Question Detail
Question
Simplify ∫ 3x2 ex3 dx
Correct Answer
Option B is the correct answer.
Detailed Explanation
This integral can be solved using a simple substitution.Let u = x3.Then, find the differential du by differentiating u with respect to x:du = d/dx(x3) dxdu = 3x2 dxNotice that 3x2 dx is exactly the remaining part of the integrand. Substitute u and du into the integral:∫ eu duThis is a standard integral:= eu + CFinally, substitute back u = x3:= ex3 + CThis matches option B.
Hint
Look for a substitution where the derivative of the chosen u is also present in the integrand.