求不定积分∫x⼀(cosx)^2

2024-12-02 10:33:04
推荐回答(2个)
回答1:

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

回答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