设 x = 2sint,则 dx = 2cost*dt
∫x^2*√(4-x^2) *dx
=∫(2sint)^2 * (2cost) * (2cost)*dt
=16*∫(sint)^2 * (cost)^2 *dt
=4*∫(2sint*cost)^2 *dt
=4*∫(sin2t)^2 *dt
=2*∫[2*(sin2t)^2] *dt
=2*∫[1 - cos4t] *dt
=2∫dt - 2∫cos4t*dt
=2t - 1/2*∫cos4t*d(4t)
=2t - 1/2*sin4t + C
=2t - sin2t *cos2t + C
=2t - 2sint*cost*[1 - 2(sint)^2] + C
=2arcsin(x/2) - x/2*√(4 - x^2).*(1-x^2/2) + C