Use Integration by Parts to Establish a Reduction Formula for the Integral

question 173

Multiple Choice

Use integration by parts to establish a reduction formula for the integral.
- $$\int \tan ^ { n } x d x , n \neq 1$$

• A) \(\int \tan ^ { n } x d x = \frac { 1 } { n - 1 } \tan ^ { n - 1 } x - \int \tan ^ { n - 2 } x d x\)
• B) \(\int \tan ^ { n } x d x = \tan ^ { n - 1 } x - \frac { 1 } { n - 1 } \int \tan ^ { n - 2 } x d x\)
• C) \(\int \tan ^ { n } x d x = \frac { 1 } { n - 1 } \tan ^ { n - 2 } x - \int \tan ^ { n - 1 } x d x\)
• D) \(\int \tan ^ { n } x d x = \frac { 1 } { n - 1 } \tan ^ { n - 1 } x + \int \tan ^ { n - 1 } x d x\)

---

Definitions:

Contract Law

A legal framework governing the binding agreements between parties, setting the rules for formation, execution, and enforcement of contracts.

Full Satisfaction

The complete fulfillment or settlement of a debt, obligation, or claim.

Debt

An amount of money borrowed by one party from another, typically under the agreement that it is to be repaid with interest.

Promissory Estoppel

A legal principle that prevents a party from withdrawing a promise when the other party has reasonably relied on that promise to their detriment.