分类：教育/科学-理工学科-数学
问题：请教一道微分计算?计算∫xln(1+x^2)dx 
计算∫xln(1+x^2)dx
回答：∫xln(1+x^2)dx=(1/2)∫ln(1+x^2)d(x^2)
=(x^2/2)ln(1+x^2)-(1/2)∫x^2dln(1+x^2)
=x^2ln(1+x^2)/2-(1/2)∫x^2[2x/(1+x^2)]dx
=x^2ln(1+x^2)/2-(1/2)∫x^2dx^2/(1+x^2)
=x^2ln(1+x^2)/2-(1/2)∫[(x^2+1)-1]dx^2/(1+x^2)
=x^2ln(1+x^2)/2-(1/2)∫dx^2+(1/2)∫dx^2/(1+x^2)
=x^2ln(1+x^2)/2-x^2/2+(1/2)∫d(x^2+1)/(1+x^2)
=x^2ln(1+x^2)/2-x^2/2+(1/2)ln(1+x^2)
=[(1+x^2)ln(1+x^2)-x^2]/2+C