Evaluate the Integral by Using a Substitution Prior to Integration $$\int x ^ { 2 } \sqrt { x + 5 } d x$$

question 88

Multiple Choice

Evaluate the integral by using a substitution prior to integration by parts.
- $$\int x ^ { 2 } \sqrt { x + 5 } d x$$

• A) \(\frac { \left( 15 x ^ { 2 } - 60 x + 200 \right) ( x + 5 ) ^ { 3 / 2 } } { 105 } + C\)
• B) \(\frac { \left( 30 x ^ { 2 } - 120 x + 80 \right) ( x + 5 ) ^ { 3 / 2 } } { 105 } + C\)
• C) \(\frac { \left( 30 x ^ { 2 } - 120 x + 400 \right) \sqrt { ( x + 5 ) } } { 105 } + C\)
• D) \(\frac { \left( 30 x ^ { 2 } - 120 x + 400 \right) ( x + 5 ) ^ { 3 / 2 } } { 105 } + C\)

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Definitions:

Diminishing Returns

A rule that asserts when one input in the production process is augmented and the rest remain unchanged, the resultant extra production will ultimately diminish.

Marginal Revenue Product

The additional revenue generated by employing one more unit of input, such as labor or capital.

Economic Rent

The excess payment made for a factor of production over its opportunity cost.

Total Supply

The total amount of a product or service available for purchase at any given price point.