Evaluate ln((x^2)-1)^(1/2) dx

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Evaluateln((x^2)-1)^(1/2)dxEvaluateln((x^2)-1)^(1/2)dxEvaluateln((x^2)-1)^(1/2)dxln((x^2)-1)^(1/2)dx

Evaluate ln((x^2)-1)^(1/2) dx
Evaluate ln((x^2)-1)^(1/2) dx

Evaluate ln((x^2)-1)^(1/2) dx
ln((x^2)-1)^(1/2) dx=(1/2)ln(x+1)(x-1)dx=(1/2)[ln(x+1)+ln(x-1)]dx
=(1/2)[ln(x+1)dx+ln(x-1)dx]
=(1/2)[ln(x+1)d(x+1)+ln(x-1)d(x-1)]
=(1/2)[d(x+1)ln(x+1)-(x+1)dln(x+1)+d(x-1)ln(x-1)-(x-1)dln(x-1)]
=(1/2)[d(x+1)ln(x+1)-dx+d(x-1)ln(x-1)-dx]
=(1/2)[d(x+1)ln(x+1)+d(x-1)ln(x-1)]-dx
我是把上式当做微分来求的,可以表示为以上几个函数的微分形式,当然如果有积分期间就可以直接代入求定积分了