令x=2sint,则dx=2cost dt ∫(x²+1)/√(4-x²) dx =∫(4sin²t+1)/2cost ·2costdt =∫(4sin²t+1) dt =2∫2sin²t dt+∫dt =2∫(1-cos2t) dt+∫ dt =2[t-(sin2t)/2]+t+C =3t-sin2t+C =3arcsin(x/2)-x·√(1-x²/4)+C
