$$ \int 3 y d y $$ 6. $$ \int\left(8 x^{3}-4 x\right) d x $$ 7. $$ \int\left(9 x^{4}-6 x^{2}+5\right) d x $$

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**1) Calcular $$ \int 3y\,dy $$:**

- Extraemos la constante:

$$
\int 3y\,dy = 3\int y\,dy
$$

- Integramos $$ y $$:

$$
\int y\,dy = \frac{y^2}{2}
$$

- Sustituyendo:

$$
3\cdot\frac{y^2}{2} = \frac{3y^2}{2}+C
$$

---

**2) Calcular $$ \int \left(8x^3-4x\right)dx $$:**

- Separamos en dos integrales:

$$
\int \left(8x^3-4x\right)dx = \int 8x^3\,dx - \int 4x\,dx
$$

- Integramos cada término:

- Para $$ 8x^3 $$:

$$
  \int 8x^3\,dx = 8\cdot \frac{x^4}{4} = 2x^4
  $$

- Para $$ 4x $$:

$$
  \int 4x\,dx = 4\cdot \frac{x^2}{2} = 2x^2
  $$

- Combinando los resultados:

$$
2x^4-2x^2+C
$$

---

**3) Calcular $$ \int \left(9x^4-6x^2+5\right)dx $$:**

- Separamos la integral:

$$
\int \left(9x^4-6x^2+5\right)dx = \int 9x^4\,dx - \int 6x^2\,dx + \int 5\,dx
$$

- Integramos cada término:

- Para $$ 9x^4 $$:

$$
  \int 9x^4\,dx = 9\cdot \frac{x^5}{5} = \frac{9x^5}{5}
  $$

- Para $$ 6x^2 $$:

$$
  \int 6x^2\,dx = 6\cdot \frac{x^3}{3} = 2x^3
  $$

- Para $$ 5 $$:

$$
  \int 5\,dx = 5x
  $$

- Combinando los resultados:

$$
\frac{9x^5}{5} - 2x^3+5x+C
$$
**1) $$ \int 3y\,dy = \frac{3y^2}{2} + C $$** **2) $$ \int \left(8x^3 - 4x\right)dx = 2x^4 - 2x^2 + C $$** **3) $$ \int \left(9x^4 - 6x^2 + 5\right)dx = \frac{9x^5}{5} - 2x^3 + 5x + C $$**

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