Identify integral: Identify the integral that needs to be solved. We need to find the indefinite integral of x^2 with respect to x, which is written as ∫x^2 dx.Apply power rule: Apply the power rule for integration. The power rule for integration states that ∫x^n dx = (x^(n+1))/(n+1) + C, where C is the constant of integration.Calculate integral: Calculate the integral using the power rule. Using the power rule, we have ∫x^2 dx = (x^(2+1))/(2+1) + C = (x^3)/3 + C.Write final answer: Write the final answer. The integral of x^2 with respect to x is (x^3)/3 + C.

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\int x^{2}dx

Identify integral: Identify the integral that needs to be solved. $\newline$ We need to find the indefinite integral of $x^2$ with respect to $x$ , which is written as $\int x^2 \, dx$ .
Apply power rule: Apply the power rule for integration. $\newline$ The power rule for integration states that $\int x^n \, dx = \frac{x^{(n+1)}}{n+1} + C$ , where $C$ is the constant of integration.
Calculate integral: Calculate the integral using the power rule. $\newline$ Using the power rule, we have $\int x^2 \, dx = \frac{x^{2+1}}{2+1} + C = \frac{x^3}{3} + C$ .
Write final answer: Write the final answer. $\newline$ The integral of $x^2$ with respect to $x$ is $(x^3)/3 + C$ .