Integrate[Sinh[a^z], z] == SinhIntegral[a^z]/Log[a]

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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> &#8747; </mo> <mrow> <mrow> <mi> sinh </mi> <mo> &#8289; </mo> <mo> ( </mo> <msup> <mi> a </mi> <mi> z </mi> </msup> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> &#8518; </mo> <mi> z </mi> </mrow> </mrow> </mrow> <mo> &#10869; </mo> <mfrac> <mrow> <mi> Shi </mi> <mo> &#8289; </mo> <mo> ( </mo> <msup> <mi> a </mi> <mi> z </mi> </msup> <mo> ) </mo> </mrow> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> a </mi> <mo> ) </mo> </mrow> </mfrac> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <int /> <bvar> <ci> z </ci> </bvar> <apply> <sinh /> <apply> <power /> <ci> a </ci> <ci> z </ci> </apply> </apply> </apply> <apply> <times /> <apply> <ci> SinhIntegral </ci> <apply> <power /> <ci> a </ci> <ci> z </ci> </apply> </apply> <apply> <power /> <apply> <ln /> <ci> a </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["\[Integral]", RowBox[List[RowBox[List["Sinh", "[", SuperscriptBox["a_", "z_"], "]"]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List["SinhIntegral", "[", SuperscriptBox["a", "z"], "]"]], RowBox[List["Log", "[", "a", "]"]]]]]]]

2002-12-18