Evaluate the Integral $\int \frac{7 d x}{\left(x^{2}+2 x+2\right)^{2}}$ A) $\frac{1}{2}\left(\tan ^{-1}(x+2)+\frac{7}{x^{2}+2}\right)+C$ B) $\frac{1}{2}\left(\tan ^{-1}(x+7)+\frac{1}{x^{2}+2 x+2}\right)+C$

question 97

Multiple Choice

Evaluate the integral. $\int \frac{7 d x}{\left(x^{2}+2 x+2\right) ^{2}}$

• A) \(\frac{1}{2}\left(\tan ^{-1}(x+2)+\frac{7}{x^{2}+2}\right)+C\)
• B) \(\frac{1}{2}\left(\tan ^{-1}(x+7)+\frac{1}{x^{2}+2 x+2}\right)+C\)
• C) \(\frac{7}{2}\left(\tan ^{-1}(x+1)+\frac{x+1}{x^{2}+2 x+2}\right)+C\)
• D) \(\frac{1}{2}\left(\tan (x+1)+\frac{17}{x^{2}+2 x+2}\right)+C\)
• E) \(\frac{7}{2}\left(\tan (x+2)+\frac{x+1}{x^{2}+2 x+2}\right)+C\)

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Definitions:

Activity Rate

A ratio used to allocate costs to products or services based on the activities that are required to produce them.

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A grouping of individual costs in accounting, typically by department or service center, from which costs are allocated to products or services based on a relevant allocation base.

Overhead Costs

Expenses associated with the day-to-day running of a business that are not directly linked to the production or selling of goods and services.

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Raw materials that are directly traceable to the manufacturing of a product and considered a part of the product’s cost.