求In(1+r^2)rdr的积分
问题描述：
求In(1+r^2)rdr的积分
答
∫In(1+r^2)rdr=(1/2)∫In(1+r^2)d(1+r^2)
=(1+r^2)ln(1+r^2)/2-(1/2)∫d(1+r^2) (应用分部积分法)
=(1+r^2)ln(1+r^2)/2-(1+r^2)/2+C (C是积分常数)
=(1+r^2)[ln(1+r^2)-1]/2+C.