Evaluate the Integral by Making a Substitution and Then Using $$\int \frac { x d x } { 25 x ^ { 2 } + 20 x + 4 }$$

question 166

Multiple Choice

Evaluate the integral by making a substitution and then using a table of integrals.
- $$\int \frac { x d x } { 25 x ^ { 2 } + 20 x + 4 }$$

• A) \(\frac { 1 } { 5 } \ln \left( 5 x ^ { 2 } + 2 x \right)\)
• B) \(\frac { 1 } { 4 } \left[ \ln ( 2 x + 5 ) + \frac { 5 } { 2 x + 5 } \right] + C\)
• C) \(\frac { x } { 5 } - \frac { 2 } { 25 } \ln ( 5 x + 2 ) + C\)
• D) \(\frac { 1 } { 25 } \left[ \ln ( 5 x + 2 ) + \frac { 2 } { 5 x + 2 } \right] + C\)

---

Definitions:

Machine-Hours

A measure of production time where one machine-hour equals one machine working for one hour, used as an allocation base in costing.

Total Job Cost

The cumulative costs associated with a specific job or project, including materials, labor, and overhead.

Job M381

A specific job or project identifier, often used in job costing scenarios to track costs and monitor progress on a particular task or project.

Departmental Predetermined Overhead Rates

The overhead rates set for specific departments within a company, based on estimated costs and activity levels.