Evaluate the Integral $$\int \frac { d x } { 5 + 13 \sin 2 x }$$

question 404

Multiple Choice

Evaluate the integral.
- $$\int \frac { d x } { 5 + 13 \sin 2 x }$$

• A) \(- \frac { 1 } { 12 } \ln \left| \frac { 5 + 13 \sin 2 x + 12 \cos 2 x } { 5 + 13 \sin 2 x } \right| + C\)
• B) \(\frac { 1 } { 24 } \ln \left| \frac { 5 + 13 \sin x + 12 \cos x } { 5 + 13 \sin 2 x } \right| + C\)
• C) \(- \frac { 1 } { 24 } \ln \left| \frac { 13 + 5 \sin 2 x + 12 \cos 2 x } { 5 + 13 \sin 2 x } \right| + C\)
• D) \(- \frac { 1 } { 24 } \ln \left| \frac { 13 + 5 \cos 2 x + 12 \sin 2 x } { 5 + 13 \sin 2 x } \right| + C\)

---

Definitions:

Standard Deviation

A measure that quantifies the amount of variation or dispersion of a set of values.

Specification Limits

Defined thresholds within which the values of a product, process, or service must fall to meet quality standards.

Pooled Standard Deviation

An estimation of standard deviation that combines two or more groups of data, assuming equal variance across these groups.

Sample Means

The average value derived from a subset of a larger population, used as an estimate of the overall population mean.