Foolish invertible g(x) !!

Calculus Level 4

1x47g(x)eln(f(sin2t)cos2t)dt=1x741x47\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 } }

For the equation given above, where g(x)=1x74g \left( x \right) =\sqrt [ 4 ]{ 1-{ x }^{ 7 } } is an invertible function, find f(12)f(13)f \left(\frac 12\right)\cdot f \left(\frac 13\right).


This is part of the set Foolish Things
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