Question Detail
Question
Simplify ∫ 3x2 ex3 dx
Correct Answer
Option B is the correct answer.
Detailed Explanation
Use the substitution method. Let u = x3.Then, the differential du = d/dx(x3) dx = 3x2 dx.Substitute u and du into the integral: ∫ eu du.The integral of eu with respect to u is eu + C.Substitute back u = x3: ex3 + C.
Hint
Look for a substitution where the derivative of the substituted term appears in the integrand.