# How do you find the integral of #6x ln x dx #?

I found:

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To find the integral of (6x \ln(x) , dx), you can use integration by parts. Let (u = \ln(x)) and (dv = 6x , dx). Then, (du = \frac{1}{x} , dx) and (v = 3x^2).

Applying the integration by parts formula:

[\int u , dv = uv - \int v , du]

Substituting the values:

[\int 6x \ln(x) , dx = 3x^2 \ln(x) - \int 3x^2 \cdot \frac{1}{x} , dx]

Simplify the integral:

[\int 6x \ln(x) , dx = 3x^2 \ln(x) - \int 3x , dx]

Now integrate the remaining term:

[\int 6x \ln(x) , dx = 3x^2 \ln(x) - \frac{3}{2}x^2 + C]

Where (C) is the constant of integration.

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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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