What is the result of integrating the expression x^3 - 4x + 1 dx?

What is the result of integrating the expression x^3 - 4x + 1 dx?

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

Answer: (A)

To find the integral of the expression \(x^3 - 4x + 1\) with respect to \(x\), we can apply the basic rules of integration to each term individually. 1. The integral of \(x^3\) is found using the power rule. According to the power rule, the integral of \(x^n\) is \(\frac{1}{n+1}x^{n+1}\). So, for \(x^3\), the integral is \(\frac{1}{3+1}x^{4} = \frac{1}{4}x^4\). 2. The integral of \(-4x\) can also be computed using the power rule. The integral of \(x\) is \(\frac{1}{2}x^2\), thus the integral of \(-4x\) is \(-4 \cdot \frac{1}{2}x^2 = -2x^2\). 3. Finally, the integral of the constant \(1\) is simply \(x\). Combining all these results, we have: \[ \int (x^3 - 4x + 1)

To find the integral of the expression (x^3 - 4x + 1) with respect to (x), we can apply the basic rules of integration to each term individually.

1. The integral of (x^3) is found using the power rule. According to the power rule, the integral of (x^n) is (\frac{1}{n+1}x^{n+1}). So, for (x^3), the integral is (\frac{1}{3+1}x^{4} = \frac{1}{4}x^4).

2. The integral of (-4x) can also be computed using the power rule. The integral of (x) is (\frac{1}{2}x^2), thus the integral of (-4x) is (-4 \cdot \frac{1}{2}x^2 = -2x^2).

3. Finally, the integral of the constant (1) is simply (x).

Combining all these results, we have:

[

\int (x^3 - 4x + 1)