Evaluate the integral ∫ (x^4 + x^2 + 1) dx.

Evaluate the integral ∫ (x^4 + x^2 + 1) dx.

• A. (1/5)x^5 + (1/3)x^3 + x + C
• B. (1/5)x^5 + (1/2)x^2 + C
• C. (1/6)x^6 + (1/3)x^3 + C
• D. (1/4)x^4 + (1/2)x^2 + x + C

Answer: (A)

To evaluate the integral ∫ (x^4 + x^2 + 1) dx, we can apply the power rule for integration, which states that ∫ x^n dx = (1/(n+1)) x^(n+1) + C, where C is the constant of integration. Let's break down the integral into its components: 1. For the term x^4: - Applying the power rule, we have ∫ x^4 dx = (1/(4+1)) x^(4+1) = (1/5)x^5. 2. For the term x^2: - Again applying the power rule, ∫ x^2 dx = (1/(2+1)) x^(2+1) = (1/3)x^3. 3. For the constant term 1: - The integral of 1 is simply x, since ∫ 1 dx = x. Now, we can combine all these results: - From x^4, we get (1/5)x^5. - From x^2, we obtain (1/3)x^3. - From the constant 1, we add x. Putting it all together

To evaluate the integral ∫ (x^4 + x^2 + 1) dx, we can apply the power rule for integration, which states that ∫ x^n dx = (1/(n+1)) x^(n+1) + C, where C is the constant of integration.

Let's break down the integral into its components:

1. For the term x^4:

• Applying the power rule, we have ∫ x^4 dx = (1/(4+1)) x^(4+1) = (1/5)x^5.

2. For the term x^2:

• Again applying the power rule, ∫ x^2 dx = (1/(2+1)) x^(2+1) = (1/3)x^3.

3. For the constant term 1:

• The integral of 1 is simply x, since ∫ 1 dx = x.

Now, we can combine all these results:

• From x^4, we get (1/5)x^5.

• From x^2, we obtain (1/3)x^3.

• From the constant 1, we add x.

Putting it all together