Use Reduction Formulas to Evaluate the Integral $$\int \tan ^ { 5 } 2 x d x$$

question 405

Multiple Choice

Use reduction formulas to evaluate the integral.
- $$\int \tan ^ { 5 } 2 x d x$$

• A) \(- \frac { 1 } { 8 } \tan ^ { 4 } 2 x + \frac { 1 } { 4 } \tan ^ { 2 } 2 x - \frac { 1 } { 2 } \ln | \cos 2 x | + C\)
• B) \(\frac { 1 } { 8 } \tan ^ { 4 } 2 x - \frac { 1 } { 4 } \tan ^ { 2 } 2 x - \frac { 1 } { 2 } \ln | \cos 2 x | + C\)
• C) \(\frac { 1 } { 4 } \tan ^ { 4 } 2 x - \frac { 1 } { 2 } \tan ^ { 2 } 2 x - \ln | \cos 2 x | + C\)
• D) \(\frac { 1 } { 8 } \tan ^ { 4 } 2 x - \frac { 1 } { 4 } \tan ^ { 2 } 2 x + \frac { 1 } { 2 } \ln | \cos 2 x | + C\)

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Definitions:

Variable Manufacturing Costs

Variable manufacturing costs are expenses that change in proportion with the level of production output, such as raw materials and labor.

Differential Effect

It is the financial impact of a business decision that differentiates between alternative choices, highlighting the relative costs or benefits.

Book Value

The net value of a company's assets minus its liabilities, as recorded on the balance sheet, often used to calculate the value of a company if it were to be liquidated.

Opportunity Cost

The price paid when one opts not to pursue the next most favorable choice during decision-making.