Question Detail
Question
Simplify ∫ 3x2ex3 dx.
Correct Answer
Option B is the correct answer.
Detailed Explanation
This integral can be solved using substitution.Let u = x3.Then, differentiate u with respect to x to find du:du/dx = 3x2, so du = 3x2 dx.Substitute u and du into the integral:∫ eu duThe integral of eu with respect to u is eu + C.Now, substitute u = x3 back into the result:ex3 + C.This matches option B.
Hint
Look for a part of the integrand whose derivative is also present (or a constant multiple of it). In this case, if you let u = x3, its derivative 3x2 is right there!