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. Q.E.D.

Free math lessons and math homework help from basic math to algebra, geometry and beyond. Students, teachers, parents, and everyone can find solutions to their math problems instantly.

The natural logarithm (ln) Another important use of e is as the base of a logarithm. When used as the base for a logarithm, we use a different notation. Rather than writing we use the notation ln(x).This is called the natural logarithm and is read phonetically as “el in of x”. Just because it is written differently does not mean we treat it differently than other logarithms.