# How do you integrate by substitution #int u^2sqrt(u^3+2)du#?

The answer is

Let's do the substitution,

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To integrate ( \int u^2 \sqrt{u^3 + 2} , du ) by substitution:

- Let ( w = u^3 + 2 ), then ( dw = 3u^2 , du ).
- Rewrite the integral in terms of ( w ): [ \int u^2 \sqrt{u^3 + 2} , du = \frac{1}{3} \int \sqrt{w} , dw ]
- Integrate ( \sqrt{w} ) with respect to ( w ).
- Substitute back ( w = u^3 + 2 ) to obtain the final result.

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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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