Integrate the Function $$\int \frac { \sqrt { x ^ { 2 } + 36 } } { 9 x ^ { 2 } } d x$$

question 1

Multiple Choice

Integrate the function.
- $$\int \frac { \sqrt { x ^ { 2 } + 36 } } { 9 x ^ { 2 } } d x$$

• A) \(x + \ln \left| \sqrt { x ^ { 2 } + 36 } \right| + \frac { \sqrt { x ^ { 2 } + 36 } } { 9 x } + C\)
• B) \(\frac { 1 } { 9 } \ln \left| \sqrt { x ^ { 2 } + 36 } + x \right| - \frac { \sqrt { x ^ { 2 } + 36 } } { 9 x } + C\)
• C) \(\frac { 1 } { 9 } \ln \left| \sqrt { x ^ { 2 } + 36 } + x \right| - \sin ^ { - 1 } \frac { x } { 6 } + C\)
• D) \(\ln \left| \sqrt { x ^ { 2 } + 36 } + x \right| + \frac { \sqrt { x ^ { 2 } + 36 } } { 9 x } + C\)

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Definitions:

Reactants

Substances initially present in a chemical reaction that are consumed during the reaction to make products.

Activation Energy

Minimum amount of energy required to start a reaction.

Reactant Molecules

Substances that take part in a chemical reaction and are consumed to form products.

Transition State

A high-energy state during a chemical reaction where reactants are converted to products, representing a point of maximum energy along the reaction pathway.