Evaluate: `intsec^(4//3)x" cosec"^(8//3)xdx`

Explanation

To evaluate the integral \( \int \sec^{\frac{4}{3}} x \csc^{\frac{8}{3}} x \, dx \), we can follow these steps:

### Step 1: Rewrite the Integral
We start by rewriting the integral in terms of sine and cosine:
\[ \int \sec^{\frac{4}{3}} x \csc^{\frac{8}{3}} x \, dx = \int \frac{1}{\cos^{\frac{4}{3}} x} \cdot \frac{1}{\sin^{\frac{8}{3}} x} \, dx \]

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