Use Integration by Parts to Evaluate $\int x ^ { 2 } e ^ { - 3 x } d x$

question 45

Multiple Choice

Use integration by parts to evaluate $\int x ^ { 2 } e ^ { - 3 x } d x$ . Note that evaluation may require integration by parts more than once.

• A) \(- \frac { \left( 2 + 6 x + 9 x ^ { 2 } \right) e ^ { - 3 x } } { 27 } + C\)
• B) \(\frac { \left( 1 + 6 x - 3 x ^ { 2 } \right) e ^ { - 3 x } } { 9 } + C\)
• C) \(- \frac { \left( 2 + 9 x + 9 x ^ { 2 } \right) e ^ { - 3 x } } { 27 } + C\)
• D) \(\frac { \left( 2 - 3 x + 9 x ^ { 2 } \right) e ^ { - 3 x } } { 9 } + C\)
• E) \(- \frac { \left( 1 - 3 x + 9 x ^ { 2 } \right) e ^ { - 3 x } } { - 27 } + C\)

---

Definitions:

Exclusively Homosexual

describes individuals who are sexually attracted only to members of the same sex, with no sexual interest in the opposite sex.

Lifespan

The period of time from birth to death in the life of an organism, considering various developmental stages across the life cycle.

Kinsey's Model

A scale developed by Alfred Kinsey to describe human sexual orientation on a continuum from exclusively heterosexual (0) to exclusively homosexual (6).

Sexual Orientation

An inherent or immutable enduring emotional, romantic or sexual attraction to other people, which can be towards the same gender, opposite gender, both, or neither.