Evaluate the integral. intx^(2)(3x-4)(x-3)dx Answer:

Expand Integrand: Expand the integrand (x^2(3x-4)(x-3)) to simplify the integral. We have the integral of a product of a quadratic and a linear term. We will first expand this product before integrating term by term. x^2(3x-4)(x-3) = x^2(3x^2 - 9x - 4x + 12) = x^2(3x^2 - 13x + 12) = 3x^4 - 13x^3 + 12x^2 Now we can integrate each term separately.Integrate Expanded Polynomial: Integrate each term of the expanded polynomial separately. The integral of 3x^4 with respect to x is (3/5)x^5, the integral of -13x^3 with respect to x is (-13/4)x^4, and the integral of 12x^2 with respect to x is (12/3)x^3 or 4x^3. So, ∫(3x^4 - 13x^3 + 12x^2)dx = (3/5)x^5 - (13/4)x^4 + 4x^3 + C, where C is the constant of integration.

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Evaluate the integral.

intx^(2)(3x-4)(x-3)dx
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Evaluate the integral. $\newline$ $\int x^{2}(3 x-4)(x-3) \mathrm{d} x$ $\newline$ Answer:

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Evaluate definite integrals using the chain rule

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Q. Evaluate the integral.

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\int x^{2}(3 x-4)(x-3) \mathrm{d} x

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Answer:

Expand Integrand: Expand the integrand $x^2(3x-4)(x-3)$ to simplify the integral. $\newline$ We have the integral of a product of a quadratic and a linear term. We will first expand this product before integrating term by term. $\newline$ $x^2(3x-4)(x-3) = x^2(3x^2 - 9x - 4x + 12) = x^2(3x^2 - 13x + 12)$ $\newline$ $= 3x^4 - 13x^3 + 12x^2$ $\newline$ Now we can integrate each term separately.
Integrate Expanded Polynomial: Integrate each term of the expanded polynomial separately. $\newline$ The integral of $3x^4$ with respect to $x$ is $(\frac{3}{5})x^5$ , the integral of $-13x^3$ with respect to $x$ is $(-\frac{13}{4})x^4$ , and the integral of $12x^2$ with respect to $x$ is $(\frac{12}{3})x^3$ or $4x^3$ . $\newline$ So, $x$ $0$ , where $x$ $1$ is the constant of integration.