Find the integral ∫ (5x^4 - 3x^2 + 7) dx.

To find the integral of the function (5x^4 - 3x^2 + 7), we can integrate each term separately using the power rule for integration, which states that (\int x^n , dx = \frac{x^{n+1}}{n+1} + C) for any (n \neq -1).

Starting with the first term, (5x^4):

[

\int 5x^4 , dx = 5 \cdot \frac{x^{4+1}}{4+1} = 5 \cdot \frac{x^5}{5} = x^5.

]

Next, for the term (-3x^2):

[

\int -3x^2 , dx = -3 \cdot \frac{x^{2+1}}{2+1} = -3 \cdot \frac{x^3}{3} = -x^3.

]

Finally, for the constant term (7):

[

\int 7 , dx = 7x.

]

Combining all these results together, we have:

[

\int (5x