Express the Integrand as a Sum of Partial Fractions and Evaluate

question 82

Multiple Choice

Express the integrand as a sum of partial fractions and evaluate the integral.
- $$\int \frac { 3 x ^ { 2 } - 11 x + 4 } { x ^ { 3 } - 3 x ^ { 2 } + 2 x } d x$$

• A) \(2 \ln | x | - 3 \ln | x - 2 | + 4 \ln | x - 1 | + C\)
• B) \(2 \ln | x | + 4 \ln | x - 2 | - 3 \ln | x - 1 | + C\)
• C) \(\ln | x | - \ln | x - 2 | + \ln | x - 1 | + C\)
• D) \(- 3 \ln | x - 2 | + 4 \ln | x - 1 | + C\)

---

Definitions:

Human Immune System

The body's defense network consisting of a complex of cells, tissues, and organs that work together to protect the body against infection and disease.

Fluid Intelligence

The ability to reason and think flexibly, solve novel problems, and process new information, typically contrasting with accumulated knowledge and experiences.

Estrogen Deficiency

A state in which there is a lower than normal level of estrogen, a key hormone in female development and reproductive health.

Hormone Replacement Therapy

A treatment aimed to alleviate symptoms caused by hormonal imbalances, often used during menopause or in cases of hormonal deficiency.