令x=2sint,dx=2costdt
代入原式得：=∫4sint^2.2cost.2costdt
=16∫sint^2.cost^2dt
=4∫sin2t^2dt
=4∫[1-(cos4t-1)/2]dt
=6t-sin4t/2+c
t=arcsinx/2代入,得
2arcsin(x/2)-x/2*√(4-x^2)+C
令x=2sint,dx=2costdt
代入原式得：=∫4sint^2.2cost.2costdt
=16∫sint^2.cost^2dt
=4∫sin2t^2dt
=4∫[1-(cos4t-1)/2]dt
=6t-sin4t/2+c
t=arcsinx/2代入,得
2arcsin(x/2)-x/2*√(4-x^2)+C