Find the Indefinite Integral $$\int \sin ^ { 3 } \frac { x } { 8 } d x$$

question 31

Multiple Choice

Find the indefinite integral. $$\int \sin ^ { 3 } \frac { x } { 8 } d x$$

• A) \(\frac { 8 \left( 1 + \cos ^ { 2 } \frac { x } { 8 } \right) \cos \frac { x } { 8 } } { 3 } + C\)
• B) \(- \frac { 8 \left( 3 - \cos ^ { 2 } \frac { x } { 8 } \right) \cos \frac { x } { 8 } } { 3 } + C\)
• C) \(\frac { 8 \left( 2 - \cos ^ { 2 } \frac { x } { 8 } \right) \cos \frac { x } { 8 } } { 3 } + C\)
• D) \(\frac { 8 \left( 3 - \cos ^ { 2 } \frac { x } { 8 } \right) \cos \frac { x } { 8 } } { 3 } + C\)
• E)\(- \frac { 8 \left( 2 - \cos ^ { 2 } \frac { x } { 8 } \right) \cos \frac { x } { 8 } } { 3 } + C\)

---

Definitions:

Trichomycosis

A bacterial infection affecting hair shafts, primarily in humid regions, most commonly found in armpit hair.

Alopecia

A condition characterized by hair loss from the scalp or other parts of the body; can be temporary or permanent, and vary in pattern and severity.

Erythroderma

A severe and potentially life-threatening skin condition characterized by widespread redness and scaling that covers most of the body.

Xanthoderma

A condition characterized by the yellowing of the skin due to an accumulation of lipochrome pigments.