Use a Trigonometric Substitution to Evaluate the Integral $$\int \frac { d x } { x \left( 1 + 25 \ln ^ { 2 } x \right) }$$

question 350

Multiple Choice

Use a trigonometric substitution to evaluate the integral.
- $$\int \frac { d x } { x \left( 1 + 25 \ln ^ { 2 } x \right) }$$

• A) \(\frac { 1 } { 5 x } \tan ^ { - 1 } ( 5 \ln x ) + C\)
• B) \(\frac { 1 } { 5 } \tan ^ { - 1 } \left( 25 \ln ^ { 2 } x \right) + C\)
• C) \(\frac { 1 } { 50 } \ln \left( 1 + 25 \ln ^ { 2 } x \right) + C\)
• D) \(\frac { 1 } { 5 } \tan ^ { - 1 } ( 5 \ln x ) + C\)

---

Definitions:

Experimental Research Design

A scientific method in which variables are manipulated and controlled to establish cause-and-effect relationships between them.

Ethical

Concerned with or relating to ethics or the standards of right and wrong behavior.

Cause and Effect

A relationship in which one event (the cause) makes another event happen (the effect).

Placebo Effect

The phenomenon where patients experience real improvements in their condition after receiving a treatment that has no therapeutic effect.