quot; &quot;, RowBox[List[&quot;log&quot;, &quot;(&quot;, &quot;c&quot;, &quot;)&quot;]]]]], Rule[Editable, True]]]], &quot;)&quot;]], InterpretTemplate[Function[List[$CellContext`e1, $CellContext`e2, $CellContext`e3], LerchPhi[$CellContext`e1, $CellContext`e2, $CellContext`e3]]]] </annotation> </semantics> <mo> &#8290; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> e </mi> <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 /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> <apply> <power /> <ci> e </ci> <apply> <times /> <ci> f </ci> <ci> z </ci> </apply> </apply> <apply> <power /> <apply> <plus /> <apply> <times /> <ci> b </ci> <apply> <power /> <ci> c </ci> <apply> <times /> <ci> d </ci> <ci> z </ci> </apply> </apply> </apply> <ci> a </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <ci> a </ci> <apply> <power /> <ci> d </ci> <cn type='integer'> 4 </cn> </apply> <ci> f </ci> <apply> <power /> <apply> <ln /> <ci> c </ci> </apply> <cn type='integer'> 4 </cn> </apply> <apply> <ln /> <ci> e </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <power /> <ci> e </ci> <apply> <times /> <ci> f </ci> <ci> z </ci> </apply> </apply> <apply> <plus /> <apply> <times /> <ci> d </ci> <ci> z </ci> <apply> <ln /> <ci> c </ci> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 6 </cn> <ci> f </ci> <apply> <ci> LerchPhi </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> b </ci> <apply> <power /> <ci> c </ci> <apply> <times /> <ci> d </ci> <ci> z </ci> </apply> </apply> <apply> <power /> <ci> a </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <cn type='integer'> 3 </cn> <apply> <times /> <ci> f </ci> <apply> <ln /> <ci> e </ci> </apply> <apply> <power /> <apply> <times /> <ci> d </ci> <apply> <ln /> <ci> c </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <ln /> <ci> e </ci> </apply> </apply> <apply> <times /> <ci> d </ci> <ci> z </ci> <apply> <ln /> <ci> c </ci> </apply> <apply> <plus /> <apply> <times /> <apply> <power /> <ci> d </ci> <cn type='integer'> 2 </cn> </apply> <ci> z </ci> <apply> <ci> Hypergeometric2F1 </ci> <cn type='integer'> 1 </cn> <apply> <times /> <ci> f </ci> <apply> <ln /> <ci> e </ci> </apply> <apply> <power /> <apply> <times /> <ci> d </ci> <apply> <ln /> <ci> c </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <plus /> <apply> <times /> <ci> f </ci> <apply> <ln /> <ci> e </ci> </apply> <apply> <power /> <apply> <times /> <ci> d </ci> <apply> <ln /> <ci> c </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> 1 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> b </ci> <apply> <power /> <ci> c </ci> <apply> <times /> <ci> d </ci> <ci> z </ci> </apply> </apply> <apply> <power /> <ci> a </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <ln /> <ci> c </ci> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 3 </cn> <ci> f </ci> <apply> <ci> LerchPhi </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> b </ci> <apply> <power /> <ci> c </ci> <apply> <times /> <ci> d </ci> <ci> z </ci> </apply> </apply> <apply> <power /> <ci> a </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <cn type='integer'> 2 </cn> <apply> <times /> <ci> f </ci> <apply> <ln /> <ci> e </ci> </apply> <apply> <power /> <apply> <times /> <ci> d </ci> <apply> <ln /> <ci> c </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <ln /> <ci> e </ci> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 6 </cn> <ci> f </ci> <apply> <ci> LerchPhi </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> b </ci> <apply> <power /> <ci> c </ci> <apply> <times /> <ci> d </ci> <ci> z </ci> </apply> </apply> <apply> <power /> <ci> a </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <cn type='integer'> 4 </cn> <apply> <times /> <ci> f </ci> <apply> <ln /> <ci> e </ci> </apply> <apply> <power /> <apply> <times /> <ci> d </ci> <apply> <ln /> <ci> c </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <ln /> <ci> e </ci> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["\[Integral]", RowBox[List[FractionBox[RowBox[List[SuperscriptBox["z_", "3"], " ", SuperscriptBox["e_", RowBox[List["f_", " ", "z_"]]]]], RowBox[List["a_", "+", RowBox[List["b_", " ", SuperscriptBox["c_", RowBox[List["d_", " ", "z_"]]]]]]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[SuperscriptBox["e", RowBox[List["f", " ", "z"]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "6"]], " ", "f", " ", RowBox[List["LerchPhi", "[", RowBox[List[RowBox[List["-", FractionBox[RowBox[List["b", " ", SuperscriptBox["c", RowBox[List["d", " ", "z"]]]]], "a"]]], ",", "4", ",", FractionBox[RowBox[List["f", " ", RowBox[List["Log", "[", "e", "]"]]]], RowBox[List["d", " ", RowBox[List["Log", "[", "c", "]"]]]]]]], "]"]], " ", RowBox[List["Log", "[", "e", "]"]]]], "+", RowBox[List["d", " ", "z", " ", RowBox[List["Log", "[", "c", "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List["6", " ", "f", " ", RowBox[List["LerchPhi", "[", RowBox[List[RowBox[List["-", FractionBox[RowBox[List["b", " ", SuperscriptBox["c", RowBox[List["d", " ", "z"]]]]], "a"]]], ",", "3", ",", FractionBox[RowBox[List["f", " ", RowBox[List["Log", "[", "e", "]"]]]], RowBox[List["d", " ", RowBox[List["Log", "[", "c", "]"]]]]]]], "]"]], " ", RowBox[List["Log", "[", "e", "]"]]]], "+", RowBox[List["d", " ", "z", " ", RowBox[List["Log", "[", "c", "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List[SuperscriptBox["d", "2"], " ", "z", " ", RowBox[List["Hypergeometric2F1", "[", RowBox[List["1", ",", FractionBox[RowBox[List["f", " ", RowBox[List["Log", "[", "e", "]"]]]], RowBox[List["d", " ", RowBox[List["Log", "[", "c", "]"]]]]], ",", RowBox[List["1", "+", FractionBox[RowBox[List["f", " ", RowBox[List["Log", "[", "e", "]"]]]], RowBox[List["d", " ", RowBox[List["Log", "[", "c", "]"]]]]]]], ",", RowBox[List["-", FractionBox[RowBox[List["b", " ", SuperscriptBox["c", RowBox[List["d", " ", "z"]]]]], "a"]]]]], "]"]], " ", SuperscriptBox[RowBox[List["Log", "[", "c", "]"]], "2"]]], "-", RowBox[List["3", " ", "f", " ", RowBox[List["LerchPhi", "[", RowBox[List[RowBox[List["-", FractionBox[RowBox[List["b", " ", SuperscriptBox["c", RowBox[List["d", " ", "z"]]]]], "a"]]], ",", "2", ",", FractionBox[RowBox[List["f", " ", RowBox[List["Log", "[", "e", "]"]]]], RowBox[List["d", " ", RowBox[List["Log", "[", "c", "]"]]]]]]], "]"]], " ", RowBox[List["Log", "[", "e", "]"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]], RowBox[List["a", " ", SuperscriptBox["d", "4"], " ", "f", " ", SuperscriptBox[RowBox[List["Log", "[", "c", "]"]], "4"], " ", RowBox[List["Log", "[", "e", "]"]]]]]]]]]










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





2002-12-18





© 1998- Wolfram Research, Inc.