有理函数的积分
问题描述：
有理函数的积分
2011李永乐复习全书p73,Im=∫[1/(t^2+a^2)^m ]dt,怎么用分部积分推导出递推公式呢?
答
Im=∫[1/(t^2+a^2)^m ]dt=(∫[a^2/(t^2+a^2)^m ]dt)/a^2=(∫[(a^2+t^2-t^2)/(t^2+a^2)^m ]dt)/a^2=Im-1/a^2 -(∫[t^2)/(t^2+a^2)^m ]dt)/a^2=Im-1/a^2 -(∫[t/(t^2+a^2)^m ]d(t^2+a^2))/2a^2=Im-1/a^2 +t/(t^2+a^2)^...