∫(1-x)^2/xdx=?
问题描述：
∫(1-x)^2/xdx=?
答
∫(1-x)^2/xdx
=∫(1/x-2+x)dx
=lnx-2x+x^2/2+C呵呵 问错了 把2改成1/2那要用换元了 令(1-x)^(1/2)=t x=1-t^2,dx=-2tdt ∫(1-x)^2/xdx =∫(1-x)^(1/2)/xdx =∫t*(-2t)/(1-t^2)dt =∫[2-2/(1-t^2)]dt =∫[2+1/(t-1)-1/(t+1)]dt =2t+ln(t-1)-ln(t+1)+C