說明一下1/cos(x)=sec(x)

∫secxdx

=∫(1/cosx)dx

=∫cosx/cos²xdx

=∫1/cos²xdsinx

=∫1/(1-sin²x)dsinx

=-∫1/(sinx+1)(sinx-1)dsinx

=-∫[1/(sinx-1)-1/(sinx+1)]/2dsinx

=-[∫1/(sinx-1)dsinx-∫1/(sinx+1)dsinx]/2

=[∫1/(sinx+1)d(sinx+1)-∫1/(sinx-1)d(sinx-1)]/2

=(ln|sinx+1|-ln|sinx-1|)/2+C

=ln√|(sinx+1)/(sinx-1)|+C

=ln√|(sinx+1)²/(sinx+1)(sinx-1)|+C

=ln√|(sinx+1)²/(sin²x-1)|+C

=ln√|-(sinx+1)²/cos²x|+C

=ln|(sinx+1)/cosx|+C

=ln|tanx+1/cosx|+C

=ln|secx+tanx|+C