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http://functions.wolfram.com/01.03.21.0305.01
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Integrate[a^(d z) b^(e z) c^(f z), z] == (a^(d z) b^(e z) c^(f z))/
(d Log[a] + e Log[b] + f Log[c])
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Cell[BoxData[RowBox[List[RowBox[List["\[Integral]", RowBox[List[SuperscriptBox["a", RowBox[List["d", " ", "z"]]], " ", SuperscriptBox["b", RowBox[List["e", " ", "z"]]], SuperscriptBox["c", RowBox[List["f", " ", "z"]]], RowBox[List["\[DifferentialD]", "z"]]]]]], "\[Equal]", FractionBox[RowBox[List[SuperscriptBox["a", RowBox[List["d", " ", "z"]]], " ", SuperscriptBox["b", RowBox[List["e", " ", "z"]]], " ", SuperscriptBox["c", RowBox[List["f", " ", "z"]]]]], RowBox[List[RowBox[List["d", " ", RowBox[List["Log", "[", "a", "]"]]]], "+", RowBox[List["e", " ", RowBox[List["Log", "[", "b", "]"]]]], "+", RowBox[List["f", " ", RowBox[List["Log", "[", "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> a </mi> <mrow> <mi> d </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> </msup> <mo> ⁢ </mo> <msup> <mi> b </mi> <mrow> <mi> e </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> </msup> <mo> ⁢ </mo> <msup> <mi> c </mi> <mrow> <mi> f </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> </msup> </mrow> <mo> ⁢ </mo> <mrow> <mo> ⅆ </mo> <mi> z </mi> </mrow> </mrow> </mrow> <mo> ⩵ </mo> <mfrac> <mrow> <msup> <mi> a </mi> <mrow> <mi> d </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> </msup> <mo> ⁢ </mo> <msup> <mi> b </mi> <mrow> <mi> e </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> </msup> <mo> ⁢ </mo> <msup> <mi> c </mi> <mrow> <mi> f </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> </msup> </mrow> <mrow> <mrow> <mi> d </mi> <mo> ⁢ </mo> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> a </mi> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mi> e </mi> <mo> ⁢ </mo> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> b </mi> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mi> f </mi> <mo> ⁢ </mo> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> c </mi> <mo> ) </mo> </mrow> </mrow> </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> <times /> <ci> d </ci> <ci> z </ci> </apply> </apply> <apply> <power /> <ci> b </ci> <apply> <times /> <ci> e </ci> <ci> z </ci> </apply> </apply> <apply> <power /> <ci> c </ci> <apply> <times /> <ci> f </ci> <ci> z </ci> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <power /> <ci> a </ci> <apply> <times /> <ci> d </ci> <ci> z </ci> </apply> </apply> <apply> <power /> <ci> b </ci> <apply> <times /> <ci> e </ci> <ci> z </ci> </apply> </apply> <apply> <power /> <ci> c </ci> <apply> <times /> <ci> f </ci> <ci> z </ci> </apply> </apply> <apply> <power /> <apply> <plus /> <apply> <times /> <ci> d </ci> <apply> <ln /> <ci> a </ci> </apply> </apply> <apply> <times /> <ci> e </ci> <apply> <ln /> <ci> b </ci> </apply> </apply> <apply> <times /> <ci> f </ci> <apply> <ln /> <ci> c </ci> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["\[Integral]", RowBox[List[RowBox[List[SuperscriptBox["a_", RowBox[List["d_", " ", "z_"]]], " ", SuperscriptBox["b_", RowBox[List["e_", " ", "z_"]]], " ", SuperscriptBox["c_", RowBox[List["f_", " ", "z_"]]]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[SuperscriptBox["a", RowBox[List["d", " ", "z"]]], " ", SuperscriptBox["b", RowBox[List["e", " ", "z"]]], " ", SuperscriptBox["c", RowBox[List["f", " ", "z"]]]]], RowBox[List[RowBox[List["d", " ", RowBox[List["Log", "[", "a", "]"]]]], "+", RowBox[List["e", " ", RowBox[List["Log", "[", "b", "]"]]]], "+", RowBox[List["f", " ", RowBox[List["Log", "[", "c", "]"]]]]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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