Evaluate the Integral Using the Indicated Trigonometric Substitution $\int \frac { x ^ { 3 } } { \sqrt { x ^ { 2 } + 25 } } d x ; \quad x = 5 \tan \theta$

question 12

Multiple Choice

Evaluate the integral using the indicated trigonometric substitution. $\int \frac { x ^ { 3 } } { \sqrt { x ^ { 2 } + 25 } } d x ; \quad x = 5 \tan \theta$

• A) \(\left( x ^ { 2 } + 25 \right) ^ { 3 / 2 } - 5 \sqrt { x ^ { 2 } + 25 } + C\)
• B) \(\left( x ^ { 2 } + 25 \right) ^ { 3 / 2 } - \sqrt { x ^ { 2 } + 25 } + C\)
• C) \(\frac { 1 } { 3 } \left( x ^ { 2 } + 25 \right) ^ { 3 / 2 } - \sqrt { x ^ { 2 } + 25 } + C\)
• D) \(\frac { 1 } { 3 } \left( x ^ { 2 } + 25 \right) ^ { 3 / 2 } - 25 \sqrt { x ^ { 2 } + 25 } + C\)
• E) \(\frac { 3 } { 2 } ( x + 25 ) ^ { 3 / 2 } - 25 \sqrt { x + 25 } + C\)

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