Mathematics

The key is recognizing that the expression under the square root, $1 + x^4$, has a derivative ($4x^3$) that appears right in front of it. This is a perfect setup for $u$-substitution: let $u$ equal the inner function, and watch how $du$ captures almost everything you need. Once you substitute, you'll have a simple power integral in $u$ that's much easier to handle than the original.

The key is recognizing that the expression under the square root, $1 + x^4$, has a derivative ($4x^3$) that appears right in front of it. This is a perfect setup for $u$-substitution: let $u$ equal the inner function, and watch how $du$ captures almost everything you need. Once you substitute, you'll have a simple power integral in $u$ that's much easier to handle than the original.