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

question 132

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) \(\frac { 3 } { 2 } ( x + 25 ) ^ { 3 / 2 } - 25 \sqrt { x + 25 } + C\)

Identify the elements that influence the formation and maintenance of friendships and relationships.

Describe strategies for initiating, maintaining, and escalating interpersonal relationships.

Understand the role of love styles in influencing relationship dynamics.

Recognize the developmental stages associated with friendship and relationship evolution.

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