19.6.1.14 Lebesgue Measure and Integration

Condition: Find the integral of the Lebaga \ (\ int _ {[0; 2]} f d \ mu \ quad \) from the function \ (f (x) = \ left \ {\ begin {aligned} x^{5}, {if} x \ text {rational, {rational, {rational, {rational, {rational, {rational. } \\ X, & \ Text {if} X \ Text {irrational algebraic,} \\ x^{2}, \ text {if} x \ text {transcendental.