ArcSinh[(2 Sqrt[1 - z^2])/z^2] == (z/(2 Sqrt[-(1/z^2)] Sqrt[-z^4 + 3 z^2 - 2])) Sqrt[(1 - z^2)/z^4] Sqrt[z^2 - 2] (Pi ((z^3/(1 - z^2)) Sqrt[(1 - z^2)/z^2] Sqrt[(1 - z^2)/z^4] + Sqrt[1/z^2] z - Sqrt[z/(z + Sqrt[2])] Sqrt[(z + Sqrt[2])/z] Sqrt[1/z] Sqrt[z] + Sqrt[(z - Sqrt[2])/z] Sqrt[z/(z - Sqrt[2])] Sqrt[-(1/z)] Sqrt[-z] - 2) + 4 ArcSec[z])

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<mrow> <msup> <mi> sec </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <arcsinh /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <apply> <times /> <ci> z </ci> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> 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2003-08-21