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

question 43

Multiple Choice

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

• A) \(\frac { 15 \tan ( 6 x ) - 10 \tan ( 6 x ) ^ { 3 } - 3 \tan ( 6 x ) ^ { 5 } } { 90 } + C\)
• B) \(\frac { 15 \tan ( 6 x ) + 10 \tan ( 6 x ) ^ { 3 } + 3 \tan ( 6 x ) ^ { 5 } } { 15 } + C\)
• C) \(\frac { 15 \tan ( 6 x ) + 10 \tan ( 6 x ) ^ { 3 } + 3 \tan ( 6 x ) ^ { 5 } } { 90 } + C\)
• D) \(\frac { 15 \tan ( 6 x ) + 10 \tan ( 6 x ) ^ { 3 } + 3 \tan ( 6 x ) ^ { 5 } } { 270 } + C\)
• E) \(\frac { 15 \tan ( 6 x ) - 10 \tan ( 6 x ) ^ { 3 } - 3 \tan ( 6 x ) ^ { 5 } } { 15 } + C\)

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Definitions:

Anterior Chambers

The anterior chamber is the fluid-filled space inside the eye between the cornea and the iris.

Iris

The colored part of the eye responsible for controlling the diameter and size of the pupil.

Conjunctiva

A thin, transparent membrane covering the white part of the eye and the inner surfaces of the eyelids, acting as a protective barrier.

Tympanic Membrane

Also known as the eardrum, a thin membrane that vibrates in response to sound waves, initiating the process of hearing.