Integral of ln²(x)

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

In red: f(x)=ln²(x); in blue F(x)

We are going to use integration by parts:

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

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 xln(x)-x, therefore:

If you want, you can factor out the x:

Finally,

That’s it!

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