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http://functions.wolfram.com/01.07.21.0466.01
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Integrate[(E^(p z) Cos[c z])/Sqrt[a z + b], z] ==
-((Sqrt[Pi] Sqrt[b + a z] (1 - Erf[Sqrt[-((((-I) c + p) (b + a z))/a)]]))/
(E^((b ((-I) c + p))/a) (2 a Sqrt[-((((-I) c + p) (b + a z))/a)]))) -
(Sqrt[Pi] Sqrt[b + a z] (1 - Erf[Sqrt[-(((I c + p) (b + a z))/a)]]))/
(E^((b (I c + p))/a) (2 a Sqrt[-(((I c + p) (b + a z))/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> ∫ </mo> <mrow> <mfrac> <mrow> <msup> <mi> ⅇ </mi> <mrow> <mi> p </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> </msup> <mo> ⁢ </mo> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> c </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <msqrt> <mrow> <mrow> <mi> a </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> + </mo> <mi> b </mi> </mrow> </msqrt> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ⅆ </mo> <mi> z </mi> </mrow> </mrow> </mrow> <mo> ⩵ </mo> <mrow> <mrow> <mo> - </mo> <mfrac> <mrow> <msup> <mi> ⅇ </mi> <mrow> <mo> - </mo> <mfrac> <mrow> <mi> b </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> - </mo> <mi> ⅈ </mi> </mrow> <mo> ⁢ </mo> <mi> c </mi> </mrow> <mo> + </mo> <mi> p </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mi> a </mi> </mfrac> </mrow> </msup> <mo> ⁢ </mo> <msqrt> <mi> π </mi> </msqrt> <mo> ⁢ </mo> <msqrt> <mrow> <mi> b </mi> <mo> + </mo> <mrow> <mi> a </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> </mrow> </msqrt> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mrow> <mi> erf </mi> <mo> ⁡ </mo> <mo> ( </mo> <msqrt> <mrow> <mo> - </mo> <mfrac> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> - </mo> <mi> ⅈ </mi> </mrow> <mo> ⁢ </mo> <mi> c </mi> </mrow> <mo> + </mo> <mi> p </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> b </mi> <mo> + </mo> <mrow> <mi> a </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mi> a </mi> </mfrac> </mrow> </msqrt> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> a </mi> <mo> ⁢ </mo> <msqrt> <mrow> <mo> - </mo> <mfrac> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> - </mo> <mi> ⅈ </mi> </mrow> <mo> ⁢ </mo> <mi> c </mi> </mrow> <mo> + </mo> <mi> p </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> b </mi> <mo> + </mo> <mrow> <mi> a </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mi> a </mi> </mfrac> </mrow> </msqrt> </mrow> </mfrac> </mrow> <mo> - </mo> <mfrac> <mrow> <msup> <mi> ⅇ </mi> <mrow> <mo> - </mo> <mfrac> <mrow> <mi> b </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> c </mi> </mrow> <mo> + </mo> <mi> p </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mi> a </mi> </mfrac> </mrow> </msup> <mo> ⁢ </mo> <msqrt> <mi> π </mi> </msqrt> <mo> ⁢ </mo> <msqrt> <mrow> <mi> b </mi> <mo> + </mo> <mrow> <mi> a </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> </mrow> </msqrt> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mrow> <mi> erf </mi> <mo> ⁡ </mo> <mo> ( </mo> <msqrt> <mrow> <mo> - </mo> <mfrac> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> c </mi> </mrow> <mo> + </mo> <mi> p </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> b </mi> <mo> + </mo> <mrow> <mi> a </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mi> a </mi> </mfrac> </mrow> </msqrt> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> a </mi> <mo> ⁢ </mo> <msqrt> <mrow> <mo> - </mo> <mfrac> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> c </mi> </mrow> <mo> + </mo> <mi> p </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> b </mi> <mo> + </mo> <mrow> <mi> a </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mi> a </mi> </mfrac> </mrow> </msqrt> </mrow> </mfrac> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <int /> <bvar> <ci> z </ci> </bvar> <apply> <times /> <apply> <power /> <exponentiale /> <apply> <times /> <ci> p </ci> <ci> z </ci> </apply> </apply> <apply> <cos /> <apply> <times /> <ci> c </ci> <ci> z </ci> </apply> </apply> <apply> <power /> <apply> <power /> <apply> <plus /> <apply> <times /> <ci> a </ci> <ci> z </ci> </apply> <ci> b </ci> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> b </ci> <apply> <plus /> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <imaginaryi /> </apply> <ci> c </ci> </apply> <ci> p </ci> </apply> <apply> <power /> <ci> a </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <power /> <pi /> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <ci> b </ci> <apply> <times /> <ci> a </ci> <ci> z </ci> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Erf </ci> <apply> <power /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <plus /> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <imaginaryi /> </apply> <ci> c </ci> </apply> <ci> p </ci> </apply> <apply> <plus /> <ci> b </ci> <apply> <times /> <ci> a </ci> <ci> z </ci> </apply> </apply> <apply> <power /> <ci> a </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> a </ci> <apply> <power /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <plus /> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <imaginaryi /> </apply> <ci> c </ci> </apply> <ci> p </ci> </apply> <apply> <plus /> <ci> b </ci> <apply> <times /> <ci> a </ci> <ci> z </ci> </apply> </apply> <apply> <power /> <ci> a </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> b </ci> <apply> <plus /> <apply> <times /> <imaginaryi /> <ci> c </ci> </apply> <ci> p </ci> </apply> <apply> <power /> <ci> a </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <power /> <pi /> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <ci> b </ci> <apply> <times /> <ci> a </ci> <ci> z </ci> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Erf </ci> <apply> <power /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <plus /> <apply> <times /> <imaginaryi /> <ci> c </ci> </apply> <ci> p </ci> </apply> <apply> <plus /> <ci> b </ci> <apply> <times /> <ci> a </ci> <ci> z </ci> </apply> </apply> <apply> <power /> <ci> a </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> a </ci> <apply> <power /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <plus /> <apply> <times /> <imaginaryi /> <ci> c </ci> </apply> <ci> p </ci> </apply> <apply> <plus /> <ci> b </ci> <apply> <times /> <ci> a </ci> <ci> z </ci> </apply> </apply> <apply> <power /> <ci> a </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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Date Added to functions.wolfram.com (modification date)
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