Evaluate the Integral by Using Multiple Substitutions $\int 3 \left( 3 x ^ { 2 } - 5 \right) \sin ^ { 5 } \left( x ^ { 3 } - 5 x \right) \cos \left( x ^ { 3 } - 5 x \right) d x$

question 1

Multiple Choice

Evaluate the integral by using multiple substitutions.
- $\int 3 \left( 3 x ^ { 2 } - 5 \right) \sin ^ { 5 } \left( x ^ { 3 } - 5 x \right) \cos \left( x ^ { 3 } - 5 x \right) d x$

• A) \(15 \sin ^ { 4 } \left( x ^ { 3 } - 5 x \right) + C\)
• B) \(\frac { 1 } { 2 } \cos ^ { 6 } \left( 3 x ^ { 2 } \right) + C\)
• C) \(\frac { 1 } { 2 } \sin ^ { 6 } \left( x ^ { 3 } - 5 x \right) + C\)
• D) \(2 \sin ^ { 6 } \left( x ^ { 3 } - 5 x \right) + C\)

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Definitions:

Night Vision

The ability to see in low-light conditions, often enhanced through the use of night vision equipment or naturally adapted vision in some animals.

Rods

Photoreceptor cells in the retina of the eye that are sensitive to low light levels and are important for night vision.

Bipolar Cells

A type of neuron found in the eyes that acts as a relay between photoreceptors and ganglion cells, playing a crucial role in visual processing.

Fovea

A small depression in the retina of the eye where visual acuity is highest, due to the concentration of cone cells.