Find the Integral $$\int \frac { 3 x - 5 } { x ^ { 2 } - 2 x - 3 } d x$$

question 6

Multiple Choice

Find the integral. $$\int \frac { 3 x - 5 } { x ^ { 2 } - 2 x - 3 } d x$$

• A) \(\ln \left| ( x + 3 ) ( x - 1 ) ^ { 2 } \right| + C\)
• B) \(\ln \left| ( x - 1 ) ( x + 3 ) ^ { 2 } \right| + C\)
• C) \(\ln \left| ( x - 3 ) ( x + 1 ) ^ { 2 } \right| + C\)
• D) \(\ln \left| ( x + 1 ) ( x - 3 ) ^ { 2 } \right| + C\)

---

Definitions:

Compare Populations

The statistical process of analyzing two or more groups to determine if there are significant differences between them, often through hypothesis testing or variance analysis.

Multiple Comparison Methods

Refers to statistical techniques used to evaluate differences among group means in a situation where multiple groups are being compared.

ANOVA

A statistical method (Analysis of Variance) used to compare means among three or more groups for significant differences.

Tukey's Multiple Comparison

Tukey's multiple comparison test is a statistical method used to find means that are significantly different from each other after performing an ANOVA, while controlling for Type I error across comparisons.