第1个回答 2012-12-29
∵∫ sec^3(x) dx = ∫ secx d( tanx) =secx tanx - ∫ tan^2 (x) secx dx
= secx tanx - ∫ (sec^2(x) - 1 ) secx dx
=secx tanx - ∫ (sec^3(x)dx+∫ secx dx
∴∫ sec^3(x)dx=1/2 secx tanx +1/2∫ secx dx
=1/2 secx tanx +1/2∫[sec^2(x)+secxtanx]/(secx+tanx)dx
=1/2 secx tanx +1/2ln|secx+tanx|+C本回答被提问者采纳