利用分部积分法求{ln[x+(x*x-1)]}的不定积分.

利用分部积分法求{ln[x+(x*x-1)]}的不定积分.
利用分部积分法求{ln[x+(x*x-1)]}的不定积分.

利用分部积分法求{ln[x+(x*x-1)]}的不定积分.
∫[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)