Question

∫secxdx=ln|secx+tanx| <<<<求步骤...

Answer 1

∫secxdx
=∫secx(secx+tanx)/(secx+tanx)dx
=∫((secx)^2+secxtanx)/(secx+tanx)dx
=∫1/(secx+tanx)d(secx+tanx)
=ln|secx+tanx|+C

Answer 2

∫secxdx
=∫(1/cosx)dx
=∫[cosx/(cosx)^2]dx
=∫[1/1-(sinx)^2]d(sinx)
=(1/2)∫[1/(1-sinx)+1/(1+sinx)]d(sinx)
=(1/2)[-ln|1-sinx|+ln|1+sinx|]+C
=(1/2)ln|(1+sinx)/(1-sinx)|+C
=ln|secx+tanx|+C