Question

How do you integrate `int ln(x)/x dx` using integration by parts?

Answer 1

`intln(x)/xdx = ln(x)^2/4`

Explanation:

Integration by parts is a bad idea here, you will constantly have `intln(x)/xdx` somewhere. It is better to change the variable here because we know that the derivative of `ln(x)` is `1/x`.

We say that `u(x) = ln(x)`, it implies that `du = 1/xdx`. We now have to integrate `intudu`.

`intudu = u^2/2` so `intln(x)/xdx = ln(x)^2/2`