令x=asecm
则分子=atanm
dx=a*secmtanmdm
secm=x/a
cosm=a/x
所以m=arccos(a/x)
(tanm)^2=x^2/a^2-1=(x^2-a^2)/a^2
所以tanm=√(x^2-a^2)/a
所以原式=∫(atanm/asecm)a*secmtanmdm
=∫a(tanm)^2dm
=a∫[(secm)^2-1]dm
=a∫(secm)^2dm-a∫dm
=atanm-am+C
=√(x^2-a^2)-a*arccos(a/x)+C