Express the Integrand as a Sum of Partial Fractions and Evaluate

question 2

Multiple Choice

Express the integrand as a sum of partial fractions and evaluate the integral.
- $$\int \frac { 4 x ^ { 4 } + 36 x ^ { 2 } + 72 } { x \left( x ^ { 2 } + 6 \right) ^ { 2 } } d x$$

• A) \(2 \ln | x | + \ln \left| x ^ { 2 } + 6 \right| - \frac { 4 } { x ^ { 2 } + 6 } + C\)
• B) \(2 \ln | x | - \frac { 4 } { x ^ { 2 } + 6 } + C\)
• C) \(2 \ln | x | + \ln \left| x ^ { 2 } + 6 \right| + C\)
• D) \(8 \ln | x | + \ln \left| x ^ { 2 } + 6 \right| + C\)

---

Definitions:

Brainstorming

A creative group technique used to generate a large number of ideas for the solution of a problem.

Clustering

A method used in writing and idea generation where related thoughts or concepts are grouped together visually.

Focused Freewriting

Focused freewriting is a writing strategy that involves continuous, non-stop writing about a particular subject or topic for a set period of time, helping writers generate ideas and content.

Lottery Winners

Individuals who have won prizes, often monetary, in a lottery, which is a form of gambling involving drawing lots.