How do you find the integral $ln x / x$ ?

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Answer 1 · 2015-09-12T19:08:24

$int ln x / x = (ln x)^2/2 + C$

$int ln x / x = ?$

This is a classic application of u -substitution.

Let $u = ln x$ . Then $du = 1/x dx$ .

Now we have

$int ln x/x dx = int u du$

We can evaluate this easily by using the power rule:

$int u du = u^2 /2 + C$

Now, substituting back $u$ , we find

$u^2 /2 + C = (ln x)^2/2 + C$

And there is our solution.

$int ln x / x = (ln x)^2/2 + C$

How do you find the integral ln x / xln x / x?