Evaluate the Integral in Terms of an Inverse Hyperbolic Function $$\int _ { \sqrt { 5 } } ^ { 6 \sqrt { 5 } } \frac { d x } { \sqrt { 36 + x ^ { 2 } } }$$

question 74

Multiple Choice

Evaluate the integral in terms of an inverse hyperbolic function.
- $$\int _ { \sqrt { 5 } } ^ { 6 \sqrt { 5 } } \frac { d x } { \sqrt { 36 + x ^ { 2 } } }$$

• A) \(\sinh ^ { - 1 } ( \sqrt { 5 } ) - \sinh ^ { - 1 } \left( \frac { \sqrt { 5 } } { 6 } \right)\)
• B) \(- \frac { 1 } { 6 } \operatorname { csch } ^ { - 1 } ( \sqrt { 5 } ) - \frac { 1 } { 6 } \operatorname { csch } ^ { - 1 } \left( \frac { \sqrt { 5 } } { 6 } \right)\)
• C) \(\cosh ^ { - 1 } ( \sqrt { 5 } ) - \cosh ^ { - 1 } \left( \frac { \sqrt { 5 } } { 6 } \right)\)
• D) \(- \frac { 1 } { 6 } \operatorname { sech } ^ { - 1 } ( \sqrt { 5 } ) + \frac { 1 } { 6 } \operatorname { sech } ^ { - 1 } \left( \frac { \sqrt { 5 } } { 6 } \right)\)

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