Use a Table of Integrals to Evaluate the Integral $$\int x \sqrt { 2 + 2 x } d x$$

question 75

Multiple Choice

Use a table of integrals to evaluate the integral.
$$\int x \sqrt { 2 + 2 x } d x$$

• A) \(\frac { 2 \sqrt { 2 } } { 15 } ( 2 x - 1 ) ( x + 1 ) ^ { 3 / 2 } + C\)
• B) \(\frac { 2 \sqrt { 2 } } { 15 } ( 3 x - 2 ) ( x + 1 ) ^ { 3 / 2 } + C\)
• C) \(\frac { 2 } { 15 } ( 3 x - 2 ) \sqrt { x + 1 } + C\)
• D) \(\frac { 2 \sqrt { 2 } } { 15 } ( 3 x - 2 ) \sqrt { x + 1 } + C\)

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Definitions:

Homoscedasticity

The condition where the variance of the residuals, or errors, in a regression model is constant across all levels of the independent variable.

Regression Analysis

Regression Analysis is a statistical method used to investigate and model the relationship between variables, typically one dependent variable and one or more independent variables.

Constant Variance

The condition in which the variance of error terms in a regression model is the same across all levels of the independent variables.

Error Variable

A variable in statistical or mathematical models that represents the difference between observed and predicted values, often due to randomness or unexplained variation.