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

question 115

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) \(\frac { 1 } { 5 } \tan ^ { 3 } x + \frac { 2 } { 3 } \tan ^ { 3 } x + \tan x + C\)
• 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:

Operant Response Rates

The frequency at which an organism performs a behavior in response to a given operant conditioning scenario.

Operant Conditioning

An instructional process that modifies the vigor of behaviors by means of rewards or sanctions.

Reinforcement

In behavioral psychology, a consequence applied to an organism's environment that increases the likelihood of a preceding response being repeated in the future.

Conditioned Taste Aversion

Conditioned taste aversion occurs when an individual associates the taste of a particular food or drink with an unpleasant symptom, leading to a lasting aversion to that item.