Find the Indefinite Integral $$\int \tan ^ { 5 } \left( \frac { x } { 5 } \right) d x$$

question 110

Multiple Choice

Find the indefinite integral. $$\int \tan ^ { 5 } \left( \frac { x } { 5 } \right) d x$$

• A) \(\tan ^ { 2 } \left( \frac { x } { 5 } \right) \cdot \left( 1 + \frac { 5 } { 4 } \tan ^ { 2 } \left( \frac { x } { 5 } \right) \right) + 5 \ln \left| \cos \left( \frac { x } { 5 } \right) \right| + C\)
• B)\(\tan ^ { 2 } \left( \frac { x } { 5 } \right) \cdot \left( 1 - \frac { 5 } { 4 } \tan ^ { 2 } \left( \frac { x } { 5 } \right) \right) - 5 \ln \left| \cos \left( \frac { x } { 5 } \right) \right| + C\)
• C) \(\frac { 5 } { 2 } \tan ^ { 2 } \left( \frac { x } { 5 } \right) \cdot \left( \frac { 1 } { 2 } \tan ^ { 2 } \left( \frac { x } { 5 } \right) - 1 \right) - 5 \ln \left| \cos \left( \frac { x } { 5 } \right) \right| + C\)
• D) \(\tan ^ { 2 } \left( \frac { x } { 5 } \right) \cdot \left( 1 + \frac { 5 } { 4 } \tan ^ { 2 } \left( \frac { x } { 5 } \right) | - 5 \ln | \cos \left( \frac { x } { 5 } \right) \mid + C \right.\)
• E)\(\frac { 5 } { 2 } \tan ^ { 2 } \left( \frac { x } { 5 } \right) \cdot \left( 1 - \frac { 5 } { 4 } \tan ^ { 2 } \left( \frac { x } { 5 } \right) - 1 \right) - 5 \ln \left| \cos \left( \frac { x } { 5 } \right) \right| + C\)

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