分类：教育/科学-学习帮助
问题：利用分部积分法求∫xln(x
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回答：∫x ln(x-1)dx=x^2/2* ln(x-1)-∫x^2/2ln(x-1)'dx
=x^2/2* ln(x-1)-∫x^2/2(x-1)dx
=x^2/2* ln(x-1)-∫(x^2-x)/2(x-1)dx-∫x/2(x-1)dx
=x^2/2* ln(x-1)-∫x/2dx-∫x/2(x-1)dx
=x^2/2* ln(x-1)-x^2/4-∫x/2(x-1)dx
=x^2/2* ln(x-1)-x^2/4-∫(x-1)/2(x-1)dx-∫1/2(x-1)dx
=x^2/2* ln(x-1)-x^2/4-∫1/2dx-∫1/2(x-1)d(x-1)
=x^2/2* ln(x-1)-x^2/4-x/2-∫1/2(x-1)d(x-1)
=x^2/2* ln(x-1)-x^2/4-x/2-ln(x-1)/2