Evaluate the Integral by Using a Substitution Prior to Integration $$\int \frac { x ^ { 2 } } { \sqrt { x ^ { 2 } + 13 } } d x$$

question 127

Multiple Choice

Evaluate the integral by using a substitution prior to integration by parts.
- $$\int \frac { x ^ { 2 } } { \sqrt { x ^ { 2 } + 13 } } d x$$

• A) \(\frac { 3 x } { 2 } \sqrt { x ^ { 2 } + 13 } + \frac { 13 } { 2 } \ln \left( x + \sqrt { x ^ { 2 } + 13 } \right) + C\)
• B) \(\frac { 3 x } { 2 } \sqrt { x ^ { 2 } + 13 } - \frac { 13 } { 2 } \ln \left( x + \sqrt { x ^ { 2 } + 13 } \right) + C\)
• C) \(\frac { x } { 2 } \sqrt { x ^ { 2 } + 13 } - \frac { 13 } { 2 } \ln \left( x + \sqrt { x ^ { 2 } + 13 } \right) + C\)
• D) \(\frac { x } { 2 } \sqrt { x ^ { 2 } + 13 } + \frac { 13 } { 2 } \ln \left( x + \sqrt { x ^ { 2 } + 13 } \right) + C\)

---

Definitions:

Job-related Stress

Stress experienced as a result of work responsibilities or environment, which can impact mental and physical health.

Chronic Pain

A persistent pain that lasts weeks to years, often beyond the expected period of healing.

PTSD

Post-Traumatic Stress Disorder is a mental health condition triggered by experiencing or witnessing a terrifying event, leading to severe anxiety, flashbacks, and uncontrollable thoughts.

Sleep Medication

Medicines prescribed to help individuals fall asleep or stay asleep, used in the treatment of various sleep disorders.