Evaluate the Integral $\int \sec ^ { 3 } 9 x d x$

question 213

Multiple Choice

Evaluate the integral.
- $\int \sec ^ { 3 } 9 x d x$

• A) \(\frac { 1 } { 18 } \sec ^ { 2 } 9 x \tan 9 x + \frac { 1 } { 18 } \ln | \sec 9 x + \tan 9 x | + C\)
• B) \(\frac { 1 } { 2 } \sec 9 x \tan 9 x - \frac { 1 } { 2 } \ln | \sec 9 x + \tan 9 x | + C\)
• C) \(\frac { 1 } { 18 } \sec 9 x \tan 9 x + \frac { x } { 18 } + C\)
• D) \(\frac { 1 } { 18 } \sec 9 x \tan 9 x + \frac { 1 } { 18 } \ln | \sec 9 x + \tan 9 x | + C\)

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Definitions:

Reciprocal Relationship

A mutual relationship in which parties exert influence on each other or benefit each other equally.

Logical Deduction

The process of reasoning from one or more statements (premises) to reach a logically certain conclusion.

Spatial Relationships

Understanding how objects or shapes are positioned in space relative to each other.

Trial-And-Error Strategies

Problem-solving methods that involve experimenting with various actions until finding a solution or an effective way to achieve a desired outcome.