设 ∫ f(x)dx=x^2 c求 ∫ xf(1-x^2)dx

∫ f(x)dx＝x^2＋C，求 ∫ xf(1-x^2)dx∫ xf(1-x^2)dx＝－1/2×∫ f(1-x^2) d(1-x^2)＝－1/2×(1－x^2)^2＋C