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Calculus Level 3

\(a\neq 0,\)

\(\int _{ 0 }^{ a^{-\frac{1}{6}} }{ \frac { \tan{(\cos^{-1}{x})}(\frac { a+x }{ \sqrt [ 3 ]{ a^{ 2 } } -\sqrt [ 3 ]{ x^{ 2 } } } -\sqrt[6]{x}(\sqrt[6]{a}-\sqrt[6]{x})+\frac { \sqrt [ 3 ]{ ax^{ 2 } } -\sqrt [ 3 ]{ a^{ 2 }x } }{ \sqrt [ 3 ]{ a^{ 2 } } -2\sqrt [ 3 ]{ ax } +\sqrt [ 3 ]{ x^{ 2 } } } )(\sqrt { \sqrt { 2 } -1 } \sqrt [ 4 ]{ 3+2\sqrt { 2 } } +\sqrt [ 3 ]{ (x+12)\sqrt { 2 } -6x-8 } )x}{(\frac{x-\sqrt{x}}{\sqrt{x}-1}-\sqrt{\sqrt{2}+1}\sqrt[4]{3-2\sqrt{2}}) \sqrt{1-x^2}(\sqrt[6]a-\sqrt[6]{x}) } dx}\)

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