Use Long Division to Evaluate the Integral $\int \frac{x^{2}}{x+3} d x$

question 17

Multiple Choice

Use long division to evaluate the integral. $\int \frac{x^{2}}{x+3} d x$

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

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Definitions:

Rolled Edge

A finishing feature where the edge of a metal sheet, part, or component is curved or folded over to eliminate sharp edges or increase strength.

Folding Metal

The process of bending metal sheets along a straight line to alter their shape for manufacturing or structural purposes.

Prevent Sharp

Aims to eliminate or mitigate harsh or abrupt transitions in a design or process to enhance safety or usability.

Overlap

A situation where parts of objects cover parts of others or the extension of one part over another, often requiring careful planning in design and assembly.