Evaluate: `inte^(3logx)(x^4+1)^(-1)\ dx`

Explanation

To evaluate the integral \( I = \int e^{3 \log x} (x^4 + 1)^{-1} \, dx \), we can follow these steps:

### Step 1: Simplify the Exponential
We start with the expression \( e^{3 \log x} \). Using the property of logarithms, we can rewrite this as:
\[ e^{3 \log x} = e^{\log x^3} = x^3 \]
Thus, the integral becomes:
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