Express the Integrand as a Sum of Partial Fractions and Evaluate

question 308

Multiple Choice

Express the integrand as a sum of partial fractions and evaluate the integral.
- $$\int \frac { 5 x ^ { 2 } + x + 36 } { x ^ { 3 } + 9 x } d x$$

• A) \(4 \ln | x | + \frac { 1 } { 2 } \ln \left| x ^ { 2 } + 9 \right| + \frac { 1 } { 3 } \tan ^ { - 1 } \left( \frac { x } { 3 } \right) + C\)
• B) \(4 \ln | x | - \frac { 1 } { 2 } \ln \left| x ^ { 2 } + 9 \right| - \tan ^ { - 1 } x + C\)
• C) \(4 \ln | x | + \frac { 1 } { 2 } \ln \left| x ^ { 2 } + 9 \right| + \sin ^ { - 1 } \left( \frac { x } { 3 } \right) + C\)
• D) \(\ln | x | + \frac { 1 } { 2 } \ln \left| x ^ { 2 } + 9 \right| + \tan ^ { - 1 } \left( \frac { x } { 3 } \right) + C\)

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Definitions:

Lateral Thinking Method

A problem-solving approach that involves looking at the situation from different perspectives rather than proceeding linearly.

Deliberate Process

A methodical or planned series of actions aimed at achieving a particular outcome, involving conscious thought and consideration.

Osborn's Creativity Process

A structured approach to generating and developing creative ideas, typically including stages such as preparation, incubation, illumination, and verification.

Electronic Brainstorming

A technique that uses digital tools to generate creative ideas and solutions by allowing participants to contribute anonymously over networks.