What is the result of ∫ (2x^4 + x^3) dx?

What is the result of ∫ (2x^4 + x^3) dx?

• A. (2/5)x^5 + (1/4)x^4 + C
• B. (2/5)x^5 + (2/3)x^4 + C
• C. (1/5)x^5 + (1/4)x^4 + C
• D. (1/3)x^5 + (2/4)x^4 + C

Answer: (A)

To find the integral of the function \(2x^4 + x^3\), we apply the power rule of integration. The power rule states that the integral of \(x^n\) is \(\frac{1}{n+1}x^{n+1} + C\), where \(C\) is the constant of integration. Starting with the first term \(2x^4\), we apply the power rule: \[ \int 2x^4 \, dx = 2 \cdot \frac{1}{4 + 1}x^{4 + 1} = 2 \cdot \frac{1}{5}x^5 = \frac{2}{5}x^5. \] Next, we integrate the second term \(x^3\): \[ \int x^3 \, dx = \frac{1}{3 + 1}x^{3 + 1} = \frac{1}{4}x^4. \] Combining these results, we get: \[ \int (2x^4 + x^3) \, dx = \frac{2}{5}x^5 + \frac{

To find the integral of the function (2x^4 + x^3), we apply the power rule of integration. The power rule states that the integral of (x^n) is (\frac{1}{n+1}x^{n+1} + C), where (C) is the constant of integration.

Starting with the first term (2x^4), we apply the power rule:

[

\int 2x^4 , dx = 2 \cdot \frac{1}{4 + 1}x^{4 + 1} = 2 \cdot \frac{1}{5}x^5 = \frac{2}{5}x^5.

]

Next, we integrate the second term (x^3):

[

\int x^3 , dx = \frac{1}{3 + 1}x^{3 + 1} = \frac{1}{4}x^4.

]

Combining these results, we get:

[

\int (2x^4 + x^3) , dx = \frac{2}{5}x^5 + \frac{