请问图中步骤是怎么得到的?
展开全部
∫sec³θdθ=∫sec²θ·secθdθ
=∫secθd(tanθ)
=secθ·tanθ-∫tanθd(secθ)
=secθ·tanθ-∫tanθ·tanθ·secθdθ
=secθ·tanθ-∫tan²θsecθdθ
=secθ·tanθ-∫(sec²θ-1)secθdθ
=secθ·tanθ-∫sec³θdθ+∫secθdθ
所以,2∫sec³θdθ=secθ·tanθ+∫secθdθ
那么,4∫sec³θdθ=2(secθ·tanθ+∫secθdθ)=2secθ·tanθ+2∫secθdθ
=∫secθd(tanθ)
=secθ·tanθ-∫tanθd(secθ)
=secθ·tanθ-∫tanθ·tanθ·secθdθ
=secθ·tanθ-∫tan²θsecθdθ
=secθ·tanθ-∫(sec²θ-1)secθdθ
=secθ·tanθ-∫sec³θdθ+∫secθdθ
所以,2∫sec³θdθ=secθ·tanθ+∫secθdθ
那么,4∫sec³θdθ=2(secθ·tanθ+∫secθdθ)=2secθ·tanθ+2∫secθdθ
推荐律师服务:
若未解决您的问题,请您详细描述您的问题,通过百度律临进行免费专业咨询