Question

图中这两个公式的积分过程是怎样的

最好写纸上

Answer 1

secxdx
=∫secx(tanx+secx)dx/(tanx+secx)
=∫(secxtanx+sec²x)dx/(tanx+secx)
=∫d(secx+tanx)/(secx+tanx)
=ln|secx+tanx|+C

∫cscxdx
=∫1/sinx dx
=∫1/[2sin(x/2)cos(x/2)] dx
=∫1/[sin(x/2)cos(x/2)] d(x/2)
=∫1/ [cos^2(x/2) * tan(x/2) ]d(x/2)
=∫sec^2(x/2)/tan(x/2) d(x/2)
=∫1/tan(x/2) d(tan(x/2))
=ln|tan(x/2)|+C
又 tan(x/2)=sin(x/2)/cos(x/2)=2sin^2(x/2)/sinx=[1-(1-2sin^2(x/2))]/sinx=(1-cosx)/sinx=cscx-cotx
所以 ∫cscxdx=ln|cscx-cotx|+C
希望我的回答能帮到你

Answer 2