Evaluate the integral. int(20x^(4)+8x^(2)+5x)/(x)dx Answer:

Given Integral Simplification: We are given the integral: int((20x^(4)+8x^(2)+5x)/(x))dx First, we simplify the integrand by dividing each term by x. int((20x^(4)/x + 8x^(2)/x + 5x/x))dx int(20x^(3) + 8x + 5)dxIntegrating Each Term: Now we integrate each term separately. int(20x^(3))dx + int(8x)dx + int(5)dx For the first term, the integral of x^n is (x^(n+1))/(n+1), so: int(20x^(3))dx = 20 * (x^(3+1))/(3+1) = 20 * (x^4)/4 For the second term: int(8x)dx = 8 * (x^(1+1))/(1+1) = 8 * (x^2)/2 For the third term: int(5)dx = 5xCombining Integrals: Now we combine the results of the integrals. 20 * (x^4)/4 + 8 * (x^2)/2 + 5x Simplify each term: (20/4)x^4 + (8/2)x^2 + 5x 5x^4 + 4x^2 + 5xAdding Constant of Integration: Finally, we add the constant of integration C to the result. 5x^4 + 4x^2 + 5x + C

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Evaluate the integral.

int(20x^(4)+8x^(2)+5x)/(x)dx
Answer:

Evaluate the integral. $\newline$ $\int \frac{20 x^{4}+8 x^{2}+5 x}{x} \mathrm{~d} x$ $\newline$ Answer:

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Calculus

Find indefinite integrals using the substitution

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Q. Evaluate the integral.

\newline

\int \frac{20 x^{4}+8 x^{2}+5 x}{x} \mathrm{~d} x

\newline

Answer:

Given Integral Simplification: We are given the integral: $\int\left(\frac{20x^{4}+8x^{2}+5x}{x}\right)dx$ First, we simplify the integrand by dividing each term by $x$ . $\int\left(\frac{20x^{4}}{x} + \frac{8x^{2}}{x} + \frac{5x}{x}\right)dx$ $\int(20x^{3} + 8x + 5)dx$
Integrating Each Term: Now we integrate each term separately. $\newline$ $\int(20x^{3})\,dx + \int(8x)\,dx + \int(5)\,dx$ $\newline$ For the first term, the integral of $x^n$ is $(x^{n+1})/(n+1)$ , so: $\newline$ $\int(20x^{3})\,dx = 20 \times (x^{3+1})/(3+1) = 20 \times (x^4)/4$ $\newline$ For the second term: $\newline$ $\int(8x)\,dx = 8 \times (x^{1+1})/(1+1) = 8 \times (x^2)/2$ $\newline$ For the third term: $\newline$ $\int(5)\,dx = 5x$
Combining Integrals: Now we combine the results of the integrals. $\newline$ $20 \times \frac{x^4}{4} + 8 \times \frac{x^2}{2} + 5x$ $\newline$ Simplify each term: $\newline$ $\frac{20}{4}x^4 + \frac{8}{2}x^2 + 5x$ $\newline$ $5x^4 + 4x^2 + 5x$
Adding Constant of Integration: Finally, we add the constant of integration $C$ to the result. $\newline$ $5x^4 + 4x^2 + 5x + C$