求它的不定积分，先拆项后凑微分

Answer 1

设 2x = 3sint，则 dx = 3/2*cost*dt
∫(1-x)/√(9-4x^2) dx
=∫(1-3/2*sint)/√[9-(3sint)^2] * 3/2*cost*dt
=3/2*∫(1-3/2*sint)/(3cost) * cost*dt
=1/2*∫(1-3/2*sint)*dt
=1/2* t -3/4*∫sint*dt
=1/2*t + 3/4*cost + C
=1/2*arcsin(2x/3) + 3/4*√[1-(2x/3)^2] + C
=1/2*arcsin(2x/3) + 1/4 * √(9 - 4x^2) + C

Answer 2