Evaluate the Integral by First Performing Long Division on the Integrand

question 103

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.
- $$\int \frac { 3 x ^ { 4 } + 15 x ^ { 2 } + 5 } { x ^ { 3 } + 5 x } d x$$

• A) \(\frac { 3 } { 2 } x ^ { 2 } - \frac { 1 } { 2 } \ln \left| x ^ { 2 } + 5 \right| + C\)
• B) \(\frac { 3 } { 2 } x ^ { 2 } + \ln | x | - x \ln \left| x ^ { 2 } + 5 \right| + C\)
• C) \(\frac { 3 } { 2 } x ^ { 2 } + \ln | x | + \frac { 1 } { 2 } \ln \left| x ^ { 2 } + 5 \right| + C\)
• D) \(\frac { 3 } { 2 } x ^ { 2 } + \ln | x | - \frac { 1 } { 2 } \ln \left| x ^ { 2 } + 5 \right| + C\)

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Definitions:

Chart of Accounts

A systematic listing of all ledger account names and numbers used by a company, organized by the assets, liabilities, equity, revenue, and expenses.

Closing Entry

Journal entries made at the end of an accounting period to transfer temporary account balances to permanent accounts and prepare the company's books for the next period.

Debit and Credit

Fundamental concepts in double-entry bookkeeping, where debits are entries on the left side of an account and credits are entries on the right.