Find the Indefinite Integral by Making the Substitution $x = 6 \tan \theta$

question 9

Multiple Choice

Find the indefinite integral by making the substitution
$x = 6 \tan \theta$ $\int x \sqrt { 36 + x ^ { 2 } } d x$

• A) \(- \frac { 2 \left( x ^ { 2 } + 36 \right) ^ { 3 / 2 } } { 3 } + C\)
• B) \(- \frac { \left( x ^ { 2 } + 36 \right) ^ { 3 / 2 } } { 3 } + C\)
• C) \(\frac { \left( x ^ { 2 } + 36 \right) ^ { 3 / 2 } } { 3 } + C\)
• D)\(\frac { 2 \left( x ^ { 2 } + 36 \right) ^ { 3 / 2 } } { 3 } + C\)
• E)\(\frac { \left( x ^ { 2 } + 36 \right) ^ { 3 / 2 } } { 2 } + C\)

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