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

question 73

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:

Sexual Spores

Reproductive cells produced by sexual reproduction in fungi and some plants that can develop into a new individual.

Fruiting Bodies

The reproductive structures produced by fungi, where spores are formed and subsequently disperse for reproduction.

Mature Zygospore

A thick-walled resting spore produced by the union of two similar fungal cells, serving as a form of resistance and survival in harsh conditions.

Young Zygospore

An early developmental stage of a zygospore, which is a thick-walled spore produced by the fusion of two similar gametes in fungi.