# How do you integrate #int (3-4x)^8# using substitution?

In this problem, we can do a u-substitution.

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To integrate (\int (3-4x)^8) using substitution, follow these steps:

- Let (u = 3-4x).
- Find (du), the differential of (u), by differentiating (u) with respect to (x).
- Substitute (u) and (du) into the integral.
- Integrate the expression in terms of (u).
- Substitute back the original expression in terms of (x).

The integral (\int (3-4x)^8) using substitution becomes:

(\int u^8 \frac{{du}}{{-4}})

Then integrate (u^8 \cdot \frac{{du}}{{-4}}) and substitute back the expression in terms of (x).

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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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