Evaluate the integral. int(9x^(3)-2x^(2)-4x)/(x)dx Answer:

Simplify Integrand: Simplify the integrand by dividing each term by x. (9x^3 - 2x^2 - 4x) / x = 9x^2 - 2x - 4Integrate Terms Separately: Integrate each term separately. ∫(9x^2 - 2x - 4)dx = ∫9x^2dx - ∫2xdx - ∫4dxApply Power Rule: Apply the power rule for integration to each term. ∫9x^2dx = 9 * (x^(2+1)/(2+1)) = 9 * (x^3/3) ∫2xdx = 2 * (x^(1+1)/(1+1)) = 2 * (x^2/2) ∫4dx = 4xSimplify Integrations: Simplify the results of the integrations. 9 * (x^3/3) = 3x^3 2 * (x^2/2) = x^2 4x = 4xCombine Results: Combine the results and add the constant of integration C. 3x^3 - x^2 - 4x + C

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Calculus

Find indefinite integrals using the substitution

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Q. Evaluate the integral.

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\int \frac{9 x^{3}-2 x^{2}-4 x}{x} \mathrm{~d} x

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Answer:

Simplify Integrand: Simplify the integrand by dividing each term by $x$ . $\frac{9x^3 - 2x^2 - 4x}{x} = 9x^2 - 2x - 4$
Integrate Terms Separately: Integrate each term separately. \int(\(9x^ $2$ - $2$ x - $4$ )\,dx = \int $9$ x^ $2$ \,dx - \int $2$ x\,dx - \int $4$ \,dx
Apply Power Rule: Apply the power rule for integration to each term. $\newline$ $\int 9x^2\,dx = 9 \times \left(\frac{x^{2+1}}{2+1}\right) = 9 \times \left(\frac{x^3}{3}\right)$ $\newline$ $\int 2x\,dx = 2 \times \left(\frac{x^{1+1}}{1+1}\right) = 2 \times \left(\frac{x^2}{2}\right)$ $\newline$ $\int 4\,dx = 4x$
Simplify Integrations: Simplify the results of the integrations. $\newline$ $9 \times \left(\frac{x^3}{3}\right) = 3x^3$ $\newline$ $2 \times \left(\frac{x^2}{2}\right) = x^2$ $\newline$ $4x = 4x$
Combine Results: Combine the results and add the constant of integration $C$ . $3x^3 - x^2 - 4x + C$