Express the Integrand as a Sum of Partial Fractions and Evaluate

question 322

Multiple Choice

Express the integrand as a sum of partial fractions and evaluate the integral.
- $$\int \frac { d x } { x ^ { 2 } \left( x ^ { 2 } - 25 \right) }$$

• A) \(\frac { 1 } { 25 x } + \frac { 1 } { 125 } \ln \left| \frac { x - 5 } { x + 5 } \right| + C\)
• B) \(\frac { 1 } { 50 x } + \frac { 1 } { 250 } \ln \left| \frac { x - 5 } { x + 5 } \right| + C\)
• C) \(\frac { 1 } { 25 x } + \frac { 1 } { 250 } \ln \left| \frac { x - 5 } { x + 5 } \right| + C\)
• D) \(\frac { 1 } { 25 x } + \frac { 1 } { 250 } \ln \left| \frac { x + 5 } { x - 5 } \right| + C\)

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Conglomerate Merger

A type of merger involving companies from unrelated business activities, aiming for diversification and risk reduction.

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The dynamics between organizations that are in the same market and compete against each other for customers, market share, and resources.

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The cost advantage achieved when production becomes efficient, leading to a reduced cost per unit as output increases.

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Resources, information, or energy required for a process, system, or project to function effectively.