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The result of the integral \(\int_0^1 x \left(x^3 + k \right)^3 dx\) with \(k = 4\) is approximately \(43.19\).

Would you like more details on how this result was obtained or have any questions?

Here are some related questions to expand your understanding:
1. How would the result change if \(k\) were a different value?
2. What is the process for integrating polynomials like this one step by step?
3. Can this integral be solved using numerical methods instead of symbolic integration?
4. How do we determine if an integral like this converges for different limits?
5. What are some applications of integrals like this in physics or engineering?

**Tip:** When integrating a function raised to a power, it's often useful to expand the terms before attempting the integration, especially for simpler polynomials.

Calcular ∫[0,1] x(x^3 + k)^3 dx con k=4. Escriba su respuesta con dos cifras decimales.

Learn how to solve the definite integral ∫[0,1] x(x^3 + 4)^3 dx using integration techniques and polynomial expansion. This problem covers advanced calculus concepts such as polynomial integration and the fundamental theorem of calculus. The solution is approximately 43.19, with two decimal places.

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