sec 与csc的原函数

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

原题应是: ∫cscxdx=?
∫cscxdx=∫(1/sinx)dx
=∫(1/(2sin(x/2)cos(x/2)))dx
=∫(1/(tan(x/2))dtan(x/2)
=ln|tan(x/2)|+C