Evaluate: `int 2^(2^(2^x)) * 2^(2^x) * 2^x dx`

Explanation

To evaluate the integral \( \int 2^{2^{2^x}} \cdot 2^{2^x} \cdot 2^x \, dx \), we will use substitution to simplify the expression step by step.

### Step 1: Simplify the Integral
We start with the integral:
\[ \int 2^{2^{2^x}} \cdot 2^{2^x} \cdot 2^x \, dx \]
We can combine the exponents of the base 2:
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