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∫1−x47g(x)eln(f(sin2t)cos2t)dt=1−x74−1−x47\large \int _{ \sqrt [ 7 ]{ 1-{ x }^{ 4 } } }^{ g\left( x \right) }{ { e }^{ \ln (f (\sin ^{ 2 }{ t } ) \cos ^{ 2 }{ t ) } } } dt =\sqrt [ 4 ]{ 1-{ x }^{ 7 } } -\sqrt [ 7 ]{ 1-{ x }^{ 4 } } ∫71−x4g(x)eln(f(sin2t)cos2t)dt=41−x7−71−x4
For the equation given above, where g(x)=1−x74g \left( x \right) =\sqrt [ 4 ]{ 1-{ x }^{ 7 } } g(x)=41−x7 is an invertible function, find f(12)⋅f(13)f \left(\frac 12\right)\cdot f \left(\frac 13\right)f(21)⋅f(31).
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