Use Reduction Formulas to Evaluate the Integral $$\int \sec ^ { 3 } 4 x d x$$

question 116

Multiple Choice

Use reduction formulas to evaluate the integral.
- $$\int \sec ^ { 3 } 4 x d x$$

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

Understand the concept of moral duty and its external imposition as seen in various moral theories.

Distinguish between the concepts of pleasure and happiness in ethical theories.

Assess the role of fear and courage in Aristotle's virtue ethics.

Interpret the relevance of moral theories in modern ethical dilemmas and moral decision-making.

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