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The integral ∫ sec^(2/3) x cosec^(4/3) x dx is equal to:

1. -3 tan^(-1/3) x + C
2. -3/4 tan^(-4/3) x + C
3. -3 cot^(-1/3) x + C
4. 3 tan^(-1/3) x + C

Correct answer: -3 tan^(-1/3) x + C

Solution

The integral evaluates to -3 tan^(-1/3) x + C because it involves the integration of sec^(2/3) x and cosec^(4/3) x, which can be simplified using trigonometric identities and substitution methods that lead to this specific antiderivative.

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