Evaluate the integral. int(3x^(2)+2)^(2)dx Answer:

Expand binomial: Expand the integrand (3x^2 + 2)^2. To integrate the function, we first need to expand the square of the binomial to simplify the integrand. (3x^2 + 2)^2 = (3x^2 + 2)(3x^2 + 2) = 9x^4 + 12x^2 + 4Set up integral: Set up the integral with the expanded integrand. Now that we have expanded the integrand, we can write the integral as: ∫(9x^4 + 12x^2 + 4)dxIntegrate each term: Integrate each term separately. We will integrate each term of the polynomial separately using the power rule for integration, which states that ∫x^n dx = (x^(n+1))/(n+1) + C, where C is the constant of integration. ∫9x^4 dx = (9/5)x^5 ∫12x^2 dx = (12/3)x^3 = 4x^3 ∫4 dx = 4xCombine integration results: Combine the results of the integrations. Now we combine the results of the individual integrations to get the final result of the original integral. ∫(9x^4 + 12x^2 + 4)dx = (9/5)x^5 + 4x^3 + 4x + C

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Evaluate the integral.

int(3x^(2)+2)^(2)dx
Answer:

Evaluate the integral. $\newline$ $\int\left(3 x^{2}+2\right)^{2} \mathrm{~d} x$ $\newline$ Answer:

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Calculus

Evaluate definite integrals using the chain rule

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Q. Evaluate the integral.

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\int\left(3 x^{2}+2\right)^{2} \mathrm{~d} x

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Answer:

Expand binomial: Expand the integrand $(3x^2 + 2)^2$ . To integrate the function, we first need to expand the square of the binomial to simplify the integrand. $(3x^2 + 2)^2 = (3x^2 + 2)(3x^2 + 2) = 9x^4 + 12x^2 + 4$
Set up integral: Set up the integral with the expanded integrand. $\newline$ Now that we have expanded the integrand, we can write the integral as: $\newline$ $\int(9x^4 + 12x^2 + 4)\,dx$
Integrate each term: Integrate each term separately. $\newline$ We will integrate each term of the polynomial separately using the power rule for integration, which states that $\int x^n \, dx = \frac{x^{(n+1)}}{n+1} + C$ , where $C$ is the constant of integration. $\newline$ $\int 9x^4 \, dx = \frac{9}{5}x^5$ $\newline$ $\int 12x^2 \, dx = \frac{12}{3}x^3 = 4x^3$ $\newline$ $\int 4 \, dx = 4x$
Combine integration results: Combine the results of the integrations. $\newline$ Now we combine the results of the individual integrations to get the final result of the original integral. $\newline$ $\int(9x^4 + 12x^2 + 4)\,dx = \frac{9}{5}x^5 + 4x^3 + 4x + C$