∫(x²)/√(4-x²)dx
令x=2sint
则dx=2costdt
原积分化为
∫[4(sint)^2/2cost]*2costdt
=∫4(sint)^2dt
=∫2(1-cos2t)dt
=2t-∫dsin2t
=2t-sin2t+C
=2arcsin(x/2)-x*√(1-x^2/4)+C
∫(x²)/√(4-x²)dx
令x=2sint
则dx=2costdt
原积分化为
∫[4(sint)^2/2cost]*2costdt
=∫4(sint)^2dt
=∫2(1-cos2t)dt
=2t-∫dsin2t
=2t-sin2t+C
=2arcsin(x/2)-x*√(1-x^2/4)+C