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

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:

R

Symbol typically representing resistance in electrical circuits, quantifying how much a material opposes the flow of electric current.

Apparent Power

The total power in an AC circuit, measured in volt-amperes, combining both active (real) and reactive power components.

RC Parallel Circuit

A type of electrical circuit combining resistors and capacitors in parallel configuration, which influences the total impedance and phase angle.

R

A symbol often used to represent resistance in electrical circuits, measured in ohms.