Find the Integral $\int \tan ^{2} x \sec ^{6} x d x$

question 78

Multiple Choice

Find the integral. $\int \tan ^{2} x \sec ^{6} x d x$

• A) \(\frac{1}{7} \tan ^{7} x+\frac{2}{5} \tan ^{5} x+\frac{1}{3} \tan ^{3} x+C\)
• B) \(\frac{1}{5} \tan ^{5} x+\frac{2}{3} \tan ^{3} x+\tan x+C\)
• C) \(\frac{1}{5} \tan ^{5} x+\frac{2}{3} \tan ^{3} x-\tan x+C\)
• D) \(\frac{1}{7} \tan ^{7} x+\frac{2}{5} \tan ^{5} x-\frac{1}{3} \tan ^{3} x+C\)

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Definitions:

Equivalent Annual Annuity

Equivalent Annual Annuity is a calculation used to compare the annualized cash flows of projects or investments with different durations.

Unequal Lives

Unequal lives refer to the comparison of investments or projects that have different durations or lifespans, complicating the analysis of their profitability or worth.

Positive Cash Flows

A situation where the cash inflows in a given period are greater than the cash outflows, indicating financial health.

Common Time Period

The standard duration used for comparing financial performance or investment returns across different assets or projects.