# How do I evaluate #int(ln(3x))^2 dx#?

Your integral becomes:

Which can now be solved by parts (twice).

By parts you have:

Where:

The integral becomes:

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To evaluate (\int (\ln(3x))^2 , dx), you can use integration by parts, where (u = (\ln(3x))^2) and (dv = dx). After differentiation and integration, the integral simplifies to (\frac{1}{3}x(\ln(3x))^2 - \frac{2}{3} \int \ln(3x) , dx). You can then integrate (\int \ln(3x) , dx) using substitution.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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