$\text { Use partial fractions to find the integral } \int \frac { 3 x ^ { 3 } - 28 x ^ { 2 } + 39 x + 82 } { x ^ { 2 } - 10 x + 21 } d x \text {. }$

question 107

Multiple Choice

$\text { Use partial fractions to find the integral } \int \frac { 3 x ^ { 3 } - 28 x ^ { 2 } + 39 x + 82 } { x ^ { 2 } - 10 x + 21 } d x \text {. }$

• A) \(\frac { 3 } { 2 } x ^ { 2 } + 2 x - 3 \ln | x - 7 | + 7 \ln | x - 3 | + C\)
• B) \(\frac { 3 } { 2 } x ^ { 2 } + 2 x + 3 \ln | x - 7 | - 7 \ln | x - 3 | + C\)
• C) \(\frac { 3 } { 2 } x ^ { 2 } + 2 x + 3 \ln | x - 7 | + 7 \ln | x - 3 | + C\)
• D) \(3 x + 2 + 3 \ln | x - 7 | - 7 \ln | x - 3 | + C\)
• E) \(\frac { 3 } { 2 } x ^ { 2 } + 2 x - 3 \ln | x - 7 | - 7 \ln | x - 3 | + C\)

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Definitions:

Genital Human Papillomavirus

A common virus that is transmitted sexually, causing genital warts and various cancers.

Genital Herpes

A common sexually transmitted infection marked by genital pain and sores, caused by the herpes simplex virus.

Herpes Simplex Virus

A virus that causes infections in various parts of the body, most notably as cold sores or genital herpes.

Genital Human Papillomavirus

A type of sexually transmitted infection (STI) caused by the human papillomavirus, affecting the genital areas.