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

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

• A. (x^5 - x^3 + 7x) + C
• B. (5/6)x^6 - (1/3)x^3 + 7x + C
• C. (1/5)x^5 - (1/3)x^3 + 7x + C
• D. (x^5 + 3x^2 + 7) + C

Answer: (A)

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

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