|x|

Column 2|x|x/2
xdx=sign(x)xdx=uvvdu=xxxdx\int |x| dx=\int sign(x)xdx=uv-\int vdu=|x|x-\int|x|dx
u=xdx,dv=sign(x)dx;du=dx,v=xu=xdx, dv=sign(x)dx; du=dx, v=|x|
2xdx=xx,x=xx22\int|x|dx=|x|x, \int |x|=\frac{|x|x}{2}

Also

https://www.youtube.com/watch?v=X2OYT2vByPQ