Evaluate the Integral by First Performing Long Division on the Integrand

question 38

Multiple Choice

Evaluate the integral by first performing long division on the integrand and then writing the proper fraction as a sum of partial fractions.
- $\int \frac { 6 y ^ { 4 } + 3 y ^ { 2 } - 6 y } { y ^ { 3 } - 1 } d y$

• A) \(3 y ^ { 2 } - \ln | y - 1 | + 6 \ln \left| y ^ { 2 } + y + 1 \right| + C\)
• B) \(3 y ^ { 2 } + 6 \ln | y - 1 | + \ln \left| y ^ { 2 } - y + 1 \right| + C\)
• C) \(3 y ^ { 2 } + \ln | y - 1 | + ( 2 y + 1 ) \ln \left| y ^ { 2 } + y + 1 \right| + C\)
• D) \(3 y ^ { 2 } + \ln | y - 1 | + \ln \left| y ^ { 2 } + y + 1 \right| + C\)

---

Definitions:

Purchase Conditions

The terms and requirements under which a sale is made, including price, delivery, and payment terms.

Prototype

An early sample, model, or release of a product built to test a concept or process, serving as a proof of concept before mass production or further development.

Idea Generation

The creative process of generating, developing, and curating new ideas, often the initial step in the development of new products or solutions.

Development

Refers to the process of growth, progress, or evolution, often in the context of economic, social, or technological advancements.