对1/根号下1+x^2积分,解了半天没解出来

Question

对1/根号下1+x^2积分,解了半天没解出来

Answer 1

令x=tanaa=arctanxseca=√(x²+1)1+x²=sec²adx=sec²ada原式=∫sec²ada/seca=∫secada=∫(1/cosa)da=∫[cosa/cos²a]da=∫d(sina)/(1-sin²a)=(1/2)∫[1/(1-sina)+1/(1+sina)]d(sina...