Integrate the Function $$\int \frac { \sqrt { x ^ { 2 } + 9 } } { 5 x ^ { 2 } } d x$$

question 5

Multiple Choice

Integrate the function.
- $$\int \frac { \sqrt { x ^ { 2 } + 9 } } { 5 x ^ { 2 } } d x$$

• A) \(\frac { 1 } { 5 } \ln \left| \sqrt { x ^ { 2 } + 9 } + x \right| - \sin ^ { - 1 } \frac { x } { 3 } + C\)
• B) \(\ln \left| \sqrt { x ^ { 2 } + 9 } + x \right| + \frac { \sqrt { x ^ { 2 } + 9 } } { 5 x } + C\)
• C) \(\frac { 1 } { 5 } \ln \left| \sqrt { \mathrm { x } ^ { 2 } + 9 } + \mathrm { x } \right| - \frac { \sqrt { \mathrm { x } ^ { 2 } + 9 } } { 5 \mathrm { x } } + \mathrm { C }\)
• D) \(x + \ln \left| \sqrt { x ^ { 2 } + 9 } \right| + \frac { \sqrt { x ^ { 2 } + 9 } } { 5 x } + C\)

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Definitions:

Formal Charge

A theoretical charge assigned to an atom in a molecule, calculated based on the assumption of equally shared electrons in bonds.

Non-Bonding Electrons

Non-bonding electrons, also known as lone pairs, are valence electrons on an atom that are not involved in chemical bonding and significantly influence molecular shape and polarity.

Formal Charge

Formal charge is a concept in chemistry that represents the charge assigned to an atom in a molecule, assuming that electrons in chemical bonds are shared equally between atoms.

Non-Bonding Electrons

Electrons in an atom or molecule that are not involved in chemical bonding and occupy the outermost shells or subshells.