Find the Integral Using an Appropriate Trigonometric Substitution $$\int \frac { 1 } { x ^ { 2 } \sqrt { x ^ { 2 } + 36 } } d x$$

question 60

Short Answer

Find the integral using an appropriate trigonometric substitution.
$$\int \frac { 1 } { x ^ { 2 } \sqrt { x ^ { 2 } + 36 } } d x$$

Develop the ability to apply properties of radicals to solve and simplify mathematical expressions.

Gain proficiency in rationalizing the denominator of fractions involving square roots.

Enhance skills in solving equations involving radicals and understanding the concept of extraneous solutions.

Apply the concepts of radicals to real-world problems, including geometric applications involving the Pythagorean theorem.

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