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http://functions.wolfram.com/01.20.21.2274.01
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Integrate[Cosh[d z]/(a + b Cosh[c z])^2, z] ==
(1/2) ((E^((c - d) z) (a (a + Sqrt[a^2 - b^2]) Hypergeometric2F1[(c - d)/c,
1, 2 - d/c, (b E^(c z))/(-a + Sqrt[a^2 - b^2])] +
a (-a + Sqrt[a^2 - b^2]) Hypergeometric2F1[(c - d)/c, 1, 2 - d/c,
-((b E^(c z))/(a + Sqrt[a^2 - b^2]))] +
(-(a^2 - b^2 + a Sqrt[a^2 - b^2])) Hypergeometric2F1[1 - d/c, 2,
2 - d/c, (b E^(c z))/(-a + Sqrt[a^2 - b^2])] -
(-a^2 + b^2 + a Sqrt[a^2 - b^2]) Hypergeometric2F1[1 - d/c, 2, 2 - d/c,
-((b E^(c z))/(a + Sqrt[a^2 - b^2]))]))/(b (a^2 - b^2)^(3/2)
(c - d)) + (E^((c + d) z) (a (a + Sqrt[a^2 - b^2])
Hypergeometric2F1[(c + d)/c, 1, 2 + d/c, (b E^(c z))/
(-a + Sqrt[a^2 - b^2])] + a (-a + Sqrt[a^2 - b^2])
Hypergeometric2F1[(c + d)/c, 1, 2 + d/c,
-((b E^(c z))/(a + Sqrt[a^2 - b^2]))] +
(-(a^2 - b^2 + a Sqrt[a^2 - b^2])) Hypergeometric2F1[(c + d)/c, 2,
2 + d/c, (b E^(c z))/(-a + Sqrt[a^2 - b^2])] -
(-a^2 + b^2 + a Sqrt[a^2 - b^2]) Hypergeometric2F1[(c + d)/c, 2,
2 + d/c, -((b E^(c z))/(a + Sqrt[a^2 - b^2]))]))/
(b (a^2 - b^2)^(3/2) (c + d)))
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</mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> c </mi> <mo> - </mo> <mi> d </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <msup> <mi> ⅇ </mi> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> c </mi> <mo> - </mo> <mi> d </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mi> z </mi> </mrow> </msup> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> - </mo> <mrow> <mo> ( </mo> <mrow> <msup> <mi> a </mi> <mn> 2 </mn> </msup> <mo> + </mo> <mrow> <msqrt> <mrow> <msup> <mi> a </mi> <mn> 2 </mn> </msup> <mo> - </mo> <msup> <mi> b </mi> <mn> 2 </mn> </msup> </mrow> </msqrt> <mo> ⁢ </mo> <mi> a </mi> </mrow> <mo> - </mo> <msup> <mi> b </mi> <mn> 2 </mn> </msup> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ⁢ </mo> <semantics> <mrow> <mrow> <msub> <mo>   </mo> <mn> 2 </mn> </msub> <msub> <mi> F </mi> <mn> 1 </mn> </msub> </mrow> <mo> ⁡ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mn> 1 </mn> <mo> - </mo> <mfrac> 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c </ci> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> 2 </cn> <apply> <plus /> <apply> <times /> <ci> d </ci> <apply> <power /> <ci> c </ci> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <ci> b </ci> <apply> <power /> <exponentiale /> <apply> <times /> <ci> c </ci> <ci> z </ci> </apply> </apply> <apply> <power /> <apply> <plus /> <apply> <power /> <apply> <plus /> <apply> <power /> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> a </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> a 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</apply> <apply> <power /> <apply> <plus /> <ci> a </ci> <apply> <power /> <apply> <plus /> <apply> <power /> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </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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