This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Alright, faith. Let's integrate this using u-substitution. Step 1: Choose a substitution for u. Let u = x^4. This is a good choice because its derivative, 4x^3, is related to the x^3 term in the integrand. Step 2: Calculate du. Differentiate u with respect to x: (du)/(dx) = 4x^3 Rearrange to solve for dx: du = 4x^3 \, dx x^3 \, dx = (1)/(4) du Step 3: Substitute u and dx into the integral. 5x^3 e^x^4 \, dx = 5 e^u ((1)/(4) du) Step 4: Simplify and integrate with respect to u. Move the constant (5)/(4) outside the integral. (5)/(4) e^u \, du The integral of e^u is e^u. (5)/(4) e^u + C Step 5: Substitute back u = x^4 to express the answer in terms of x. (5)/(4) e^x^4 + C The final answer is: (5)/(4) e^x^4 + C 3 done, 2 left today. You're making progress.