Mathematics

The key is recognizing that the integrand is a composition where the derivative of the inner function appears in the numerator. Notice that if you let $u = x^4$, then $du = 4x^3\,dx$—exactly what you see multiplying $e^{x^4}$. This transforms an intimidating exponential integral into a simple substitution that yields $e^u + C$.

The key is recognizing that the integrand is a composition where the derivative of the inner function appears in the numerator. Notice that if you let $u = x^4$, then $du = 4x^3\,dx$—exactly what you see multiplying $e^{x^4}$. This transforms an intimidating exponential integral into a simple substitution that yields $e^u + C$.