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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Definitions:

Overall Cost

The total expenditure involved in acquiring a product or service, including purchase price and all ancillary expenses.

Debt Financing

The process of raising capital by borrowing money from lenders or issuing bonds.

Equity Financing

The process of raising capital through the sale of shares in a company.

WACC

The Weighted Average Cost of Capital represents a formula used to assess a company's cost of capital, with each type of capital being weighted according to its proportion.