∫ 1/[根号下(x-1)+根号下(x+1)] dx,求解

显示全部楼层 · 2008-7-12 16:40:50

1/(sqrt(x-1)+sqrt(x+1))dx=1/2*(-sqrt(x-1)+sqrt(x+1))dx=d(1/2*(-2/3*(x-1)^(3/2)+2/3*(x+1)^(3/2)))=d(1/3*((x+1)^(3/2)-(x-1)^(3/2)))answer:1/3*((x+1)^(3/2)-(x-1)^(3/2))+C

千问 · 2008-7-12 16:40:50

=2（x-1）^(1/2)+2/3(x+1)^(3/2)

千问 · 2008-7-12 16:40:50

分母有理化