$\text { Use partial fractions to find } \int \frac { 6 x ^ { 2 } + 14 x - 3 } { x ^ { 3 } + 3 x ^ { 2 } } d x$

question 8

Multiple Choice

$\text { Use partial fractions to find } \int \frac { 6 x ^ { 2 } + 14 x - 3 } { x ^ { 3 } + 3 x ^ { 2 } } d x$

• A)\(\int \frac { 6 x ^ { 2 } + 14 x - 3 } { x ^ { 2 } ( x + 3 ) } d x = \ln \left| x ^ { 6 } + 3 x ^ { 5 } \right| + C\)
• B)\(\int \frac { 6 x ^ { 2 } + 14 x - 3 } { x ^ { 2 } ( x + 3 ) } d x = \frac { 1 } { x } + \left( x ^ { 6 } + 3 x ^ { 5 } \right) + C\)
• C)\(\int \frac { 6 x ^ { 2 } + 14 x - 3 } { x ^ { 2 } ( x + 3 ) } d x = \frac { 1 } { x } + \ln \left| x ^ { 7 } + x ^ { 5 } \right| + C\)
• D)\(\int \frac { 6 x ^ { 2 } + 14 x - 3 } { x ^ { 2 } ( x + 3 ) } d x = \ln \left| x ^ { 6 } + 5 x ^ { 4 } \right| + C\)
• E)\(\int \frac { 6 x ^ { 2 } + 14 x - 3 } { x ^ { 2 } ( x + 3 ) } d x = \frac { 1 } { x } + \ln \left| x ^ { 6 } + 3 x ^ { 5 } \right| + C\)

---

Definitions:

Span of Control

The number of subordinates or direct reports that a manager or supervisor can effectively oversee.

Subordinates

Employees or team members who are lower in rank or position and report to someone higher in the organizational hierarchy.

Direct Reporting

The process where employees report directly to their immediate supervisor without intermediaries.

Organizational Designs

The planning and structuring of an organization's roles, responsibilities, and processes to achieve its goals efficiently.