不定积分 ：∫ x^2/√a^2-x^2 dx

设x=asint,dx=acostdt
原式=∫(asint)^2*acostdt/acost
=∫a^2sin^2tdt
=a^2/2∫(1-cos2t)dt
=a^2/2(t-1/2sin2t)+C
=a^2/2[arcain(x/a)-(x/a)√(1-(x/a)^2)]+C
=a^2/2*arcsin(x/a)-x/2*√(a^2-x^2)+C