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http://functions.wolfram.com/01.20.21.0404.01
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Integrate[(E^(p z) Cosh[c z])/Sqrt[a z + b], z] ==
(Sqrt[Pi] ((-E^((2 b c)/a)) (c + p) Sqrt[((c - p) (b + a z))/a]
Erfc[Sqrt[((c - p) (b + a z))/a]] +
(c - p) Sqrt[-(((c + p) (b + a z))/a)]
Erfc[Sqrt[-(((c + p) (b + a z))/a)]]))/E^((b (c + p))/a)/
(2 (c^2 - p^2) Sqrt[b + a z])
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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> cosh </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> c </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <msqrt> <mrow> <mi> b </mi> <mo> + </mo> <mrow> <mi> a </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> </mrow> </msqrt> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ⅆ </mo> <mi> z </mi> </mrow> </mrow> </mrow> <mo> ⩵ </mo> <mrow> <mfrac> <mn> 1 </mn> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <msup> <mi> c </mi> <mn> 2 </mn> </msup> <mo> - </mo> <msup> <mi> p </mi> <mn> 2 </mn> </msup> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msqrt> <mrow> <mi> b </mi> <mo> + </mo> <mrow> <mi> a </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> </mrow> </msqrt> </mrow> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <msup> <mi> ⅇ </mi> <mrow> <mo> - 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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["\[Integral]", RowBox[List[FractionBox[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["p_", " ", "z_"]]], " ", RowBox[List["Cosh", "[", RowBox[List["c_", " ", "z_"]], "]"]]]], SqrtBox[RowBox[List[RowBox[List["a_", " ", "z_"]], "+", "b_"]]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["-", FractionBox[RowBox[List["b", " ", RowBox[List["(", RowBox[List["c", "+", "p"]], ")"]]]], "a"]]]], " ", SqrtBox["\[Pi]"], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", SuperscriptBox["\[ExponentialE]", FractionBox[RowBox[List["2", " ", "b", " ", "c"]], "a"]]]], " ", RowBox[List["(", RowBox[List["c", "+", "p"]], ")"]], " ", SqrtBox[FractionBox[RowBox[List[RowBox[List["(", RowBox[List["c", "-", "p"]], ")"]], " ", RowBox[List["(", RowBox[List["b", "+", RowBox[List["a", " ", "z"]]]], ")"]]]], "a"]], " ", RowBox[List["Erfc", "[", SqrtBox[FractionBox[RowBox[List[RowBox[List["(", RowBox[List["c", "-", "p"]], ")"]], " ", RowBox[List["(", RowBox[List["b", "+", RowBox[List["a", " ", "z"]]]], ")"]]]], "a"]], "]"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List["c", "-", "p"]], ")"]], " ", SqrtBox[RowBox[List["-", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["c", "+", "p"]], ")"]], " ", RowBox[List["(", RowBox[List["b", "+", RowBox[List["a", " ", "z"]]]], ")"]]]], "a"]]]], " ", RowBox[List["Erfc", "[", SqrtBox[RowBox[List["-", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["c", "+", "p"]], ")"]], " ", RowBox[List["(", RowBox[List["b", "+", RowBox[List["a", " ", "z"]]]], ")"]]]], "a"]]]], "]"]]]]]], ")"]]]], RowBox[List["2", " ", RowBox[List["(", RowBox[List[SuperscriptBox["c", "2"], "-", SuperscriptBox["p", "2"]]], ")"]], " ", SqrtBox[RowBox[List["b", "+", RowBox[List["a", " ", "z"]]]]]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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