Indefinite integration of ln(x) ?

Question

Please explain.

Answer 1

Use the formula of integration by parts,

Int(u dv) = u*v - Int(v du)

Set u=ln(x), dv=dx --> du = (1/x)*dx, v=x.
Then, u*v = x*ln(x) and v du = dx, so

Int(ln(x) dx) = x*ln(x) - Int(dx) = x*ln(x) - x .

You can also add any constant to the result.
This is how you must do these kinds of integrals, and also for inverse trigonometric functions, such as arcsin(x) and arccos(x).

Answer 2

1/x

natural log and 1/x are related functions ... accually they are inverses.


the indefinate part just means it is a general form and that is where there is no real values put into it.
they are asking for you to find the general form of the area underneath the graph of ln(x) form some unknown point to another unknown point.