设x=asect,dx=asecttantdt原式=∫asecttantdt/(atant)^3=1/a^2∫dt/sintcost=1/a^2∫2dt/sin2t=1/a^2∫2csc2tdt=1/a^2ln|tant|+C=1/a^2ln|√(x/a)^2-1|+C=1/2a^2ln|x^2-a^2|+C