Evaluate the Integral in Terms of Natural Logarithms $$\int _ { 3 } ^ { 18 } \frac { d x } { x \sqrt { x ^ { 2 } + 9 } }$$

question 53

Multiple Choice

Evaluate the integral in terms of natural logarithms.
- $$\int _ { 3 } ^ { 18 } \frac { d x } { x \sqrt { x ^ { 2 } + 9 } }$$

• A) \(\frac { 1 } { 3 } \ln \left( \frac { 6 ( 1 + \sqrt { 2 } ) } { 1 + \sqrt { 37 } } \right)\)
• B) \(- \ln \frac { 1 + \sqrt { 37 } } { 6 }\)
• C) \(\frac { 1 } { 3 } \ln \left( \frac { 1 + \sqrt { 2 } } { 1 + \sqrt { 35 } } \right)\)
• D) \(- \frac { 1 } { 3 } \ln \left( \frac { 1 + \sqrt { 2 } } { 1 + \sqrt { 37 } } \right)\)

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