温馨宠爱文

∫secx dx=∫(dx)/cosx=∫(cosx/cos²x)dx=∫(d
sinx)/(1-sin²x)=(1/2)ln│(1+sinx)/(1-sinx)│+C=(1/2)ln(1+sinx)²/(1-sin²x)+C=(1/2)ln[(1+sinx)/cosx]²+C=ln│secx+tanx│+C
详细的:∫secxdx=∫sec²x/secxdx=∫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