Identify Integral: Identify the integral that needs to be solved. We need to find the integral of the function 9x^2 + 2 with respect to x.Apply Power Rule: Apply the power rule for integration to each term separately. The power rule for integration states that the integral of x^n with respect to x is (x^(n+1))/(n+1) + C, where C is the constant of integration.Integrate 9x^2: Integrate the first term 9x^2. Using the power rule, the integral of 9x^2 with respect to x is 9 * (x^(2+1))/(2+1). This simplifies to (9/3)x^3, which is 3x^3.Integrate Constant 2: Integrate the second term 2. The integral of a constant is the constant times x. So, the integral of 2 with respect to x is 2x.Combine Integrals: Combine the results of the integrals of both terms and add the constant of integration. The integral of 9x^2 + 2 with respect to x is 3x^3 + 2x + C, where C is the constant of integration.

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$\int 9x^{2} + 2 \, dx$

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Algebra 2

Simplify radical expressions involving fractions

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\int 9x^{2} + 2 \, dx

Identify Integral: Identify the integral that needs to be solved. $\newline$ We need to find the integral of the function $9x^2 + 2$ with respect to $x$ .
Apply Power Rule: Apply the power rule for integration to each term separately. $\newline$ The power rule for integration states that the integral of $x^n$ with respect to $x$ is $(x^{(n+1)})/(n+1) + C$ , where $C$ is the constant of integration.
Integrate $9x^2$ : Integrate the first term $9x^2$ . Using the power rule, the integral of $9x^2$ with respect to $x$ is $9 \times (x^{2+1})/(2+1)$ . This simplifies to $(9/3)x^3$ , which is $3x^3$ .
Integrate Constant $2$ : Integrate the second term $2$ . The integral of a constant is the constant times $x$ . So, the integral of $2$ with respect to $x$ is $2x$ .
Combine Integrals: Combine the results of the integrals of both terms and add the constant of integration. $\newline$ The integral of $9x^2 + 2$ with respect to $x$ is $3x^3 + 2x + C$ , where $C$ is the constant of integration.