Find the Indefinite Integral $$\int \left( 5 - 8 x ^ { 3 } + 3 x ^ { 6 } \right) d x$$

question 121

Multiple Choice

Find the indefinite integral.
$$\int \left( 5 - 8 x ^ { 3 } + 3 x ^ { 6 } \right) d x$$

• A) \(\frac { 3 } { 7 } x ^ { 7 } - 2 x ^ { 4 } + 5 x + C\)
• B) \(5 x - 8 x ^ { 4 } + 3 x ^ { 7 } + C\)
• C) \(\frac { 3 } { 7 } x ^ { 6 } - 2 x ^ { 3 } + 5 x + C\)
• D) \(5 x - 24 x ^ { 2 } + 18 x ^ { 5 } + C\)

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Definitions:

Budget Constraints

The limitations on the spending behavior of consumers based on their income and the prices of goods and services, determining the possible combinations of goods and services they can afford.

Substitution Effect

The economic understanding that as prices rise or incomes decrease, consumers will replace more expensive items with less costly alternatives.

Income Effect

The variation in a person's or economy's earnings and the effect of this variation on the demanded quantity of a product or service.

Ernst Ludwig Kirchner

A German expressionist painter and printmaker, one of the founders of the Die Brücke group, known for his vibrant colors and stark representations of modern life.