Evaluate the integral of x^3 dx.

The integral of x^3 dx is (1/4)x^4 + C, where C is the constant of integration.

To evaluate the integral of x^3 dx, we use the power rule of integration, which states that the integral of x^n dx is (1/(n+1))x^(n+1) + C, where C is the constant of integration. Applying this rule to x^3, we get:

∫ x^3 dx = (1/4) x^4 + C

To check our answer, we can differentiate (1/4) x^4 + C with respect to x using the power rule of differentiation, which states that the derivative of x^n is nx^(n-1). Applying this rule to (1/4) x^4 + C, we get:

d/dx [(1/4) x^4 + C] = (1/4) d/dx (x^4) + d/dx (C)
= (1/4) (4x^3) + 0
= x^3

Therefore, the derivative of (1/4) x^4 + C is x^3, which confirms that our answer is correct.