不定积分x^2/(a^2-x^2)^1/2dx怎么求求过程

Question

不定积分x^2/(a^2-x^2)^1/2 dx怎么求 求过程

Answer 1

=∫a^2(x/a)^2/(1-(x/a)^2)^0.5dx/ax/a=sin(t)=∫a^2sin^2(t)/cos(t)dsin(t)=a^2∫sin^2(t)dt=a^2∫(1/2-(1-2sin^2(t))/2)dt= a^2∫(1/2dt-a^2∫cos(2t))/4)d2t= a^2(t-sin(2t)/4)+Ct=arcsin(x/a)= a^2(t-sin(2t)/4)...