Evaluate : `int (x^(3))/(1+x^(8)) ds`

Explanation

To evaluate the integral \( I = \int \frac{x^3}{1 + x^8} \, dx \), we can follow these steps:

### Step 1: Substitution
Let \( t = x^4 \). Then, we differentiate \( t \) with respect to \( x \):
\[ dt = 4x^3 \, dx \quad \Rightarrow \quad dx = \frac{dt}{4x^3} \]
From this, we can express \( x^3 \, dx \):
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