>>31
∫[0,2π]{(cosθ)^(2n)+2(sinθ)^(2n)}dθ
=∫[-π,π]{(cosθ)^(2n)+2(sinθ)^(2n)}dθ
=2∫[0,π]{(cosθ)^(2n)+2(sinθ)^(2n)}dθ
=2∫[-π/2,π/2]{(sinθ)^(2n)+2(cosθ)^(2n)}dθ
=4∫[0,π/2]{(sinθ)^(2n)+2(cosθ)^(2n)}dθ
=2(B(1/2,n+1/2)+2*B(n+1/2,1/2))
=6*B(1/2,n+1/2)
=6*Γ(1/2)*Γ(n+1/2)/Γ(n+1)
=6*(n-1/2)*(n-3/2)*・・・*(1/2)*{Γ(1/2)}^2/n!
=3π*(2n)!/{2^(2n)*(n!)^2}