Use a Trigonometric Substitution to Evaluate the Integral $$\int \frac { d x } { x \left( 1 + 4 \ln ^ { 2 } x \right) }$$

question 55

Multiple Choice

Use a trigonometric substitution to evaluate the integral.
- $$\int \frac { d x } { x \left( 1 + 4 \ln ^ { 2 } x \right) }$$

• A) \(\frac { 1 } { 2 x } \tan ^ { - 1 } ( 2 \ln x ) + C\)
• B) \(\frac { 1 } { 8 } \ln \left( 1 + 4 \ln ^ { 2 } x \right) + C\)
• C) \(\frac { 1 } { 2 } \tan ^ { - 1 } ( 2 \ln x ) + C\)
• D) \(\frac { 1 } { 2 } \tan ^ { - 1 } \left( 4 \ln ^ { 2 } x \right) + C\)

---

Definitions:

Status Quo Bias

A cognitive bias that causes people to prefer things to stay the same by doing nothing or by sticking with a decision made previously.

Decision-Making

The cognitive process of selecting a course of action from among multiple alternatives, often involving elements of judgment and reasoning.

Temporal Discounting

The tendency to value immediate rewards more highly than future rewards, leading to a preference for sooner over later outcomes.

Avoidance

A psychological mechanism or behavior aimed at steering clear from a specific stimulus or situation due to its perceived negative consequences.