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Exp




Mathematica Notation

Traditional Notation









Elementary Functions > Exp[z] > Integration > Indefinite integration > Involving one direct function and elementary functions > Arguments involving inverse trigonometric functions > Involving cos-1





http://functions.wolfram.com/01.03.21.0186.01









  


  








Input Form





Integrate[E^(a ArcCos[z]), z] == (E^(a ArcCos[z]) (z - a Sqrt[1 - z^2]))/ (1 + a^2)








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["\[Integral]", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["a", " ", RowBox[List["ArcCos", "[", "z", "]"]]]]], RowBox[List["\[DifferentialD]", "z"]]]]]], "\[Equal]", FractionBox[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["a", " ", RowBox[List["ArcCos", "[", "z", "]"]]]]], " ", RowBox[List["(", RowBox[List["z", "-", RowBox[List["a", " ", SqrtBox[RowBox[List["1", "-", SuperscriptBox["z", "2"]]]]]]]], ")"]]]], RowBox[List["1", "+", SuperscriptBox["a", "2"]]]]]]]]








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> <msup> <mi> &#8519; </mi> <mrow> <mi> a </mi> <mo> &#8290; </mo> <mrow> <msup> <mi> cos </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> </msup> <mo> &#8290; </mo> <mrow> <mo> &#8518; </mo> <mi> z </mi> </mrow> </mrow> </mrow> <mo> &#10869; </mo> <mfrac> <mrow> <msup> <mi> &#8519; </mi> <mrow> <mi> a </mi> <mo> &#8290; </mo> <mrow> <msup> <mi> cos </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> </msup> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <mo> - </mo> <mrow> <mi> a </mi> <mo> &#8290; </mo> <msqrt> <mrow> <mn> 1 </mn> <mo> - </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> </msqrt> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mrow> <msup> <mi> a </mi> <mn> 2 </mn> </msup> <mo> + </mo> <mn> 1 </mn> </mrow> </mfrac> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <int /> <bvar> <ci> z </ci> </bvar> <apply> <power /> <exponentiale /> <apply> <times /> <ci> a </ci> <apply> <arccos /> <ci> z </ci> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <power /> <exponentiale /> <apply> <times /> <ci> a </ci> <apply> <arccos /> <ci> z </ci> </apply> </apply> </apply> <apply> <plus /> <ci> z </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> a </ci> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <plus /> <apply> <power /> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> 1 </cn> </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[SuperscriptBox["\[ExponentialE]", RowBox[List["a_", " ", RowBox[List["ArcCos", "[", "z_", "]"]]]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["a", " ", RowBox[List["ArcCos", "[", "z", "]"]]]]], " ", RowBox[List["(", RowBox[List["z", "-", RowBox[List["a", " ", SqrtBox[RowBox[List["1", "-", SuperscriptBox["z", "2"]]]]]]]], ")"]]]], RowBox[List["1", "+", SuperscriptBox["a", "2"]]]]]]]]


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





2002-12-18