Calculate the integral and write the answer in simplest form. int(3+x)dx Answer:

Split Function: We need to find the indefinite integral of the function (3 + x) with respect to x. The integral of a sum is the sum of the integrals, so we can integrate 3 and x separately. ∫(3 + x)dx = ∫3dx + ∫xdxIntegrate Constant: First, we integrate the constant 3 with respect to x. The integral of a constant a with respect to x is ax, so: ∫3dx = 3xIntegrate Variable: Next, we integrate x with respect to x. The integral of x with respect to x is (1/2)x^2, because the power rule for integration states that ∫x^n dx = (x^(n+1))/(n+1) for n ≠ -1. ∫xdx = (1/2)x^2Combine Results: Now, we combine the results of the two integrals and add the constant of integration C, since this is an indefinite integral. ∫(3 + x)dx = 3x + (1/2)x^2 + C

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Calculate the integral and write the answer in simplest form.

int(3+x)dx
Answer:

Calculate the integral and write the answer in simplest form. $\newline$ $\int(3+x) d x$ $\newline$ Answer:

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Calculus

Evaluate definite integrals using the power rule

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Q. Calculate the integral and write the answer in simplest form.

\newline

\int(3+x) d x

\newline

Answer:

Split Function: We need to find the indefinite integral of the function $(3 + x)$ with respect to $x$ . The integral of a sum is the sum of the integrals, so we can integrate $3$ and $x$ separately. $\newline$ $\int(3 + x)dx = \int 3dx + \int xdx$
Integrate Constant: First, we integrate the constant $3$ with respect to $x$ . The integral of a constant $a$ with respect to $x$ is $ax$ , so: $\newline$ $\int 3\,dx = 3x$
Integrate Variable: Next, we integrate $x$ with respect to $x$ . The integral of $x$ with respect to $x$ is $(1/2)x^2$ , because the power rule for integration states that $\int x^n \, dx = \frac{x^{(n+1)}}{(n+1)}$ for $n \neq -1$ . $\newline$ $\int x\,dx = (1/2)x^2$
Combine Results: Now, we combine the results of the two integrals and add the constant of integration $C$ , since this is an indefinite integral. $\newline$ $\int(3 + x)\,dx = 3x + \frac{1}{2}x^2 + C$