积分∫xdx/(1-x^2)^2=多少?
问题描述：
积分∫xdx/(1-x^2)^2=多少?
∫xdx/(1-x^2)^2
^2是平方
答
∫xdx/(1-x²)²
=∫xdx/(1-x)²(1+x)²
=¼∫[1/(1-x)² - 1/(1+x)²]dx
=¼[1/(1-x) + 1/(1+x)] + C
= 1/[2(1-x²)] + C