# Integral of ln²(x)

In this post I will show you how to find the anti-derivative of the function *f*(*x*)=ln²(*x*).

We are going to use integration by parts:

Now we can write *u* times *v* minus the integral of *v* times d*u*:

Let’s bring out the 2 (linearity); also, the two *x*‘s will cancel out.

We saw here that the integral of ln(*x*) is equal to *x*ln(*x*)-*x*, therefore:

If you want, you can factor out the *x*:

Finally,

That’s it!

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