# How do you use substitution to integrate #(x^2)(sinx^3) #?

Out integral becomes:

Check the answer by differentiating:

Looks good, so that's it.

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To integrate (x^2 \sin(x^3)) using substitution, you can use the following steps:

- Let (u = x^3).
- Calculate (du/dx), which is (3x^2).
- Rearrange the equation to solve for (dx), yielding (dx = du/(3x^2)).
- Substitute (u) and (dx) into the integral, resulting in (\int x^2 \sin(u) \cdot \frac{1}{3x^2} du).
- Simplify the expression to (\frac{1}{3} \int \sin(u) du).
- Integrate (\sin(u)) with respect to (u) to get (-\frac{1}{3} \cos(u) + C).
- Finally, substitute back (u = x^3) to get the final answer: (-\frac{1}{3} \cos(x^3) + 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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