# How do you find the integral of #x^3 * sqrt(x^2 + 4) dx#?

The simplified answer is here.

Read below for the work.

Now we get:

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There it is.

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To find the integral of (x^3 \sqrt{x^2 + 4} , dx), use the substitution method:

- Let (u = x^2 + 4), then (du = 2x , dx).
- Solve for (x , dx) in terms of (du), which gives (x , dx = \frac{1}{2} du).
- Substitute (u) and (x , dx) in terms of (du) into the integral.
- Simplify the integral in terms of (u).
- Integrate with respect to (u).
- Finally, resubstitute (x^2 + 4) for (u) to find the antiderivative in terms of (x).

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