Evaluate int(2x^(3)+4x^(2)-5)/(x+3)dx. Choose 1 answer: (A) (2x^(3))/(3)-(1)/(2)x^(2)+6x+13 ln |x+3|+C (B) (2x^(3))/(3)-x^(2)+6x+13 ln |x+3|+C (C) (2x^(3))/(3)-x^(2)+6x-23 ln |x+3|+C (D) (2x^(3))/(3)-x^(2)-6x-23 ln |x+3|+C

Polynomial Long Division: First, let's try to simplify the integral by doing polynomial long division for (2x^3 + 4x^2 - 5) divided by (x + 3).Simplify Result: After dividing, we get 2x^2 - 2x + 10 - (32/(x + 3)).Integrate Terms Separately: Now, let's integrate each term separately: ∫2x^2 dx, -∫2x dx, ∫10 dx, and -∫(32/(x + 3)) dx.Integrate 2x^2: Integrating ∫2x^2 dx gives us (2/3)x^3.Integrate -2x: Integrating -∫2x dx gives us -x^2.Integrate 10: Integrating ∫10 dx gives us 10x.Integrate -32/(x + 3): Integrating -∫(32/(x + 3)) dx gives us -32 ln|x + 3|.Combine Integrated Parts: Adding all the integrated parts together, we get (2/3)x^3 - x^2 + 10x - 32 ln|x + 3| + C.

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Evaluate
int(2x^(3)+4x^(2)-5)/(x+3)dx.
Choose 1 answer:
(A)
(2x^(3))/(3)-(1)/(2)x^(2)+6x+13 ln |x+3|+C
(B)
(2x^(3))/(3)-x^(2)+6x+13 ln |x+3|+C
(C)
(2x^(3))/(3)-x^(2)+6x-23 ln |x+3|+C
(D)
(2x^(3))/(3)-x^(2)-6x-23 ln |x+3|+C

Evaluate $\int \frac{2 x^{3}+4 x^{2}-5}{x+3} d x$ . $\newline$ Choose $1$ answer: $\newline$ (A) $\frac{2 x^{3}}{3}-\frac{1}{2} x^{2}+6 x+13 \ln |x+3|+C$ $\newline$ (B) $\frac{2 x^{3}}{3}-x^{2}+6 x+13 \ln |x+3|+C$ $\newline$ (C) $\frac{2 x^{3}}{3}-x^{2}+6 x-23 \ln |x+3|+C$ $\newline$ (D) $\frac{2 x^{3}}{3}-x^{2}-6 x-23 \ln |x+3|+C$

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Find derivatives of using multiple formulae

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Q. Evaluate

\int \frac{2 x^{3}+4 x^{2}-5}{x+3} d x

\newline

Choose

1

answer:

\newline

(A)

\frac{2 x^{3}}{3}-\frac{1}{2} x^{2}+6 x+13 \ln |x+3|+C

\newline

(B)

\frac{2 x^{3}}{3}-x^{2}+6 x+13 \ln |x+3|+C

\newline

(C)

\frac{2 x^{3}}{3}-x^{2}+6 x-23 \ln |x+3|+C

\newline

(D)

\frac{2 x^{3}}{3}-x^{2}-6 x-23 \ln |x+3|+C

Polynomial Long Division: First, let's try to simplify the integral by doing polynomial long division for $(2x^3 + 4x^2 - 5)$ divided by $(x + 3)$ .
Simplify Result: After dividing, we get $2x^2 - 2x + 10 - \left(\frac{32}{x + 3}\right)$ .
Integrate Terms Separately: Now, let's integrate each term separately: $\int 2x^2 \, dx$ , $-\int 2x \, dx$ , $\int 10 \, dx$ , and $-\int \frac{32}{x + 3} \, dx$ .
Integrate $2x^2$ : Integrating $\int 2x^2 \, dx$ gives us $\frac{2}{3}x^3$ .
Integrate $-2x$ : Integrating $-\int 2x \, dx$ gives us $-x^2$ .
Integrate $10$ : Integrating $\int 10 \, dx$ gives us $10x$ .
Integrate $-\frac{32}{x + 3}$ : Integrating $-\int\left(\frac{32}{x + 3}\right) dx$ gives us $-32 \ln|x + 3|$ .
Combine Integrated Parts: Adding all the integrated parts together, we get $(\frac{2}{3})x^3 - x^2 + 10x - 32 \ln|x + 3| + C$ .