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http://functions.wolfram.com/01.20.21.2356.01
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Integrate[Sqrt[(a + b Cosh[2 c z])^3] Cosh[c z], z] ==
(Sqrt[(a + b Cosh[2 c z])^3]
(3 Sqrt[2] (a + b)^2 ArcTanh[(Sqrt[2] Sqrt[b] Sinh[c z])/
Sqrt[a + b Cosh[2 c z]]] + 2 Sqrt[b] Sqrt[a + b Cosh[2 c z]]
(5 a + 3 b + 2 b Cosh[2 c z]) Sinh[c z]))/
(16 Sqrt[b] c (a + b Cosh[2 c z])^(3/2))
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</mi> </msqrt> <mo> ⁢ </mo> <msqrt> <mrow> <mi> a </mi> <mo> + </mo> <mrow> <mi> b </mi> <mo> ⁢ </mo> <mrow> <mi> cosh </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> c </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </msqrt> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 5 </mn> <mo> ⁢ </mo> <mi> a </mi> </mrow> <mo> + </mo> <mrow> <mn> 3 </mn> <mo> ⁢ </mo> <mi> b </mi> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <mrow> <mi> cosh </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> c </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> sinh </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> c </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> / </mo> <mrow> <mo> ( </mo> <mrow> <mn> 16 </mn> <mo> ⁢ </mo> <msqrt> <mi> b </mi> </msqrt> 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Date Added to functions.wolfram.com (modification date)
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