Question

求不定积分∫x/(cosx)^2

Answer 1

∫x*(secx)^2 * dx
=∫x * d(tanx)
=x*tanx - ∫tanx *dx
=x*tanx + ∫d(cosx)/cosx
=x*tanx + ln|cosx| + C

Answer 2

∫x/(cosx)^2dx
=∫x (secx)^2dx
=∫xd(tanx)
=xtanx-∫tanxdx
=xtanx+ln|cosx|+C

说明：
∫tanxdx=-∫(1/cosx)d(cosx)=-ln|cosx|+C