Question Detail
Question
Simplify the integral ∫ 3x2ex3 dx.
Correct Answer
Option B is the correct answer.
Detailed Explanation
This integral can be solved using u-substitution.Let u = x3.Then, find the derivative of u with respect to x: du/dx = 3x2.So, du = 3x2 dx.Substitute u and du into the integral: ∫ eu du.The integral of eu with respect to u is eu + C.Substitute x3 back for u: ex3 + C.This matches option B.
Hint
Identify a part of the integrand whose derivative is also present in the integrand (up to a constant factor).