Find the Integral $\int \tan ^{3} x \sec ^{5} x d x$

question 54

Multiple Choice

Find the integral. $\int \tan ^{3} x \sec ^{5} x d x$

• A) \(\frac{1}{5} \sec ^{5} x-\frac{1}{3} \sec ^{3} x+C\)
• B) \(\frac{1}{5} \sec ^{3} x+\frac{1}{3} \sec ^{3} x+C\)
• C) \(\frac{1}{7} \sec ^{7} x-\frac{1}{5} \sec ^{3} x+C\)
• D) \(\frac{1}{7} \sec ^{7} x+\frac{1}{5} \sec ^{3} x+C\)

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Definitions:

Risk-free Rates

The expected profit from an investment that carries no risk of losing money, often linked to government securities.

Spot Exchange Rate

The current rate for instant purchase or sale of a currency in the exchange market.

Futures Price

The agreed-upon price for a futures contract, which is a legal agreement to buy or sell a particular commodity or asset at a predetermined price at a specified time in the future.

Annual Risk-free Rate

The return on investment expected from a risk-free asset over a one-year period.