4. \( \int\left(x^{2}+3\right)^{2} d x \)

Calculate the integral \( \int\left(x^{2}+3\right)^{2} dx \). Evaluate the integral by following steps: - step0: Evaluate using formulas and rules: \(\int \left(x^{2}+3\right)^{2} dx\) - step1: Expand the expression: \(\int x^{4}+6x^{2}+9 dx\) - step2: Use properties of integrals: \(\int x^{4} dx+\int 6x^{2} dx+\int 9 dx\) - step3: Evaluate the integral: \(\frac{x^{5}}{5}+\int 6x^{2} dx+\int 9 dx\) - step4: Evaluate the integral: \(\frac{x^{5}}{5}+2x^{3}+\int 9 dx\) - step5: Evaluate the integral: \(\frac{x^{5}}{5}+2x^{3}+9x\) - step6: Add the constant of integral C: \(\frac{x^{5}}{5}+2x^{3}+9x + C, C \in \mathbb{R}\) La integral de \( \int\left(x^{2}+3\right)^{2} dx \) es igual a \( \frac{x^{5}}{5}+2x^{3}+9x + C \), donde \( C \) es una constante real.