Integrate the Function $$\int \frac { d x } { \left( 16 x ^ { 2 } + 1 \right) ^ { 2 } }$$

question 159

Multiple Choice

Integrate the function.
- $$\int \frac { d x } { \left( 16 x ^ { 2 } + 1 \right) ^ { 2 } }$$

• A) \(\frac { 4 x } { 16 x ^ { 2 } + 1 } + C\)
• B) \(\ln \left| \sqrt { 16 x ^ { 2 } + 1 } + 4 x \right| + C\)
• C) \(\frac { 1 } { 8 } \tan ^ { - 1 } 4 x + \frac { x } { 32 x ^ { 2 } + 2 } + C\)
• D) \(\tan ^ { - 1 } 4 x - \frac { 4 x } { 16 x ^ { 2 } + 1 } + C\)

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Definitions:

Uniformly Distributed

Describes a distribution in which all outcomes are equally likely, showing no preference for any interval of values within the range of the distribution.

Assembling Product

The process of combining various components or elements to create a finished product.

Probability

The probability of an event happening, quantified by a number ranging from 0 to 1.

Uniformly Distributed

Describes a type of distribution where all outcomes are equally likely over a specific interval.