Evaluate the Integral by Making a Substitution (Possibly Trigonometric) and Then

question 450

Multiple Choice

Evaluate the integral by making a substitution (possibly trigonometric) and then applying a reduction formula.
- $$\int \frac { d x } { \left( 25 - x ^ { 2 } \right) ^ { 2 } }$$

• A) \(\frac { 1 } { 10 } \ln \left| \frac { x + 5 } { x - 5 } \right| + C\)
• B) \(\frac { x } { 50 \left( 25 - x ^ { 2 } \right) } + C\)
• C) \(\frac { 1 } { 50 } \left( \frac { x } { 25 - x ^ { 2 } } + \frac { 1 } { 10 } \ln \left| \frac { x + 5 } { x - 5 } \right| \right) + C\)
• D) \(\frac { 1 } { 50 } \left( \frac { x } { 25 - x ^ { 2 } } - \frac { 1 } { 10 } \ln \left| \frac { x + 5 } { x - 5 } \right| \right) + C\)

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