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

Simplify integrand: First, let's try to simplify the integrand by doing polynomial long division of (x^3 - 3x^2 + 5x - 3) by (x - 1).Divide by x - 1: After dividing x^3 by x, we get x^2. Multiply x^2 by (x - 1) to get x^3 - x^2. Subtract this from the original polynomial to get -2x^2 + 5x - 3.Divide by x: Next, divide -2x^2 by x to get -2x. Multiply -2x by (x - 1) to get -2x^2 + 2x. Subtract this from -2x^2 + 5x - 3 to get 3x - 3.Integrate quotient: Now, divide 3x by x to get 3. Multiply 3 by (x - 1) to get 3x - 3. Subtract this from 3x - 3 to get 0. So, the quotient is x^2 - 2x + 3 and the remainder is 0.Add constant of integration: The integral of the quotient x^2 - 2x + 3 is (x^3)/3 - x^2 + 3x. Since there's no remainder, we don't need to add any additional terms involving ln|x - 1|.Finally, we add the constant of integration C to our result. The integral is (x^3)/3 - x^2 + 3x + C.

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

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

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Q. Evaluate

\int \frac{x^{3}-3 x^{2}+5 x-3}{x-1} d x

\newline

Choose

1

answer:

\newline

(A)

\frac{x^{3}}{3}-x^{2}+3 x+C

\newline

(B)

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

\newline

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

\newline

(D)

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

Simplify integrand: First, let's try to simplify the integrand by doing polynomial long division of $(x^3 - 3x^2 + 5x - 3)$ by $(x - 1)$ .
Divide by $x - 1$ : After dividing $x^3$ by $x$ , we get $x^2$ . Multiply $x^2$ by $(x - 1)$ to get $x^3 - x^2$ . Subtract this from the original polynomial to get $-2x^2 + 5x - 3$ .
Divide by $x$ : Next, divide $-2x^2$ by $x$ to get $-2x$ . Multiply $-2x$ by $(x - 1)$ to get $-2x^2 + 2x$ . Subtract this from $-2x^2 + 5x - 3$ to get $3x - 3$ .
Integrate quotient: Now, divide $3x$ by $x$ to get $3$ . Multiply $3$ by $(x - 1)$ to get $3x - 3$ . Subtract this from $3x - 3$ to get $0$ . So, the quotient is $x^2 - 2x + 3$ and the remainder is $0$ .
Add constant of integration: The integral of the quotient $x^2 - 2x + 3$ is $\frac{x^3}{3} - x^2 + 3x$ . Since there's no remainder, we don't need to add any additional terms involving $\ln|x - 1|$ .
Add constant of integration: The integral of the quotient $x^2 - 2x + 3$ is $(x^3)/3 - x^2 + 3x$ . Since there's no remainder, we don't need to add any additional terms involving $\ln|x - 1|$ . Finally, we add the constant of integration $C$ to our result. The integral is $(x^3)/3 - x^2 + 3x + C$ .