Identify Function: Step 1: Identify the function to integrate. We have the function 2x + 3. Apply Power Rule: Step 2: Apply the power rule for integration to each term separately. Integrate 2x. The integral of x^n is (x^(n+1))/(n+1) for n ≠ -1, so the integral of 2x is 2*(x^(1+1))/(1+1) = x^2. Integrate 2x: Step 3: Integrate the constant 3. The integral of a constant a is ax, so the integral of 3 is 3x. Integrate Constant: Step 4: Combine the results of the integrations. Add x^2 and 3x together. So, the integral of 2x + 3 is x^2 + 3x. Combine Integrations: Step 5: Don't forget to add the constant of integration, C. The final answer is x^2 + 3x + C.

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Integral of $2x+3$

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Math Problems

Grade 6

Evaluate numerical expressions involving integers

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Q. Integral of

2x+3

Identify Function: Step $1$ : Identify the function to integrate. We have the function $2x + 3$ .
Apply Power Rule: Step $2$ : Apply the power rule for integration to each term separately. Integrate $2x$ . The integral of $x^n$ is $\frac{x^{(n+1)}}{n+1}$ for $n \neq -1$ , so the integral of $2x$ is $2\cdot\frac{x^{(1+1)}}{1+1} = x^2$ .
Integrate $2x$ : Step $3$ : Integrate the constant $3$ . The integral of a constant $a$ is $ax$ , so the integral of $3$ is $3x$ .
Integrate Constant: Step $4$ : Combine the results of the integrations. Add $x^2$ and $3x$ together. So, the integral of $2x + 3$ is $x^2 + 3x$ .
Combine Integrations: Step $5$ : Don't forget to add the constant of integration, $C$ . The final answer is $x^2 + 3x + C$ .