Evaluate the integral ∫ (3x^2 + 1) dx.

Evaluate the integral ∫ (3x^2 + 1) dx.

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

Answer: (A)

To evaluate the integral ∫ (3x^2 + 1) dx, we can apply the power rule of integration, which states that the integral of x^n is (1/(n+1))x^(n+1) + C, where C is the constant of integration. For the term 3x^2, we recognize that we can factor the 3 out and integrate x^2. The integral becomes: ∫ (3x^2 + 1) dx = ∫ 3x^2 dx + ∫ 1 dx. Now, applying the power rule: 1. The integral of 3x^2 is: ∫ 3x^2 dx = 3 * (1/(2 + 1)) x^(2 + 1) = 3 * (1/3) x^3 = x^3. 2. The integral of 1 is: ∫ 1 dx = x. Combining these results gives us the full expression: ∫ (3x^2 + 1) dx = x^3 + x + C. This confirms that the evaluated integral is indeed x^3 + x + C. Thus, the correct

To evaluate the integral ∫ (3x^2 + 1) dx, we can apply the power rule of integration, which states that the integral of x^n is (1/(n+1))x^(n+1) + C, where C is the constant of integration.

For the term 3x^2, we recognize that we can factor the 3 out and integrate x^2. The integral becomes:

∫ (3x^2 + 1) dx = ∫ 3x^2 dx + ∫ 1 dx.

Now, applying the power rule:

1. The integral of 3x^2 is:

∫ 3x^2 dx = 3 * (1/(2 + 1)) x^(2 + 1) = 3 * (1/3) x^3 = x^3.

2. The integral of 1 is:

∫ 1 dx = x.

Combining these results gives us the full expression:

∫ (3x^2 + 1) dx = x^3 + x + C.

This confirms that the evaluated integral is indeed x^3 + x + C. Thus, the correct