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

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