$\text { Find the indefinite integral by making the substitution } x = 9 \sin \theta \text {. }$

question 80

Multiple Choice

$\text { Find the indefinite integral by making the substitution } x = 9 \sin \theta \text {. }$ $$\int \frac { \sqrt { 81 - x ^ { 2 } } } { x } d x$$

• A) \(\sqrt{81-x^{2}}-9 \ln \left|\frac{9-\sqrt{81-x^{2}}}{x}\right|+C\)
• B)\(\sqrt { 81 - x ^ { 2 } } - 9 \ln \left| \frac { 9 - \sqrt { 81 - x ^ { 2 } } } { x } \right| + C\)
• \(\left( 81 - x ^ { 2 } \right) ^ { 3 / 2 } + 9 \ln \left| \frac { 9 - \sqrt { 81 - x ^ { 2 } } } { x } \right| + C\)
• C)\(\sqrt { 81 - x ^ { 2 } } + 9 \ln \left| \frac { 9 - \sqrt { 81 - x ^ { 2 } } } { x } \right| + C\)
• D)\(\sqrt { 81 - x ^ { 2 } } + 9 \ln \left| \frac { 9 + \sqrt { 81 - x ^ { 2 } } } { x } \right| + C\)
• E)\(\left( 81 - x ^ { 2 } \right) ^ { 3 / 2 } - 9 \ln \left| \frac { 9 + \sqrt { 81 - x ^ { 2 } } } { x } \right| + C\)

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