Recognize the integral: Recognize the integral to be solved. We need to find the integral of the function 2x + 4 with respect to x. This is a basic indefinite integral involving a linear function.Apply power rule: Apply the power rule for integration to the term 2x. 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. For the term 2x, which is x to the power of 1, we apply the power rule.Calculate integral of 2x: Calculate the integral of 2x. The integral of 2x with respect to x is 2 * (x^(1+1))/(1+1) = 2 * (x^2)/2 = x^2.Integrate constant term: Integrate the constant term 4. The integral of a constant a with respect to x is a*x + C. Therefore, the integral of 4 with respect to x is 4x.Combine results: Combine the results of Step 3 and Step 4. The integral of 2x + 4 with respect to x is the sum of the integrals of 2x and 4, which is x^2 + 4x + C, where C is the constant of integration.

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$\int 2 x+4 d x$

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Algebra 2

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\int 2 x+4 d x

Recognize the integral: Recognize the integral to be solved. $\newline$ We need to find the integral of the function $2x + 4$ with respect to $x$ . This is a basic indefinite integral involving a linear function.
Apply power rule: Apply the power rule for integration to the term $2x$ . 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. For the term $2x$ , which is $x$ to the power of $1$ , we apply the power rule.
Calculate integral of $2x$ : Calculate the integral of $2x$ . The integral of $2x$ with respect to $x$ is $2 \times (x^{1+1})/(1+1) = 2 \times (x^2)/2 = x^2$ .
Integrate constant term: Integrate the constant term $4$ . The integral of a constant $a$ with respect to $x$ is $a*x + C$ . Therefore, the integral of $4$ with respect to $x$ is $4x$ .
Combine results: Combine the results of Step $3$ and Step $4$ . $\newline$ The integral of $2x + 4$ with respect to $x$ is the sum of the integrals of $2x$ and $4$ , which is $x^2 + 4x + C$ , where $C$ is the constant of integration.