3. $$ \int_{1}^{5}\left(x^{3}+18 x\right) d x $$

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Calculate the integral $$ \int_{1}^{5}\left(x^{3}+18 x\right) d x $$.
Evaluate the integral by following steps:
- step0: Evaluate using formulas and rules:
  $$\int_{1}^{5} x^{3}+18x dx$$
- step1: Evaluate the integral:
  $$\int x^{3}+18x dx$$
- step2: Use properties of integrals:
  $$\int x^{3} dx+\int 18x dx$$
- step3: Evaluate the integral:
  $$\frac{x^{4}}{4}+\int 18x dx$$
- step4: Evaluate the integral:
  $$\frac{x^{4}}{4}+9x^{2}$$
- step5: Return the limits:
  $$\left(\frac{x^{4}}{4}+9x^{2}\right)\bigg |_{1}^{5}$$
- step6: Calculate the value:
  $$372$$
La integral de $$ \int_{1}^{5}\left(x^{3}+18 x\right) d x $$ es igual a 372.
La integral de $$ \int_{1}^{5}\left(x^{3}+18 x\right) d x $$ es 372.

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