∫ x^2/√( 1-x^4 ) dx ( x = 0〜1 )
=
( 1/2 )∫ x/√( x-x^3 ) dx ( x = 0〜1 )
=
A.G.M.( 1 , √2 )/2
∫ 1/√( 1+x^4 ) dx ( x = 0〜1 )
=
( 1/2 )∫ 1/√( x+x^3 ) dx ( x = 0〜1 )
=
ω/2√2
∫ x^2/√( 1+x^4 ) dx ( x = 0〜1 )
=
( 1/2 )∫ x/√( x+x^3 ) dx ( x = 0〜1 )
=
( 2-A.G.M.( 1 , √2 ) )/2√2