Integration At Its Best

Calculus Level 5

(01x2dx1x4)(01dx1+x4) \displaystyle \left( \int _{ 0 }^{ 1 }{ \dfrac { { x }^{ 2 }\cdot dx }{ \sqrt { 1-{ x }^{ 4 } } } } \right) \cdot \left( \int _{ 0 }^{ 1 }{ \dfrac { dx }{ \sqrt { 1+{ x }^{ 4 } } } } \right)

The value of the expression above can be expressed in the form of πβγ.\dfrac { \pi }{ \beta \sqrt { \gamma } } . Find βγ.{ \beta }^{ \gamma }.

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