Use a Trigonometric Substitution to Evaluate the Integral $$\int \frac { d x } { 2 \sqrt { x } ( 1 + x ) }$$

question 102

Multiple Choice

Use a trigonometric substitution to evaluate the integral.
- $$\int \frac { d x } { 2 \sqrt { x } ( 1 + x ) }$$

• A) \(\frac { 1 } { 2 } \tan ^ { - 1 } \sqrt { x } + C\)
• B) \(\frac { 1 } { 2 } \sin ^ { - 1 } \sqrt { x } + C\)
• C) \(\frac { 1 } { 2 } \ln | x | + C\)
• D) \(\tan ^ { - 1 } \sqrt { x } + C\)

---

Definitions:

Delayed Healing

The process where healing takes longer than the typical recovery time for injuries or wounds.

Subsequent Encounter

A follow-up visit or interaction with healthcare professionals regarding continued treatment or assessment of a condition.

Fracture

Broken cartilage or bone.

NEC

Not Elsewhere Classified, used in coding systems for conditions that don't have a specific category allocation.