Evaluate int(x^(3)-1)/(x+2)dx. Choose 1 answer: (A) (x^(3))/(3)-x^(2)+4x-7ln |x+2|+C (B) (x^(3))/(3)-2x^(2)+4x-7ln |x+2|+C (C) (x^(3))/(3)-x^(2)+4x-9ln |x+2|+C (D) (x^(3))/(3)-2x^(2)+4x-9ln |x+2|+C

Perform Polynomial Long Division: First, let's do polynomial long division to simplify the integrand. (x^3 - 1) / (x + 2) = x^2 - 2x + 4 - (7/(x + 2))Integrate Each Term: Now, we integrate each term separately. ∫x^2 dx = (x^3)/3 + C1 ∫(-2x) dx = -x^2 + C2 ∫4 dx = 4x + C3 ∫(-7/(x + 2)) dx = -7ln|x + 2| + C4Combine Integrals and Constants: Combine all the integrals and constants. ∫(x^3 - 1)/(x + 2) dx = (x^3)/3 - x^2 + 4x - 7ln|x + 2| + CMatch with Given Options: Match the result with the given options. The correct answer is (A) (x^3)/3 - x^2 + 4x - 7ln|x + 2| + C.

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Evaluate
int(x^(3)-1)/(x+2)dx.
Choose 1 answer:
(A)
(x^(3))/(3)-x^(2)+4x-7ln |x+2|+C
(B)
(x^(3))/(3)-2x^(2)+4x-7ln |x+2|+C
(C)
(x^(3))/(3)-x^(2)+4x-9ln |x+2|+C
(D)
(x^(3))/(3)-2x^(2)+4x-9ln |x+2|+C

Evaluate $\int \frac{x^{3}-1}{x+2} d x$ . $\newline$ Choose $1$ answer: $\newline$ (A) $\frac{x^{3}}{3}-x^{2}+4 x-7 \ln |x+2|+C$ $\newline$ (B) $\frac{x^{3}}{3}-2 x^{2}+4 x-7 \ln |x+2|+C$ $\newline$ (C) $\frac{x^{3}}{3}-x^{2}+4 x-9 \ln |x+2|+C$ $\newline$ (D) $\frac{x^{3}}{3}-2 x^{2}+4 x-9 \ln |x+2|+C$

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Math Problems

Calculus

Evaluate definite integrals using the chain rule

Full solution

Q. Evaluate

\int \frac{x^{3}-1}{x+2} d x

\newline

Choose

1

answer:

\newline

(A)

\frac{x^{3}}{3}-x^{2}+4 x-7 \ln |x+2|+C

\newline

(B)

\frac{x^{3}}{3}-2 x^{2}+4 x-7 \ln |x+2|+C

\newline

(C)

\frac{x^{3}}{3}-x^{2}+4 x-9 \ln |x+2|+C

\newline

(D)

\frac{x^{3}}{3}-2 x^{2}+4 x-9 \ln |x+2|+C

Perform Polynomial Long Division: First, let's do polynomial long division to simplify the integrand. $\newline$ $(x^3 - 1) / (x + 2) = x^2 - 2x + 4 - (\frac{7}{x + 2})$
Integrate Each Term: Now, we integrate each term separately. $\newline$ $\int x^2 \, dx = \frac{x^3}{3} + C_1$ $\newline$ $\int (-2x) \, dx = -x^2 + C_2$ $\newline$ $\int 4 \, dx = 4x + C_3$ $\newline$ $\int \frac{-7}{x + 2} \, dx = -7\ln|x + 2| + C_4$
Combine Integrals and Constants: Combine all the integrals and constants. $\newline$ $\int\frac{x^3 - 1}{x + 2} dx = \frac{x^3}{3} - x^2 + 4x - 7\ln|x + 2| + C$
Match with Given Options: Match the result with the given options. $\newline$ The correct answer is (A) $(x^3)/3 - x^2 + 4x - 7\ln|x + 2| + C$ .