求x^2/(1+x-x^2)^1/2的不定积分,

Question

求x^2/(1+x-x^2)^1/2的不定积分,

Answer 1

∫ x²/√(1 + x - x²) dx= ∫ x²/√[5/4 - (x - 1/2)²] dx令x - 1/2 = ρ,a² = 5/4= ∫ (ρ + 1/2)²/√(a² - ρ²) dρ令ρ = asinz,dρ = acosz dz= ∫ (asinz + 1/2)²...