Integral ln x dx

Strategy: Use Integration by Parts.
ln(x) dx

set
u = ln(x), dv = dx
then we find
du = (1/x) dx, v = x

substitute

ln(x) dx = u dv

and use integration by parts

= uv - v du

substitute u=ln(x), v=x, and du=(1/x)dx

= ln(x) x - x (1/x) dx
= ln(x) x - dx
= ln(x) x - x + C
= x ln(x) - x + C.

Solar Snake

Image courtesy SDO/NASA

A long loop of plasma that had been snaking around the sun erupted on Monday, and NASA's Solar Dynamics Observatory was on hand to catch the action.
Known as a solar filament, the loop is a cloud of relatively cool gas held aloft by magnetic forces. Such features are unstable, though, and often break away from the sun.
The pictured filament grew extra long, according to NASA: It spanned almost 621,000 miles (a million kilometers) before snapping.

nationalgeographic.com