Find the Indefinite Integral $$\int \left[ r + \frac { 5 } { ( r - 2 ) ^ { 4 } } \right] d r$$

question 47

Multiple Choice

Find the indefinite integral. $$\int \left[ r + \frac { 5 } { ( r - 2 ) ^ { 4 } } \right] d r$$

• A) \(\frac { r ^ { 2 } } { 2 } + \frac { 5 } { 4 ( r - 2 ) ^ { 4 } } + C\)
• B) \(\frac { r ^ { 2 } } { 2 } - \frac { 5 } { 3 ( r - 2 ) ^ { 4 } } + C\)
• C) \(\frac { r ^ { 2 } } { 2 } + \frac { 1 } { ( r - 2 ) ^ { 5 } } + C\)
• D) \(\frac { r ^ { 2 } } { 2 } - \frac { 5 } { 3 ( r - 2 ) ^ { 3 } } + C\)
• E) \(\frac { r ^ { 2 } } { 2 } - \frac { 5 } { 3 ( r - 2 ) ^ { 5 } } + C\)

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Definitions:

Femur

The longest and strongest bone in the human body, located in the thigh, connecting the hip to the knee.

Movable Synovial Joint

A movable synovial joint is a type of joint in the body enclosed by a fluid-filled synovial capsule, facilitating a wide range of movements between bones.

Fibrous Joint

Type of joint between two bones that is immovable; sutures are examples of fibrous joints.

Knee

A joint that connects the thigh bone (femur) to the shin bone (tibia), allowing for flexion, extension, and minimal rotation of the leg.