Evaluate the Integral by Making the Given Substitution $$\int x ^ { 2 } \sqrt { x ^ { 3 } + 2 } d x , \quad u = x ^ { 3 } + 2$$

question 10

Short Answer

Evaluate the integral by making the given substitution.
$$\int x ^ { 2 } \sqrt { x ^ { 3 } + 2 } d x , \quad u = x ^ { 3 } + 2$$

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Definitions:

Americas

A term collectively referring to the continents of North and South America, including Central America and the Caribbean, characterized by diverse cultures, histories, and ecosystems.

Indian Civilizations

Advanced societies and cultures that existed in the Americas before the arrival of Europeans, including the Aztec, Maya, and Inca empires.

Mesoamerican Civilizations

Pre-Columbian societies in Central and North America known for their advanced architectural, mathematical, and astronomical achievements, including the Aztec and Maya.

Aztec Civilization

An advanced Mesoamerican civilization that dominated large parts of central Mexico from the 14th until the 16th century, known for its architectural, mathematical, and astronomical achievements.