$\text { Use integration tables to find } \int ( 2 x + 5 ) ^ { 2 } \sqrt { ( 2 x + 5 ) ^ { 2 } - 9 } d x \text {. }$

question 27

Multiple Choice

$\text { Use integration tables to find } \int ( 2 x + 5 ) ^ { 2 } \sqrt { ( 2 x + 5 ) ^ { 2 } - 9 } d x \text {. }$

• A) \(\frac { 1 } { 32 } \left[ ( 2 x + 5 ) \left( 2 ( 2 x + 5 ) ^ { 2 } + 9 \right) \sqrt { ( 2 x + 5 ) ^ { 2 } - 9 } - 81 \ln \left| ( 2 x + 5 ) + \sqrt { ( 2 x + 5 ) ^ { 2 } + 9 } \right| \right] + C\)
• B) \(\frac { 1 } { 16 } \left[ ( 2 x + 5 ) \left( 2 ( 2 x + 5 ) ^ { 2 } - 9 \right) \sqrt { ( 2 x + 5 ) ^ { 2 } - 9 } - 81 \ln \left| ( 2 x + 5 ) + \sqrt { ( 2 x + 5 ) ^ { 2 } - 9 } \right| \right] + C\)
• C) \(\frac { 1 } { 16 } \left[ ( 2 x + 5 ) \left( 2 ( 2 x + 5 ) ^ { 2 } \pm 9 \right) \sqrt { ( 2 x + 5 ) ^ { 2 } \pm 9 } - 81 \ln \left| ( 2 x + 5 ) + \sqrt { ( 2 x + 5 ) ^ { 2 } \pm 9 } \right| \right] + C\)
• D)
• \(\frac { 1 } { 8 } \left[ ( 2 x + 5 ) \left( 2 ( 2 x + 5 ) ^ { 2 } - 9 \right) \sqrt { ( 2 x + 5 ) ^ { 2 } - 9 } - 81 \ln \left| ( 2 x + 5 ) + \sqrt { ( 2 x + 5 ) ^ { 2 } - 9 } \right| \right] + C\)
• E)
• \(\frac { 1 } { 16 } \left[ ( 2 x + 5 ) \left( 2 ( 2 x + 5 ) ^ { 2 } + 9 \right) \sqrt { ( 2 x + 5 ) ^ { 2 } + 9 } - 81 \ln \left| ( 2 x + 5 ) + \sqrt { ( 2 x + 5 ) ^ { 2 } + 9 } \right| \right] + C\)

---

Definitions:

Blocked

Prevented from progressing or moving forward, often referring to an impediment in a process or pathway.

Thwarted

Refers to being prevented from accomplishing something or obstructed in achieving an objective.

Goal

An aim or desired outcome that a person or a group of people envision, plan, and commit to achieve.

Frustration

The feeling of being upset or annoyed as a result of being unable to change or achieve something.