设 x = asint,dx = a cost dt,t = arcsin(x/a)
则：
∫x^2/√(a^2-x^2) dx
=∫a^2*(sint)^2 * acost dt/(acost)
=a^2*∫(sint)^2 dt
=a^2/2*∫(1-cos2t)dt 注：cos2t = 1 - 2(sint)^2
=a^2/2*[t - ∫cos2tdt]
=a^2*t/2 - a^2/4*∫cos2t*d(2t)
=a^2*t/2 -a^2/4*sin2t + C
=a^2*arcsin(x/a)/2 -a^2/2 * sint*cost + C
=a^2*arcsin(x/a)/2 - x*√(a^2-x^2)/2 + C