利用分部积分法求{ln[x+(x*x-1)]}的不定积分._数学解答

利用分部积分法求{ln[x+(x*x-1)]}的不定积分.

人气：376 ℃　时间：2020-06-10 13:10:06

解答

∫[log(x + (x^2 - 1)^(1/2))]dx=x*log(x + (x^2 - 1)^(1/2)) -∫x*d[log(x + (x^2 - 1)^(1/2))]=x*log(x + (x^2 - 1)^(1/2))- ∫x/( (x^2 - 1)^(1/2))*dx=x*log(x + (x^2 - 1)^(1/2)) - (x^2 - 1)^(1/2)