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:

Recessive

A type of gene that generally does not manifest in the presence of a dominant gene; it requires two copies (one from each parent) for the trait to be expressed.

Homozygous

Having two identical alleles for a particular gene or genes, contributing to specific traits or conditions.

Recessive Inheritance

A genetic phenomenon where a trait is expressed only when two copies of a recessive allele are present, one from each parent.

Genetic Mutation

A change in the DNA sequence within a gene or chromosome of an organism that can lead to differences in physical traits or health.