Recognize the integral: Recognize the integral to be solved. The integral given is ∫(x^2 + 3)dx. This is an indefinite integral of a polynomial function.Apply power rule: Apply the power rule for integration to the term x^2. The power rule for integration states that ∫x^n dx = (x^(n+1))/(n+1) + C, where C is the constant of integration. For the term x^2, n = 2, so we get ∫x^2 dx = (x^(2+1))/(2+1) = (x^3)/3.Integrate constant term: Integrate the constant term 3. The integral of a constant a with respect to x is ax + C, where C is the constant of integration. For the term 3, we get ∫3 dx = 3x + C.Combine results: Combine the results from Step 2 and Step 3. The integral of the entire expression ∫(x^2 + 3)dx is the sum of the integrals of its terms. So, ∫(x^2 + 3)dx = (x^3)/3 + 3x + C.Write final answer: Write the final answer. The final answer is the antiderivative of the given function.

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$\int x^{2} + 3 \, dx$

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Algebra 2

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\int x^{2} + 3 \, dx

Recognize the integral: Recognize the integral to be solved. $\newline$ The integral given is $\int(x^2 + 3)\,dx$ . This is an indefinite integral of a polynomial function.
Apply power rule: Apply the power rule for integration to the term $x^2$ . 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. For the term $x^2$ , $n = 2$ , so we get $\int x^2 \, dx = \frac{x^{2+1}}{2+1} = \frac{x^3}{3}$ .
Integrate constant term: Integrate the constant term $3$ . The integral of a constant $a$ with respect to $x$ is $ax + C$ , where $C$ is the constant of integration. For the term $3$ , we get $\int 3 \, dx = 3x + C$ .
Combine results: Combine the results from Step $2$ and Step $3$ . $\newline$ The integral of the entire expression $\int(x^2 + 3)\,dx$ is the sum of the integrals of its terms. $\newline$ So, $\int(x^2 + 3)\,dx = \frac{x^3}{3} + 3x + C$ .
Write final answer: Write the final answer. $\newline$ The final answer is the antiderivative of the given function. $\newline$ $\frac{x^3}{3} +="" 3x="" c$