The expression you provided appears to be an integral with a rational function in the integrand. The expression inside the integral is:

$\int \frac{x + 2}{x^3 \sqrt{x^4}} \, dx.$

We can simplify this function and proceed with solving the integral. Here's how:

1. Simplify the denominator. Since $\sqrt{x^4} = x^2$, the expression becomes: $\int \frac{x + 2}{x^3 \cdot x^2} \, dx = \int \frac{x + 2}{x^5} \, dx.$

2. Now, split the fraction into two simpler terms: $\int \frac{x}{x^5} \, dx + \int \frac{2}{x^5} \, dx = \int x^{-4} \, dx + 2 \int x^{-5} \, dx.$

3. Integrate each term: $\int x^{-4} \, dx = \frac{x^{-3}}{-3} = -\frac{1}{3x^3},$ $2 \int x^{-5} \, dx = 2 \cdot \frac{x^{-4}}{-4} = -\frac{1}{2x^4}.$

4. Combine the results: $-\frac{1}{3x^3} - \frac{1}{2x^4} + C.$

This is the solution to the integral.

Would you like more details or have any questions about this? Here are some related topics you might find interesting:

1. How to handle integrals with square roots in the denominator.
2. The power rule for integration.
3. Understanding fractional exponents in integrals.
4. Techniques for simplifying complex integrals.
5. How to integrate rational functions with higher powers in the denominator.

Tip: Always simplify the integrand as much as possible before attempting the integration!