Find the Indefinite Integral $$\int x \ln ( x - 8 ) d x$$

question 38

Multiple Choice

Find the indefinite integral. $$\int x \ln ( x - 8 ) d x$$

• A) \(\left( \frac { x ^ { 2 } - 64 } { 2 } \right) \ln ( x - 8 ) - \frac { x ^ { 2 } + 16 x } { 4 } + C\)
• B) \(\left( \frac { x ^ { 2 } - 64 } { 2 } \right) \ln ( x - 8 ) + \frac { x ^ { 2 } + 8 x } { 4 } + C\)
• C) \(\left( \frac { x ^ { 2 } - 64 } { 2 } \right) \ln ( x - 8 ) + \frac { x ^ { 2 } + 16 x } { 4 } + C\)
• D) \(\left( \frac { x ^ { 2 } - 64 } { 2 } \right) \ln ( x - 8 ) - \frac { x ^ { 2 } + 16 x } { 2 } + C\)
• E) \(\left( \frac { x ^ { 2 } + 64 } { 2 } \right) \ln ( x - 8 ) - \frac { x ^ { 2 } - 8 x } { 4 } + C\)

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Definitions:

Cross-sectional Area

The area of a particular section of an object or material that is exposed when it is cut through by a plane.

Deposition

The geological process by which sediments, soil, and rocks are added to a landform or landmass, often carried by wind, water, or ice.

Cutbank

A steep cut or slope formed by lateral erosion of a stream, especially on the outside bend of a channel.

Gradient

The rate of change of a quantity (e.g., temperature, pressure, or elevation) with respect to distance in a given direction.