Express the Integrand as a Sum of Partial Fractions and Evaluate

question 82

Multiple Choice

Express the integrand as a sum of partial fractions and evaluate the integral.
- $$\int \frac { 3 x ^ { 2 } - 11 x + 4 } { x ^ { 3 } - 3 x ^ { 2 } + 2 x } d x$$

• A) \(2 \ln | x | - 3 \ln | x - 2 | + 4 \ln | x - 1 | + C\)
• B) \(2 \ln | x | + 4 \ln | x - 2 | - 3 \ln | x - 1 | + C\)
• C) \(\ln | x | - \ln | x - 2 | + \ln | x - 1 | + C\)
• D) \(- 3 \ln | x - 2 | + 4 \ln | x - 1 | + C\)

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Definitions:

Nominal Interest Rates

The interest rate before taking inflation into account, representing the face value rate at which money can be borrowed.

R&D Decisions

Choices made by businesses or governments regarding the allocation of resources for research and development to innovate or improve products and services.

Loanable Funds Theory

An economic theory that describes the market interaction between borrowers and lenders, determining the equilibrium interest rate.

Equilibrium Interest Rate

The interest rate at which the demand for money to borrow is equal to the supply of money available to lend in the financial markets.