Evaluate the integral. int(3x^(2)-5)^(2)dx Answer:

Expand the integrand: Expand the integrand (3x^2 - 5)^2. To integrate the function, we first need to expand the square of the binomial to simplify the integrand. (3x^2 - 5)^2 = (3x^2 - 5)(3x^2 - 5) = 9x^4 - 30x^2 + 25Set up the integral: Set up the integral with the expanded form. Now we can write the integral as: ∫(9x^4 - 30x^2 + 25)dxIntegrate each term separately: Integrate each term separately. The integral of a sum is the sum of the integrals, so we can integrate each term separately. ∫9x^4dx - ∫30x^2dx + ∫25dxApply the power rule: Apply the power rule for integration to each term. The power rule states that ∫x^n dx = (x^(n+1))/(n+1) + C, where C is the constant of integration. ∫9x^4dx = (9/5)x^5 ∫30x^2dx = (30/3)x^3 = 10x^3 ∫25dx = 25xCombine the integration results: Combine the results of the integrations. Now we combine the results from the previous step to get the antiderivative of the original function. (9/5)x^5 - 10x^3 + 25x + CCheck for errors: Check for any mathematical errors. Review the steps to ensure that there are no mathematical errors in the calculations. No errors found.

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Evaluate the integral.

int(3x^(2)-5)^(2)dx
Answer:

Evaluate the integral. $\newline$ $\int\left(3 x^{2}-5\right)^{2} \mathrm{~d} x$ $\newline$ Answer:

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Calculus

Evaluate definite integrals using the chain rule

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Q. Evaluate the integral.

\newline

\int\left(3 x^{2}-5\right)^{2} \mathrm{~d} x

\newline

Answer:

Expand the integrand: Expand the integrand $(3x^2 - 5)^2$ . To integrate the function, we first need to expand the square of the binomial to simplify the integrand. $(3x^2 - 5)^2 = (3x^2 - 5)(3x^2 - 5) = 9x^4 - 30x^2 + 25$
Set up the integral: Set up the integral with the expanded form. $\newline$ Now we can write the integral as: $\newline$ $\int(9x^4 - 30x^2 + 25)\,dx$
Integrate each term separately: Integrate each term separately. $\newline$ The integral of a sum is the sum of the integrals, so we can integrate each term separately. $\newline$ $\int 9x^4 \, dx - \int 30x^2 \, dx + \int 25 \, dx$
Apply the power rule: Apply the power rule for integration to each term. $\newline$ The power rule states that $\int x^n \, dx = \frac{x^{(n+1)}}{n+1} + C$ , where $C$ is the constant of integration. $\newline$ $\int 9x^4\,dx = \frac{9}{5}x^5$ $\newline$ $\int 30x^2\,dx = \frac{30}{3}x^3 = 10x^3$ $\newline$ $\int 25\,dx = 25x$
Combine the integration results: Combine the results of the integrations. $\newline$ Now we combine the results from the previous step to get the antiderivative of the original function. $\newline$ $\frac{9}{5}x^5 - 10x^3 + 25x + C$
Check for errors: Check for any mathematical errors. Review the steps to ensure that there are no mathematical errors in the calculations. No errors found.