令x=asint,则dx=acost dt
∫x²/√(a²-x²) dx
=∫a²sin²t/(acost)·acost dt
=a²∫sin²t dt
=a²∫(1-cos2x)/2 dt
=a²[t-1/4·sin2x]+C
=a²[arcsin(x/a)-1/2·x/a·√(1-x²/x²)]+C
令x=asint,则dx=acost dt
∫x²/√(a²-x²) dx
=∫a²sin²t/(acost)·acost dt
=a²∫sin²t dt
=a²∫(1-cos2x)/2 dt
=a²[t-1/4·sin2x]+C
=a²[arcsin(x/a)-1/2·x/a·√(1-x²/x²)]+C