一般怎么可以看出一个按摩店是不是正经的？

∫(x 1 1-2√(x 1))/(x 1-1)dx

=∫(x 2-2√(x 1))/xdx

=∫1 2/x-2√(x 1))/xdx

=x 2ln|x|-2∫√(x 1))/xdx

x=tan2t

dx=2sec2t*tantdt

∫√(x 1))/xdx

=∫(sect/tan2t)(2sec2ttant)dt

=∫2sec3t/tantdt

=2∫sint/cos^4tdt

=-2/3cos3t C

=(-2/3)(sec3t) C

=(-2/3)(1 x2)^(3/2) C

带回原式

=x 2ln|x|-2∫√(x 1))/xdx

=x 2ln|x|-2(-2/3)(1 x2)^(3/2) C

=x 2ln|x| (4/3)(1 x2)^(3/2) C