6. $$ \int_{2}^{5}\left(x^{4}+5 x^{2}+5+9\right) \cdot d x $$ - 7. $$ \int_{0}^{12}\left(5 x^{2}+3\right) \cdot d x $$

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Calculate or simplify the expression $$ \int_{2}^{5}(x^{4}+5x^{2}+5+9)dx $$.
Evaluate the integral by following steps:
- step0: Evaluate using formulas and rules:
  $$\int_{2}^{5} x^{4}+5x^{2}+5+9 dx$$
- step1: Add the numbers:
  $$\int_{2}^{5} x^{4}+5x^{2}+14 dx$$
- step2: Evaluate the integral:
  $$\int x^{4}+5x^{2}+14 dx$$
- step3: Use properties of integrals:
  $$\int x^{4} dx+\int 5x^{2} dx+\int 14 dx$$
- step4: Evaluate the integral:
  $$\frac{x^{5}}{5}+\int 5x^{2} dx+\int 14 dx$$
- step5: Evaluate the integral:
  $$\frac{x^{5}}{5}+\frac{5x^{3}}{3}+\int 14 dx$$
- step6: Evaluate the integral:
  $$\frac{x^{5}}{5}+\frac{5x^{3}}{3}+14x$$
- step7: Return the limits:
  $$\left(\frac{x^{5}}{5}+\frac{5x^{3}}{3}+14x\right)\bigg |_{2}^{5}$$
- step8: Calculate the value:
  $$\frac{4278}{5}$$
Calculate or simplify the expression $$ \int_{0}^{12}(5x^{2}+3)dx $$.
Evaluate the integral by following steps:
- step0: Evaluate using formulas and rules:
  $$\int_{0}^{12} 5x^{2}+3 dx$$
- step1: Evaluate the integral:
  $$\int 5x^{2}+3 dx$$
- step2: Use properties of integrals:
  $$\int 5x^{2} dx+\int 3 dx$$
- step3: Evaluate the integral:
  $$\frac{5x^{3}}{3}+\int 3 dx$$
- step4: Evaluate the integral:
  $$\frac{5x^{3}}{3}+3x$$
- step5: Return the limits:
  $$\left(\frac{5x^{3}}{3}+3x\right)\bigg |_{0}^{12}$$
- step6: Calculate the value:
  $$2916$$
La integral de $$ \int_{2}^{5}(x^{4}+5x^{2}+5+9)dx $$ es $$ 855.6 $$ y la integral de $$ \int_{0}^{12}(5x^{2}+3)dx $$ es $$ 2916 $$.
La integral de $$ \int_{2}^{5}(x^{4}+5x^{2}+5+9)dx $$ es $$ 855.6 $$ y la integral de $$ \int_{0}^{12}(5x^{2}+3)dx $$ es $$ 2916 $$.

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