Find the Indefinite Integral of the Following Function and Check $\int x ^ { 4 } \sqrt { \left( 4 + x ^ { 5 } \right) } d x$

question 12

Multiple Choice

Find the indefinite integral of the following function and check the result by differentiation. $\int x ^ { 4 } \sqrt { \left( 4 + x ^ { 5 } \right) } d x$

• A) \(\frac { \left( 4 + x ^ { 5 } \right) ^ { \frac { 3 } { 2 } } } { 10 } + C\)
• B) \(\frac { 2 \left( 4 + x ^ { 5 } \right) ^ { \frac { 2 } { 3 } } } { 15 } + C\)
• C) \(\frac { \left( 4 + x ^ { 5 } \right) ^ { \frac { 3 } { 2 } } } { 15 } + C\)
• D) \(\frac { 2 \left( 4 + x ^ { 5 } \right) ^ { \frac { 3 } { 2 } } } { 15 } + C\)
• E)none of the above

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Definitions:

Capital Intensive

A description of industries or businesses that require large investments in capital assets to produce goods or services.

Variable Cost

Costs that change in proportion to the level of production or activity within a company.

Long Run

A time period in economics during which all inputs or factors of production can be varied, and no costs are fixed.

Expenditures

Money spent on goods, services, or other expenses by individuals, businesses, or governments.