先算一下1/sinx原函数
S表示积分号
S1/sinxdx
=S1/(2sin(x/2)cos(x/2))dx
=S1/[tan(x/2)cos²(x/2)]d(x/2)
=S1/[tan(x/2)]d(tan(x/2))
=ln|tan(x/2)|+C
因为tan(x/2)=sin(x/2)/cos(x/2)=2sin²(x/2)/[2sin(x/2)cos(x/2)]=(1-cosx0/sinx=cscx-cotx
所以S1/sinxdx=ln|cscx-cotx|+C
S1/cosxdx
=S1/sin(x+派/2)d(x+派/2)
=ln|csc(x+派/2)-cot(x+派/2)|+C
=ln|secx+tanx|+C
∫1/cosxdx
=∫secx(secx+tanx)/(secx+tanx)dx
=∫1/(secx+tanx)d(secx+tanx)
=ln/secx+tanx/+C
/secx+tanx/是secx+tanx的绝对值
y=1/cosx
x=arccos(1/y)
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