Find the Integral $$\int \frac { x ^ { 3 } - 3 x ^ { 2 } + 6 x - 2 } { x ^ { 3 } - 2 x ^ { 2 } + x } d x$$

question 52

Multiple Choice

Find the integral. Select the correct answer.
$$\int \frac { x ^ { 3 } - 3 x ^ { 2 } + 6 x - 2 } { x ^ { 3 } - 2 x ^ { 2 } + x } d x$$

• A) \(\ln \left| \frac { x - 1 } { x ^ { 2 } } \right| - \frac { 2 } { x - 1 } + x + C\)
• B) \(\ln \left| \frac { x ^ { 2 } } { x - 1 } \right| - \frac { 2 } { x - 1 } + x + C\)
• C) \(\ln \left| \frac { x ^ { 2 } } { x - 1 } \right| - \frac { 1 } { x - 1 } + x + C\)
• D) \(\ln \left| \frac { x - 1 } { x ^ { 2 } } \right| - \frac { 1 } { x - 1 } + x + C\)

---

Definitions:

Near-Death Experience

A profound psychological event that may occur to a person close to death or in situations of extreme physical or emotional distress.

Oxygen Deprivation

A condition resulting from inadequate oxygen supply to the body that can lead to serious health issues, including brain damage.

Rush of Euphoria

A sudden, intense feeling of happiness, excitement, or well-being, often experienced without a direct external cause.

Cocaine

A powerful stimulant drug derived from the leaves of the coca plant, notorious for its addictive properties and high potential for abuse.