Evaluate `int_-1^1 5x^4sqrt(x^5+1)dx`

Explanation

To evaluate the integral \( \int_{-1}^{1} 5x^4 \sqrt{x^5 + 1} \, dx \), we can use a substitution method. Here’s a step-by-step solution:

### Step 1: Substitution
Let’s set \( t^2 = x^5 + 1 \). This will help us simplify the square root in the integral.

### Step 2: Differentiate
Now, differentiate both sides with respect to \( x \):
\[
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